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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
2.2-a1 2.2-a 3.3.316.1 \( 2 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $171.4772930$ 0.602896961 \( \frac{200481}{16} a^{2} - \frac{325027}{8} a + \frac{233973}{8} \) \( \bigl[a^{2} + a - 3\) , \( -a - 1\) , \( a^{2} - 3\) , \( 971347319857519 a^{2} - 514150241464297 a - 4127391273410075\) , \( 22425156860537519167317 a^{2} - 11870007338272500196506 a - 95287643090023949417928\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(971347319857519a^{2}-514150241464297a-4127391273410075\right){x}+22425156860537519167317a^{2}-11870007338272500196506a-95287643090023949417928$
2.2-a2 2.2-a 3.3.316.1 \( 2 \) $0$ $\Z/16\Z$ $1$ $171.4772930$ 0.602896961 \( \frac{4108077233}{65536} a^{2} - \frac{5810733523}{32768} a + \frac{2294990397}{32768} \) \( \bigl[a^{2} + a - 3\) , \( -a\) , \( a\) , \( -608022265892705467026233 a^{2} + 321836266424514724186808 a + 2583572058090078441238362\) , \( -627730820434767876188418741768082419 a^{2} + 332268331114001902947589285516929027 a + 2667316476142693080354081387519995775\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-608022265892705467026233a^{2}+321836266424514724186808a+2583572058090078441238362\right){x}-627730820434767876188418741768082419a^{2}+332268331114001902947589285516929027a+2667316476142693080354081387519995775$
2.2-a3 2.2-a 3.3.316.1 \( 2 \) $0$ $\Z/2\Z$ $1$ $2.679332704$ 0.602896961 \( \frac{89069256294443128323}{2} a^{2} - 125302919348047971845 a + 49111676741552886754 \) \( \bigl[a^{2} + a - 3\) , \( -a + 1\) , \( a^{2} - 3\) , \( -310 a^{2} + 882 a - 364\) , \( -6966 a^{2} + 19620 a - 7728\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-310a^{2}+882a-364\right){x}-6966a^{2}+19620a-7728$
2.2-a4 2.2-a 3.3.316.1 \( 2 \) $0$ $\Z/8\Z$ $1$ $171.4772930$ 0.602896961 \( \frac{32251567931279}{16} a^{2} + \frac{21655756210331}{8} a - \frac{13765401110581}{8} \) \( \bigl[a^{2} + a - 3\) , \( -a^{2} + 2\) , \( a\) , \( 469933301874402734133 a^{2} - 248743488236812365957 a - 1996812643211595590900\) , \( -8108483751005890586477675293469 a^{2} + 4291954889112701686585656294515 a + 34454087009163876680154219600725\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(469933301874402734133a^{2}-248743488236812365957a-1996812643211595590900\right){x}-8108483751005890586477675293469a^{2}+4291954889112701686585656294515a+34454087009163876680154219600725$
2.2-a5 2.2-a 3.3.316.1 \( 2 \) $0$ $\Z/2\Z\oplus\Z/8\Z$ $1$ $342.9545861$ 0.602896961 \( \frac{130050481}{256} a^{2} + \frac{87514925}{128} a - \frac{54929731}{128} \) \( \bigl[a^{2} + a - 3\) , \( -a^{2} + 2\) , \( a\) , \( 30965253611602296633 a^{2} - 16390422144515520442 a - 131575714394521753905\) , \( -112172935746444460857621319378 a^{2} + 59374994732320022090359795265 a + 476638568561218377704701696552\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(30965253611602296633a^{2}-16390422144515520442a-131575714394521753905\right){x}-112172935746444460857621319378a^{2}+59374994732320022090359795265a+476638568561218377704701696552$
