Table 4 Formulas of $\mathit{T}\mathbf{(}\mathit{x}\mathbf{(}\mathit{p}\mathbf{)}\mathbf{,}\mathit{y}\mathbf{(}\mathit{p}\mathbf{)}\mathbf{)}\mathbf{=}\mathbf{0}$

$(a_1,a_2)$

$-3a_1^3+6a_1^4+5a_1^2{a}_2+12a_1{a}_2^2-20a_2^3$

$(a_1,a_3)$

$\begin{array}{l}168a_1^2+162\text{,}358a_1^3-143\text{,}775a_1^4+83\text{,}349a_1^5-750a_1{a}_3-1\text{,}045\text{,}050a_1^2{a}_3\\ +283\text{,}500a_1^3{a}_3+825a_3^2+2\text{,}221\text{,}875a_1{a}_3^2-1\text{,}562\text{,}500a_3^3\end{array}$

$(a_1,a_4)$

$-5a_1^2+32a_1^3+32a_1{a}_4-480a_1^2{a}_4-44a_4^2+2\text{,}400a_1{a}_4^2-4\text{,}000a_4^3$

$(a_1,a_5)$

$\begin{array}{l}-61a_1^2+194a_1^3-180a_1^4+72a_1^5+6\text{,}100a_1{a}_5-28\text{,}000a_1^2{a}_5+18\text{,}000a_1^3{a}_5\\ +67\text{,}100a_5^2+1\text{,}525\text{,}000a_1{a}_5^2-12\text{,}500\text{,}000a_5^3\end{array}$

$(a_1,a_6)$

$\begin{array}{l}-415a_1^2+408a_1^3-360a_1^4+144a_1^5+2\text{,}656a_1{a}_6+304a_1^2{a}_6\\ -3\text{,}600a_1^3{a}_6-3\text{,}652a_6^2+38\text{,}000a_1{a}_6^2-200\text{,}000a_6^3\end{array}$

$(a_1,a_7)$

$\begin{array}{l}22\text{,}032a_1^3+3\text{,}402a_1^4+243a_1^5-3\text{,}264a_1{a}_7-217\text{,}152a_1^2{a}_7\\ -32\text{,}400a_1^3{a}_7+5\text{,}984a_7^2+762\text{,}000a_1{a}_7^2-800\text{,}000a_7^3\end{array}$

$(a_1,a_8)$

$-a_1^2+2a_1^3+10a_1{a}_8-30a_1^2{a}_8+11a_8^2+150a_1{a}_8^2-250a_8^3$

$(a_1,a_9)$

$\begin{array}{l}-111a_1^2+258a_1^3-81a_1^4+18a_1^5-1\text{,}110a_1{a}_9+3\text{,}940a_1^2{a}_9\\ -900a_1^3{a}_9+1\text{,}221a_9^2+22\text{,}750a_1{a}_9^2+25\text{,}000a_9^3\end{array}$

$(a_1,a_{10})$

$\begin{array}{l}3a_1^2-12a_1^3+12a_1^4+72a_1{a}_{10}-94a_1^2{a}_{10}+132a_{10}^2\\ +2\text{,}400a_1{a}_{10}^2-5\text{,}000a_{10}^3\end{array}$

$(a_1,a_{11})$

$105a_1^4+a_1^5-10\text{,}224a_1^2{a}_{11}+2\text{,}400a_1^3{a}_{11}+5\text{,}808a_{11}^2+350\text{,}000a_1{a}_{11}^2-2\text{,}400\text{,}000a_{11}^3$

$(a_1,a_{12})$

$-9a_1^4+18a_1^5-1\text{,}440a_1^2{a}_{12}+3\text{,}600a_1^3{a}_{12}+1\text{,}936a_{12}^2+124\text{,}000a_1{a}_{12}^2-1\text{,}600\text{,}000a_{12}^3$