2.2-a6 2.2-a 3.3.316.1 \( 2 \) $0$ $\Z/4\Z$ $1$ $85.73864654$ 0.602896961 \( \frac{427}{4} a^{2} + \frac{383}{2} a - \frac{47}{2} \) \( \bigl[1\) , \( -a^{2} + 2\) , \( a^{2} - 2\) , \( -397482296655616833 a^{2} + 210393969927507918 a + 1688958139908216880\) , \( 849554077046907793046157006 a^{2} - 449683058696981763869697464 a - 3609874668113250400329290553\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-397482296655616833a^{2}+210393969927507918a+1688958139908216880\right){x}+849554077046907793046157006a^{2}-449683058696981763869697464a-3609874668113250400329290553$
2.2-a7 2.2-a 3.3.316.1 \( 2 \) $0$ $\Z/2\Z$ $1$ $2.679332704$ 0.602896961 \( -\frac{10154621765056003}{2} a^{2} + 2687505089603077 a + 21574207961612782 \) \( \bigl[1\) , \( -a^{2} + a + 3\) , \( 1\) , \( 3795999062 a^{2} - 2009285242 a - 16129733497\) , \( 186167522763990 a^{2} - 98541556480493 a - 791051967859626\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(3795999062a^{2}-2009285242a-16129733497\right){x}+186167522763990a^{2}-98541556480493a-791051967859626$
2.2-a8 2.2-a 3.3.316.1 \( 2 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $21.43466163$ 0.602896961 \( \frac{8525185037}{4} a^{2} - \frac{12150636535}{2} a + \frac{5069473275}{2} \) \( \bigl[1\) , \( -a^{2} + a + 3\) , \( 1\) , \( 237250327 a^{2} - 125580532 a - 1008109982\) , \( 2909065137552 a^{2} - 1539816409981 a - 12361026604032\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(237250327a^{2}-125580532a-1008109982\right){x}+2909065137552a^{2}-1539816409981a-12361026604032$
4.3-a1 4.3-a 3.3.316.1 \( 2^{2} \) $0$ $\Z/2\Z$ $1$ $98.10329547$ 1.379685384 \( 342336 a^{2} + 460416 a - 292544 \) \( \bigl[a^{2} + a - 2\) , \( a^{2} + a - 3\) , \( a + 1\) , \( -2770 a^{2} + 1478 a + 11792\) , \( 1679357 a^{2} - 888891 a - 7135787\bigr] \) ${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(-2770a^{2}+1478a+11792\right){x}+1679357a^{2}-888891a-7135787$
4.3-a2 4.3-a 3.3.316.1 \( 2^{2} \) $0$ $\Z/2\Z$ $1$ $98.10329547$ 1.379685384 \( 510768 a^{2} - 1452320 a + 597920 \) \( \bigl[a^{2} + a - 2\) , \( a + 1\) , \( a + 1\) , \( 32 a^{2} - 8 a - 120\) , \( 138 a^{2} - 59 a - 561\bigr] \) ${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(32a^{2}-8a-120\right){x}+138a^{2}-59a-561$
8.1-a1 8.1-a 3.3.316.1 \( 2^{3} \) $0$ $\Z/6\Z$ $1$ $145.9386959$ 0.684141088 \( \frac{33759}{2} a^{2} + 32803 a + 4371 \) \( \bigl[a^{2} - 2\) , \( -a^{2} - a + 4\) , \( a^{2} - 2\) , \( -a^{2} - 8 a + 8\) , \( 5 a^{2} - 22 a + 11\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-a^{2}-8a+8\right){x}+5a^{2}-22a+11$
8.1-a2 8.1-a 3.3.316.1 \( 2^{3} \) $0$ $\Z/2\Z$ $1$ $5.405136888$ 0.684141088 \( \frac{5335424117455903}{8} a^{2} + \frac{3582532102104931}{4} a - \frac{2277251078226861}{4} \) \( \bigl[a^{2} - 2\) , \( -a^{2} - a + 4\) , \( a^{2} - 2\) , \( -126 a^{2} - 98 a + 78\) , \( -1365 a^{2} - 1026 a + 787\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-126a^{2}-98a+78\right){x}-1365a^{2}-1026a+787$