$(a_2,a_3)$

$\begin{array}{l}10\text{,}080a_2^2+16\text{,}307\text{,}536a_2^3-36\text{,}244\text{,}800a_2^4+28\text{,}005\text{,}264a_2^5-2\text{,}700a_2{a}_3\\ -23\text{,}500\text{,}980a_2^2{a}_3-37\text{,}184\text{,}400a_2^3{a}_3-12\text{,}375a_3^2-14\text{,}849\text{,}125a_2{a}_3^2\\ +208\text{,}935\text{,}000a_2^2{a}_3^2+23\text{,}536\text{,}500a_3^3+22\text{,}500\text{,}000a_2{a}_3^3-187\text{,}500\text{,}000a_3^4\end{array}$

$(a_2,a_4)$

$-15a_2^2+128a_2^3-18a_2{a}_4-768a_2^2{a}_4+33a_4^2-944a_2{a}_4^2+2\text{,}736a_4^3-24\text{,}000a_4^4$

$(a_2,a_5)$

$\begin{array}{l}61a_2^3-120a_2^4+144a_2^5+7\text{,}320a_2^2{a}_5-18\text{,}000a_2^3{a}_5+236\text{,}375a_2{a}_5^2\\ -165\text{,}000a_2^2{a}_5^2+1\text{,}006\text{,}500a_5^3+22\text{,}500\text{,}000a_2{a}_5^3-187\text{,}500\text{,}000a_5^4\end{array}$

$(a_2,a_6)$

$\begin{array}{l}-415a_2^2+1\text{,}344a_2^3-1\text{,}344a_2^4+384a_2^5-498a_2{a}_6+5\text{,}192a_2^2{a}_6-6\text{,}528a_2^3{a}_6\\ +913a_6^2+21\text{,}816a_2{a}_6^2-68\text{,}800a_2^2{a}_6^2+35\text{,}392a_6^3-480\text{,}000a_2{a}_6^3-800\text{,}000a_6^4\end{array}$

$(a_2,a_7)$

$\begin{array}{l}55\text{,}080a_2^3+7\text{,}290a_2^4+243a_2^5-2\text{,}040a_2{a}_7-121\text{,}140a_2^2{a}_7\\ -16\text{,}956a_2^3{a}_7-1\text{,}870a_7^2+127\text{,}401a_2{a}_7^2-747\text{,}000a_2^2{a}_7^2\\ +261\text{,}968a_7^3-2\text{,}160\text{,}000a_2{a}_7^3-1\text{,}600\text{,}000a_7^4\end{array}$

$(a_2,a_8)$

$4a_2^3+36a_2^2{a}_8+83a_2{a}_8^2+33a_8^3-750a_8^4$

$(a_2,a_9)$

$\begin{array}{l}444a_2^3-240a_2^4+48a_2^5-4\text{,}440a_2^2{a}_9+2\text{,}880a_2^3{a}_9+11\text{,}877a_2{a}_9^2\\ +5\text{,}800a_2^2{a}_9^2-4\text{,}884a_9^3-60\text{,}000a_2{a}_9^3-100\text{,}000a_9^4\end{array}$

$(a_2,a_{10})$

$\begin{array}{l}2a_2^4+3a_2^2{a}_{10}-40a_2^3{a}_{10}-30a_2{a}_{10}^2+300a_2^2{a}_{10}^2-33a_{10}^3\\ -1\text{,}000a_2{a}_{10}^3+1\text{,}250a_{10}^4\end{array}$

$(a_2,a_{11})$

$\begin{array}{l}-315a_2^4+a_2^5+7\text{,}668a_2^2{a}_{11}+30\text{,}228a_2^3{a}_{11}-1\text{,}089a_{11}^2-110\text{,}101a_2{a}_{11}^2\\ -916\text{,}200a_2^2{a}_{11}^2+554\text{,}544a_{11}^3+10\text{,}800\text{,}000a_2{a}_{11}^3\\ -43\text{,}200\text{,}000a_{11}^4\end{array}$

$(a_2,a_{12})$

$\begin{array}{l}9a_2^5+360a_2^3{a}_{12}-121a_2{a}_{12}^2-30\text{,}600a_2^2{a}_{12}^2+5\text{,}808a_{12}^3\\ +720\text{,}000a_2{a}_{12}^3-4\text{,}800\text{,}000a_{12}^4\end{array}$