8.1-a3 8.1-a 3.3.316.1 \( 2^{3} \) $0$ $\Z/2\Z$ $1$ $5.405136888$ 0.684141088 \( -\frac{596658698344264096415}{8} a^{2} + \frac{157910670855855346189}{4} a + \frac{1267643331281111416669}{4} \) \( \bigl[a\) , \( -a^{2} - a + 2\) , \( a\) , \( 696542 a^{2} - 368715 a - 2959749\) , \( 463057095 a^{2} - 245103850 a - 1967594769\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(696542a^{2}-368715a-2959749\right){x}+463057095a^{2}-245103850a-1967594769$
8.1-a4 8.1-a 3.3.316.1 \( 2^{3} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $10.81027377$ 0.684141088 \( -\frac{266664752495}{64} a^{2} + \frac{71121115277}{32} a + \frac{567573953693}{32} \) \( \bigl[a\) , \( -a^{2} - a + 2\) , \( a\) , \( 43522 a^{2} - 23060 a - 184974\) , \( 7250072 a^{2} - 3837642 a - 30806682\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(43522a^{2}-23060a-184974\right){x}+7250072a^{2}-3837642a-30806682$
8.1-a5 8.1-a 3.3.316.1 \( 2^{3} \) $0$ $\Z/6\Z$ $1$ $145.9386959$ 0.684141088 \( \frac{2097153}{2} a^{2} - 6340607 a + 9585409 \) \( \bigl[a\) , \( -a^{2} - a + 2\) , \( a\) , \( 8597 a^{2} - 4555 a - 36539\) , \( 638631 a^{2} - 338020 a - 2713601\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(8597a^{2}-4555a-36539\right){x}+638631a^{2}-338020a-2713601$
8.1-a6 8.1-a 3.3.316.1 \( 2^{3} \) $0$ $\Z/2\Z\oplus\Z/6\Z$ $1$ $291.8773919$ 0.684141088 \( \frac{113}{4} a^{2} - \frac{1939}{2} a + \frac{7773}{2} \) \( \bigl[a\) , \( -a^{2} - a + 2\) , \( a\) , \( 587 a^{2} - 310 a - 2494\) , \( 8248 a^{2} - 4366 a - 35048\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(587a^{2}-310a-2494\right){x}+8248a^{2}-4366a-35048$
8.1-a7 8.1-a 3.3.316.1 \( 2^{3} \) $0$ $\Z/2\Z$ $1$ $2.702568444$ 0.684141088 \( \frac{532560105997425}{4096} a^{2} - \frac{749207151764755}{2048} a + \frac{293646661918461}{2048} \) \( \bigl[a\) , \( -a^{2} - a + 4\) , \( a\) , \( 420286700 a^{2} - 222464805 a - 1785857409\) , \( 6903318103765 a^{2} - 3654040730844 a - 29333168803431\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(420286700a^{2}-222464805a-1785857409\right){x}+6903318103765a^{2}-3654040730844a-29333168803431$
8.1-a8 8.1-a 3.3.316.1 \( 2^{3} \) $0$ $\Z/6\Z$ $1$ $72.96934799$ 0.684141088 \( \frac{19825}{16} a^{2} - \frac{24115}{8} a + \frac{15581}{8} \) \( \bigl[a\) , \( -a^{2} - a + 4\) , \( a\) , \( -15155975 a^{2} + 8022315 a + 64399881\) , \( 50371899485 a^{2} - 26662681574 a - 214037280091\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-15155975a^{2}+8022315a+64399881\right){x}+50371899485a^{2}-26662681574a-214037280091$
8.2-a1 8.2-a 3.3.316.1 \( 2^{3} \) $0$ $\Z/4\Z$ $1$ $172.6937124$ 0.607173770 \( -343127540 a^{2} + 181623451 a + 1457997356 \) \( \bigl[a\) , \( -a - 1\) , \( a^{2} + a - 2\) , \( 2190935255 a^{2} - 1159698357 a - 9309591809\) , \( -81630791102268 a^{2} + 43208531179462 a + 346860703632228\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2190935255a^{2}-1159698357a-9309591809\right){x}-81630791102268a^{2}+43208531179462a+346860703632228$
8.2-a2 8.2-a 3.3.316.1 \( 2^{3} \) $0$ $\Z/4\Z$ $1$ $86.34685623$ 0.607173770 \( -97 a^{2} - 314 a + 1270 \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -272 a^{2} + 144 a + 1157\) , \( 2826 a^{2} - 1496 a - 12008\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-272a^{2}+144a+1157\right){x}+2826a^{2}-1496a-12008$
8.2-a3 8.2-a 3.3.316.1 \( 2^{3} \) $0$ $\Z/2\Z$ $1$ $2.698339257$ 0.607173770 \( -2320978186626 a^{2} + 1226457049213 a + 9867024470514 \) \( \bigl[a\) , \( a + 1\) , \( a^{2} + a - 2\) , \( -91 a^{2} + 363 a - 351\) , \( -1638 a^{2} + 5248 a - 3310\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-91a^{2}+363a-351\right){x}-1638a^{2}+5248a-3310$
8.2-a4 8.2-a 3.3.316.1 \( 2^{3} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $21.58671405$ 0.607173770 \( 155385857 a^{2} + 210010108 a - 130120956 \) \( \bigl[a\) , \( a + 1\) , \( a^{2} + a - 2\) , \( -6 a^{2} + 23 a - 21\) , \( -25 a^{2} + 80 a - 56\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-6a^{2}+23a-21\right){x}-25a^{2}+80a-56$
8.2-a5 8.2-a 3.3.316.1 \( 2^{3} \) $0$ $\Z/2\Z$ $1$ $2.698339257$ 0.607173770 \( 189657446701367682 a^{2} + 254695362995847043 a - 161898141766190114 \) \( \bigl[a\) , \( a + 1\) , \( a^{2} + a - 2\) , \( -a^{2} + 3 a - 11\) , \( -72 a^{2} + 200 a - 106\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-a^{2}+3a-11\right){x}-72a^{2}+200a-106$
8.2-a6 8.2-a 3.3.316.1 \( 2^{3} \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $172.6937124$ 0.607173770 \( 4165 a^{2} + 5890 a - 1058 \) \( \bigl[a\) , \( a + 1\) , \( a^{2} + a - 2\) , \( -a^{2} + 3 a - 1\) , \( -2 a\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-a^{2}+3a-1\right){x}-2a$
8.2-a7 8.2-a 3.3.316.1 \( 2^{3} \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $345.3874249$ 0.607173770 \( 95505 a^{2} - 288104 a + 153504 \) \( \bigl[a\) , \( -a^{2} + a + 3\) , \( a\) , \( 14246 a^{2} - 7541 a - 60535\) , \( -1307660 a^{2} + 692166 a + 5556430\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(14246a^{2}-7541a-60535\right){x}-1307660a^{2}+692166a+5556430$
8.2-a8 8.2-a 3.3.316.1 \( 2^{3} \) $0$ $\Z/4\Z$ $1$ $172.6937124$ 0.607173770 \( 103101005876 a^{2} - 290083733531 a + 113696309796 \) \( \bigl[a\) , \( -a^{2} + a + 3\) , \( a\) , \( -2419 a^{2} + 1279 a + 10275\) , \( -4236156 a^{2} + 2242268 a + 18000022\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-2419a^{2}+1279a+10275\right){x}-4236156a^{2}+2242268a+18000022$
8.3-a1 8.3-a 3.3.316.1 \( 2^{3} \) $0$ $\Z/2\Z$ $1$ $2.922549717$ 0.739828198 \( -\frac{541255732825}{8192} a^{2} + \frac{6091495909813}{32768} a - \frac{2387470670643}{32768} \) \( \bigl[a^{2} - 3\) , \( a^{2} - 3\) , \( a^{2} + a - 2\) , \( -25 a^{2} + 70 a - 27\) , \( -153 a^{2} + 417 a - 163\bigr] \) ${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-25a^{2}+70a-27\right){x}-153a^{2}+417a-163$
8.3-a2 8.3-a 3.3.316.1 \( 2^{3} \) $0$ $\Z/6\Z$ $1$ $78.90884237$ 0.739828198 \( \frac{56079}{8} a^{2} - \frac{116333}{32} a - \frac{958845}{32} \) \( \bigl[a^{2} - 3\) , \( a^{2} - 3\) , \( a^{2} + a - 2\) , \( -2\) , \( -a^{2}\bigr] \) ${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}-2{x}-a^{2}$
8.3-a3 8.3-a 3.3.316.1 \( 2^{3} \) $0$ $\Z/2\Z$ $1$ $5.845099435$ 0.739828198 \( \frac{10610687801034935261}{256} a^{2} - \frac{29854300194558708471}{256} a + \frac{1462650220091725987}{32} \) \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 16 a^{2} + a - 111\) , \( -52 a^{2} + 36 a + 69\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(16a^{2}+a-111\right){x}-52a^{2}+36a+69$