$(a_3,a_4)$

$\begin{array}{l}-6\text{,}625a_3^2+64\text{,}000a_3^3+20\text{,}140a_3{a}_4-612\text{,}000a_3^2{a}_4-11\text{,}872a_4^2\\ +1\text{,}492\text{,}080a_3{a}_4^2-1\text{,}040\text{,}816a_4^3-2\text{,}721\text{,}600a_3{a}_4^3\\ +4\text{,}723\text{,}920a_4^4-10\text{,}668\text{,}672a_4^5\end{array}$

$(a_3,a_5)$

$\begin{array}{l}-a_3^2+8a_3^3-144a_3^4+1\text{,}152a_3^5+52a_3{a}_5+56a_3^2{a}_5\\ +4\text{,}896a_3^3{a}_5-120\text{,}960a_3^4{a}_5+224a_5^2-22\text{,}736a_3{a}_5^2+144\text{,}576a_3^2{a}_5^2\\ +5\text{,}080\text{,}320a_3^3{a}_5^2-181\text{,}328a_5^3-735\text{,}264a_3{a}_5^3-106\text{,}686\text{,}720a_3^2{a}_5^3\\ +50\text{,}985\text{,}936a_5^4+1\text{,}120\text{,}210\text{,}560a_3{a}_5^4-4\text{,}704\text{,}884\text{,}352a_5^5\end{array}$

$(a_3,a_6)$

$\begin{array}{l}-341\text{,}375a_3^2+4\text{,}749\text{,}000a_3^3-18\text{,}000\text{,}000a_3^4+7\text{,}200\text{,}000a_3^5+1\text{,}037\text{,}780a_3{a}_6\\ -21\text{,}435\text{,}400a_3^2{a}_6+133\text{,}848\text{,}000a_3^3{a}_6-151\text{,}200\text{,}000a_3^4{a}_6-611\text{,}744a_6^2\\ +43\text{,}392\text{,}400a_3{a}_6^2-587\text{,}858\text{,}400a_3^2{a}_6^2+1\text{,}270\text{,}080\text{,}000a_3^3{a}_6^2\\ -43\text{,}483\text{,}216a_6^3+1\text{,}153\text{,}638\text{,}720a_3{a}_6^3-5\text{,}334\text{,}336\text{,}000a_3^2{a}_6^3\\ -669\text{,}437\text{,}136a_6^4+11\text{,}202\text{,}105\text{,}600a_3{a}_6^4-9\text{,}409\text{,}768\text{,}704a_6^5\end{array}$

$(a_3,a_7)$

$\begin{array}{l}1\text{,}155\text{,}060\text{,}000a_3^3+104\text{,}034\text{,}375a_3^4+3\text{,}037\text{,}500a_3^5-27\text{,}379\text{,}200a_3{a}_7\\ -4\text{,}160\text{,}682\text{,}000a_3^2{a}_7-566\text{,}676\text{,}000a_3^3{a}_7-85\text{,}050\text{,}000a_3^4{a}_7+25\text{,}553\text{,}920a_7^2\\ +6\text{,}748\text{,}222\text{,}080a_3{a}_7^2-20\text{,}313\text{,}741\text{,}600a_3^2{a}_7^2+952\text{,}560\text{,}000a_3^3{a}_7^2-3\text{,}624\text{,}210\text{,}688a_7^3\\ +20\text{,}040\text{,}791\text{,}040a_3{a}_7^3-5\text{,}334\text{,}336\text{,}000a_3^2{a}_7^3+176\text{,}788\text{,}224a_7^4\\ +14\text{,}936\text{,}140\text{,}800a_3{a}_7^4-16\text{,}728\text{,}477\text{,}696a_7^5\end{array}$

$(a_3,a_8)$

$\begin{array}{l}-125a_3^2+1\text{,}000a_3^3+650a_3{a}_8-6\text{,}750a_3^2{a}_8+280a_8^2+5\text{,}820a_3{a}_8^2\\ -5\text{,}978a_8^3+56\text{,}700a_3{a}_8^3-7\text{,}695a_8^4-166\text{,}698a_8^5\end{array}$

$(a_3,a_9)$

$\begin{array}{l}-52\text{,}125a_3^2+360\text{,}750a_3^3+421\text{,}875a_3^4+225\text{,}000a_3^5-271\text{,}050a_3{a}_9\\ +2\text{,}621\text{,}450a_3^2{a}_9+3\text{,}667\text{,}500a_3^3{a}_9+4\text{,}725\text{,}000a_3^4{a}_9+116\text{,}760a_9^2+4\text{,}007\text{,}030a_3{a}_9^2\\ -780\text{,}750a_3^2{a}_9^2+39\text{,}690\text{,}000a_3^3{a}_9^3+2\text{,}270\text{,}618a_9^3-43\text{,}218\text{,}900a_3{a}_9^3+166\text{,}698\text{,}000a_3^2{a}_9^3\\ +9\text{,}146\text{,}115a_9^4+350\text{,}065\text{,}800a_3{a}_9^4+294\text{,}055\text{,}272a_9^5\end{array}$

$(a_3,a_{10})$

$\begin{array}{l}1\text{,}875a_3^2-30\text{,}000a_3^3+120\text{,}000a_3^4+22\text{,}500a_3{a}_{10}-311\text{,}950a_3^2{a}_{10}\\ +1\text{,}440\text{,}000a_3^3{a}_{10}+16\text{,}800a_{10}^2+37\text{,}800a_3{a}_{10}^2+2\text{,}826\text{,}000a_3^2{a}_{10}^2\\ -955\text{,}472a_{10}^3-2\text{,}613\text{,}600a_3{a}_{10}^3+12\text{,}946\text{,}608a_{10}^4-56\text{,}010\text{,}528a_{10}^5\end{array}$

$(a_3,a_{11})$

$\begin{array}{l}5\text{,}315\text{,}625a_3^4+6\text{,}250a_3^5-133\text{,}844\text{,}400a_3^2{a}_{11}+358\text{,}344\text{,}000a_3^3{a}_{11}\\ -1\text{,}575\text{,}000a_3^4{a}_{11}+12\text{,}192\text{,}768a_{11}^2+1\text{,}542\text{,}181\text{,}760a_3{a}_{11}^2+607\text{,}773\text{,}600a_3^2{a}_{11}^2\\ +158\text{,}760\text{,}000a_3^3{a}_{11}^2-5\text{,}851\text{,}104\text{,}000a_{11}^3-41\text{,}822\text{,}645\text{,}760a_3{a}_{11}^3-8\text{,}001\text{,}504\text{,}000a_3^2{a}_{11}^3\\ +213\text{,}353\text{,}968\text{,}896a_{11}^4+201\text{,}637\text{,}900\text{,}800a_3{a}_{11}^4-2\text{,}032\text{,}510\text{,}040\text{,}064a_{11}^5\end{array}$

$(a_3,a_{12})$

$\begin{array}{l}-28\text{,}125a_3^4+225\text{,}000a_3^5-1\text{,}170\text{,}000a_3^2{a}_{12}+12\text{,}420\text{,}000a_3^3{a}_{12}\\ -18\text{,}900\text{,}000a_3^4{a}_{12}+250\text{,}880a_{12}^2+33\text{,}272\text{,}960a_3{a}_{12}^2-205\text{,}380\text{,}000a_3^2{a}_{12}^2\\ +635\text{,}040\text{,}000a_3^3{a}_{12}^2-228\text{,}392\text{,}192a_{12}^3+287\text{,}539\text{,}200a_3{a}_{12}^3-10\text{,}668\text{,}672\text{,}000a_3^2{a}_{12}^3\\ +5\text{,}816\text{,}344\text{,}320a_{12}^4+89\text{,}616\text{,}844\text{,}800a_3{a}_{12}^4-301\text{,}112\text{,}598\text{,}528a_{12}^5\end{array}$

$(a_4,a_5)$

$\begin{array}{l}-13a_4^2+176a_4^3-720a_4^4+1\text{,}152a_4^5+260a_4{a}_5-4\text{,}880a_4^2{a}_5+14\text{,}400a_4^3{a}_5\\ +1\text{,}625a_5^2+52\text{,}000a_4{a}_5^2-64\text{,}000a_5^3\end{array}$

$(a_4,a_6)$

$\begin{array}{l}-25a_4^2+168a_4^3-576a_4^4+1\text{,}152a_4^5+50a_4{a}_6-200a_4^2{a}_6-576a_4^3{a}_6\\ -25a_6^2+544a_4{a}_6^2-512a_6^3\end{array}$

$(a_4,a_7)$

$\begin{array}{l}6\text{,}156a_4^3+5\text{,}589a_4^4+1\text{,}944a_4^5-228a_4{a}_7-10\text{,}980a_4^2{a}_7-9\text{,}072a_4^3{a}_7\\ +95a_7^2+8\text{,}544a_4{a}_7^2-2\text{,}048a_7^3\end{array}$

$(a_4,a_8)$

$-4a_4^2+32a_4^3+8a_4{a}_8-96a_4^2{a}_8+5a_8^2+96a_4{a}_8^2-32a_8^3$

$(a_4,a_9)$

$\begin{array}{l}-84a_4^2+816a_4^3-1\text{,}296a_4^4+1\text{,}152a_4^5-168a_4{a}_9+2\text{,}432a_4^2{a}_9\\ -2\text{,}880a_4^3{a}_9+105a_9^2+2\text{,}848a_4{a}_9^2+512a_9^3\end{array}$

$(a_4,a_{10})$

$3a_4^2-48a_4^3+192a_4^4+18a_4{a}_{10}-112a_4^2{a}_{10}+15a_{10}^2+384a_4{a}_{10}^2-128a_{10}^3$

$(a_4,a_{11})$

$175a_4^4+8a_4^5-900a_4^2{a}_{11}+816a_4^3{a}_{11}+125a_{11}^2+5\text{,}920a_4{a}_{11}^2-6\text{,}144a_{11}^3$

$(a_4,a_{12})$

$-9a_4^4+72a_4^5-72a_4^2{a}_{12}+720a_4^3{a}_{12}+25a_{12}^2+1\text{,}312a_4{a}_{12}^2-2\text{,}048a_{12}^3$

$(a_5,a_6)$

$\begin{array}{l}-125a_5^2+24\text{,}000a_5^3-1\text{,}800\text{,}000a_5^4+7\text{,}200\text{,}000a_5^5-20a_5{a}_6+2\text{,}600a_5^2{a}_6\\ -432\text{,}000a_5^3{a}_6-7\text{,}200\text{,}000a_5^4{a}_6+a_6^2+200a_5{a}_6^2-158\text{,}400a_5^2{a}_6^2\\ +2\text{,}880\text{,}000a_5^3{a}_6^2-16a_6^3+4\text{,}320a_5{a}_6^3-576\text{,}000a_5^2{a}_6^3+144a_6^4\\ +57\text{,}600a_5{a}_6^4-2\text{,}304a_6^5\end{array}$

$(a_5,a_7)$

$\begin{array}{l}10\text{,}732\text{,}500a_5^3+15\text{,}946\text{,}875a_5^4+6\text{,}075\text{,}000a_5^5-15\text{,}900a_5{a}_7-4\text{,}972\text{,}500a_5^2{a}_7\\ -10\text{,}827\text{,}000a_5^3{a}_7-8\text{,}100\text{,}000a_5^4{a}_7+265a_7^2+183\text{,}960a_5{a}_7^2-12\text{,}355\text{,}200a_5^2{a}_7^2\\ +4\text{,}320\text{,}000a_5^3{a}_7^2-2\text{,}016a_7^3+17\text{,}280a_5{a}_7^3-1\text{,}152\text{,}000a_5^2{a}_7^3+3\text{,}328a_7^4\\ +153\text{,}600a_5{a}_7^4-8\text{,}192a_7^5\end{array}$

$(a_5,a_8)$

$2\text{,}000a_5^3-500a_5^2{a}_8+40a_5{a}_8^2-a_8^3-36a_8^5$

$(a_5,a_9)$

$\begin{array}{l}1\text{,}500a_5^3+450\text{,}000a_5^5+400a_5^2{a}_9+450\text{,}000a_5^4{a}_9+35a_5{a}_9^2+180\text{,}000a_5^3{a}_9^2\\ +a_9^3+36\text{,}000a_5^2{a}_9^3+3\text{,}600a_5{a}_9^4+144a_9^5\end{array}$

$(a_5,a_{10})$

$60\text{,}000a_5^4+25a_5^2{a}_{10}-3\text{,}000a_5^2{a}_{10}^2-a_{10}^3+24a_{10}^4-144a_{10}^5$

$(a_5,a_{11})$

$\begin{array}{l}809\text{,}375a_5^4+25\text{,}000a_5^5-11\text{,}100a_5^2{a}_{11}+561\text{,}000a_5^3{a}_{11}-300\text{,}000a_5^4{a}_{11}\\ +37a_{11}^2-760a_5{a}_{11}^2-1\text{,}353\text{,}600a_5^2{a}_{11}^2+1\text{,}440\text{,}000a_5^3{a}_{11}^2-5\text{,}280a_{11}^3\\ -51\text{,}840a_5{a}_{11}^3-3\text{,}456\text{,}000a_5^2{a}_{11}^3+186\text{,}624a_{11}^4+4\text{,}147\text{,}200a_5{a}_{11}^4-1\text{,}990\text{,}656a_{11}^5\end{array}$

$(a_5,a_{12})$

$\begin{array}{l}28\text{,}125a_5^5-112\text{,}500a_5^4{a}_{12}-5a_5{a}_{12}^2+180\text{,}000a_5^3{a}_{12}^2\\ -4a_{12}^3-144\text{,}000a_5^2{a}_{12}^3+57\text{,}600a_5{a}_{12}^4-9\text{,}216a_{12}^5\end{array}$

$(a_6,a_7)$

$\begin{array}{l}44\text{,}388a_6^3+12\text{,}879a_6^4+3\text{,}888a_6^5-1\text{,}644a_6{a}_7+756a_6^2{a}_7+7\text{,}776a_6^3{a}_7\\ -25\text{,}920a_6^4{a}_7+685a_7^2-6\text{,}840a_6{a}_7^2-101\text{,}088a_6^2{a}_7^2+69\text{,}120a_6^3{a}_7^2\\ -672a_7^3+43\text{,}776a_6{a}_7^3-92\text{,}160a_6^2{a}_7^3+61\text{,}440a_6{a}_7^4-16\text{,}384a_7^5\end{array}$

$(a_6,a_8)$

$\begin{array}{l}-4a_6^2+64a_6^3+8a_6{a}_8-176a_6^2{a}_8+5a_8^2+16a_6{a}_8^2+24a_8^3\\ +432a_6{a}_8^3+72a_8^4-144a_8^5\end{array}$

$(a_6,a_9)$

$\begin{array}{l}-4a_6^2+48a_6^3+240a_6^4+256a_6^5-8a_6{a}_9+144a_6^2{a}_9+960a_6^3{a}_9\\ +1\text{,}280a_6^4{a}_9+5a_9^2+72a_6{a}_9^2+288a_6^2{a}_9^2+2\text{,}560a_6^3{a}_9^2\\ -24a_9^3-1\text{,}344a_6{a}_9^3+2\text{,}560a_6^2{a}_9^3+384a_9^4+1\text{,}280a_6{a}_9^4+256a_9^5\end{array}$

$(a_6,a_{10})$

$\begin{array}{l}{a}_6^2-32a_6^3+256a_6^4+6a_6{a}_{10}-168a_6^2{a}_{10}+1\text{,}536a_6^3{a}_{10}+5a_{10}^2\\ -88a_6{a}_{10}^2+2\text{,}624a_6^2{a}_{10}^2-48a_{10}^3+1\text{,}344a_6{a}_{10}^3+384a_{10}^4-384a_{10}^5\end{array}$

$(a_6,a_{11})$

$\begin{array}{l}4\text{,}025a_6^4+16a_6^5-20\text{,}700a_6^2{a}_{11}+124\text{,}512a_6^3{a}_{11}-960a_6^4{a}_{11}\\ +2\text{,}875a_{11}^2-13\text{,}000a_6{a}_{11}^2+705\text{,}888a_6^2{a}_{11}^2+23\text{,}040a_6^3{a}_{11}^2-99\text{,}936a_{11}^3\\ +546\text{,}048a_6{a}_{11}^3-276\text{,}480a_6^2{a}_{11}^3+1\text{,}327\text{,}104a_{11}^4+1\text{,}658\text{,}880a_6{a}_{11}^4-3\text{,}981\text{,}312a_{11}^5\end{array}$

$(a_6,a_{12})$

$\begin{array}{l}-9a_6^4+144a_6^5-72a_6^2{a}_{12}+1\text{,}440a_6^3{a}_{12}-2\text{,}880a_6^4{a}_{12}+25a_{12}^2-184a_6{a}_{12}^2\\ +5\text{,}472a_6^2{a}_{12}^2+23\text{,}040a_6^3{a}_{12}^2-1\text{,}632a_{12}^3-6\text{,}912a_6{a}_{12}^3-92\text{,}160a_6^2{a}_{12}^3\\ +36\text{,}864a_{12}^4+184\text{,}320a_6{a}_{12}^4-147\text{,}456a_{12}^5\end{array}$

$(a_7,a_8)$

$\begin{array}{l}-80a_7^2+512a_7^3+480a_7{a}_8-4\text{,}512a_7^2{a}_8+9\text{,}360a_7{a}_8^2-3\text{,}240a_8^3\\ +3\text{,}888a_7{a}_8^3-1\text{,}215a_8^4-486a_8^5\end{array}$

$(a_7,a_9)$

$\begin{array}{l}-2\text{,}480a_7^2+14\text{,}592a_7^3+6\text{,}912a_7^4+8\text{,}192a_7^5-14\text{,}880a_7{a}_9+139\text{,}392a_7^2{a}_9\\ +129\text{,}024a_7^3{a}_9+30\text{,}720a_7^4{a}_9+378\text{,}000a_7{a}_9^2+505\text{,}440a_7^2{a}_9^2+46\text{,}080a_7^3{a}_9^2\\ +100\text{,}440a_9^3-147\text{,}744a_7{a}_9^3+34\text{,}560a_7^2{a}_9^3-27\text{,}945a_9^4+12\text{,}960a_7{a}_9^4+1\text{,}944a_9^5\end{array}$

$(a_7,a_{10})$

$\begin{array}{l}25a_7^2-320a_7^3+1\text{,}024a_7^4+300a_7{a}_{10}-2\text{,}010a_7^2{a}_{10}+9\text{,}216a_7^3{a}_{10}+17\text{,}460a_7{a}_{10}^2\\ +22\text{,}320a_7^2{a}_{10}^2-8\text{,}100a_{10}^3+9\text{,}288a_7{a}_{10}^3-3\text{,}645a_{10}^4-486a_{10}^5\end{array}$

$(a_7,a_{11})$

$\begin{array}{l}4\text{,}655a_7^4+16a_7^5-134\text{,}064a_7^2{a}_{11}+241\text{,}812a_7^3{a}_{11}-720a_7^4{a}_{11}+1\text{,}034\text{,}208a_7{a}_{11}^2\\ +2\text{,}320\text{,}650a_7^2{a}_{11}^2+12\text{,}960a_7^3{a}_{11}^2-1\text{,}994\text{,}544a_{11}^3+1\text{,}787\text{,}508a_7{a}_{11}^3-116\text{,}640a_7^2{a}_{11}^3\\ -2\text{,}735\text{,}937a_{11}^4+524\text{,}880a_7{a}_{11}^4-944\text{,}784a_{11}^5\end{array}$

$(a_7,a_{12})$

$\begin{array}{l}-5a_7^4+32a_7^5-240a_7^2{a}_{12}+1\text{,}836a_7^3{a}_{12}-480a_7^4{a}_{12}+4\text{,}320a_7{a}_{12}^2\\ +29\text{,}322a_7^2{a}_{12}^2+2\text{,}880a_7^3{a}_{12}^2-19\text{,}440a_{12}^3+8\text{,}316a_7{a}_{12}^3-8\text{,}640a_7^2{a}_{12}^3\\ -23\text{,}085a_{12}^4+12\text{,}960a_7{a}_{12}^4-7\text{,}776a_{12}^5\end{array}$

$(a_8,a_9)$

$3a_8^3+9a_8^5+10a_8^2{a}_9+11a_8{a}_9^2+4a_9^3$

$(a_8,a_{10})$

$6a_8^4+a_8^2{a}_{10}-4a_{10}^3$

$(a_8,a_{11})$

$35a_8^4+2a_8^5-48a_8^2{a}_{11}+144a_8^3{a}_{11}+16a_{11}^2-32a_8{a}_{11}^2-1\text{,}536a_{11}^3$

$(a_8,a_{12})$

$9a_8^5-16a_8{a}_{12}^2-256a_{12}^3$

$(a_9,a_{10})$

$32a_9^4+3a_9^2{a}_{10}-104a_9^2{a}_{10}^2-12a_{10}^3+48a_{10}^4-48a_{10}^5$

$(a_9,a_{11})$

$\begin{array}{l}-1\text{,}365a_9^4+8a_9^5+1\text{,}872a_9^2{a}_{11}+7\text{,}584a_9^3{a}_{11}+480a_9^4{a}_{11}-624a_{11}^2\\ -1\text{,}280a_9{a}_{11}^2+103\text{,}392a_9^2{a}_{11}^2+11\text{,}520a_9^3{a}_{11}^2+66\text{,}816a_{11}^3-27\text{,}648a_9{a}_{11}^3\\ +138\text{,}240a_9^2{a}_{11}^3-684\text{,}288a_{11}^4+829\text{,}440a_9{a}_{11}^4+1\text{,}990\text{,}656a_{11}^5\end{array}$

$(a_9,a_{12})$

$\begin{array}{l}9a_9^5+180a_9^4{a}_{12}-16a_9{a}_{12}^2+1\text{,}440a_9^3{a}_{12}^2+192a_{12}^3\\ +5\text{,}760a_9^2{a}_{12}^3+11\text{,}520a_9{a}_{12}^4+9\text{,}216a_{12}^5\end{array}$

$(a_{10},a_{11})$

$\begin{array}{l}-105a_{10}^4+2a_{10}^5+36a_{10}^2{a}_{11}+1\text{,}752a_{10}^3{a}_{11}-3a_{11}^2-290a_{10}{a}_{11}^2\\ -10\text{,}512a_{10}^2{a}_{11}^2+576a_{11}^3+27\text{,}648a_{10}{a}_{11}^3-27\text{,}648a_{11}^4\end{array}$

$(a_{10},a_{12})$

$9a_{10}^5-a_{10}{a}_{12}^2-72a_{10}^2{a}_{12}^2-1\text{,}536a_{12}^4$

$(a_{11},a_{12})$

$\begin{array}{l}-81a_{11}^4+7\text{,}776a_{11}^5+108a_{11}^3{a}_{12}-12\text{,}960a_{11}^4{a}_{12}+594a_{11}^2{a}_{12}^2+8\text{,}640a_{11}^3{a}_{12}^2\\ -420a_{11}{a}_{12}^3-2\text{,}880a_{11}^2{a}_{12}^3-1\text{,}225a_{12}^4+480a_{11}{a}_{12}^4-32a_{12}^5\end{array}$