8.3-a4 8.3-a 3.3.316.1 \( 2^{3} \) $0$ $\Z/6\Z$ $1$ $157.8176847$ 0.739828198 \( -\frac{1780690961}{8} a^{2} + \frac{941301753}{8} a + \frac{3785006083}{4} \) \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 21 a^{2} - 9 a - 86\) , \( -59 a^{2} + 32 a + 252\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(21a^{2}-9a-86\right){x}-59a^{2}+32a+252$
16.1-a1 16.1-a 3.3.316.1 \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $29.47640287$ 1.658177211 \( \frac{63684217}{2} a^{2} - 89592107 a + 35115877 \) \( \bigl[a^{2} - 2\) , \( a^{2} - a - 3\) , \( a^{2} - 2\) , \( -3 a^{2} + 2 a + 9\) , \( -2 a^{2} + 3 a + 2\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-3a^{2}+2a+9\right){x}-2a^{2}+3a+2$
16.1-a2 16.1-a 3.3.316.1 \( 2^{4} \) $0$ $\Z/4\Z$ $1$ $117.9056115$ 1.658177211 \( -\frac{58508563841049}{4} a^{2} + \frac{15484776480827}{2} a + \frac{124305555260903}{2} \) \( \bigl[a\) , \( a^{2} + a - 4\) , \( 0\) , \( 89717 a^{2} - 47509 a - 381256\) , \( -21491631 a^{2} + 11375920 a + 91321039\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(89717a^{2}-47509a-381256\right){x}-21491631a^{2}+11375920a+91321039$
16.1-a3 16.1-a 3.3.316.1 \( 2^{4} \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $235.8112230$ 1.658177211 \( -\frac{29580655}{16} a^{2} + \frac{7825805}{8} a + \frac{62873277}{8} \) \( \bigl[a\) , \( a^{2} + a - 4\) , \( 0\) , \( 5607 a^{2} - 2969 a - 23826\) , \( -340349 a^{2} + 180146 a + 1446179\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(5607a^{2}-2969a-23826\right){x}-340349a^{2}+180146a+1446179$
16.1-a4 16.1-a 3.3.316.1 \( 2^{4} \) $0$ $\Z/8\Z$ $1$ $117.9056115$ 1.658177211 \( \frac{285267441}{256} a^{2} - \frac{401089939}{128} a + \frac{156913533}{128} \) \( \bigl[a\) , \( a^{2} - 2\) , \( a^{2} - 2\) , \( 49623936 a^{2} - 26266736 a - 210859010\) , \( -374288977427 a^{2} + 198117361452 a + 1590406466852\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(49623936a^{2}-26266736a-210859010\right){x}-374288977427a^{2}+198117361452a+1590406466852$
16.1-a5 16.1-a 3.3.316.1 \( 2^{4} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $117.9056115$ 1.658177211 \( \frac{1401505}{4} a^{2} + \frac{928349}{2} a - \frac{584947}{2} \) \( \bigl[a\) , \( -a\) , \( a^{2} - 2\) , \( -a^{2} - a + 1\) , \( -a^{2} + a - 1\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}-2\right){y}={x}^{3}-a{x}^{2}+\left(-a^{2}-a+1\right){x}-a^{2}+a-1$
16.1-a6 16.1-a 3.3.316.1 \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $14.73820143$ 1.658177211 \( \frac{1898088202191}{2} a^{2} + 1274493239347 a - 810136780017 \) \( \bigl[a\) , \( -a\) , \( a^{2} - 2\) , \( -6 a^{2} - 11 a + 6\) , \( -16 a^{2} - 18 a + 11\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}-2\right){y}={x}^{3}-a{x}^{2}+\left(-6a^{2}-11a+6\right){x}-16a^{2}-18a+11$
16.2-a1 16.2-a 3.3.316.1 \( 2^{4} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $93.59270615$ 1.316250266 \( 95505 a^{2} - 288104 a + 153504 \) \( \bigl[a\) , \( -a - 1\) , \( a\) , \( 37178 a^{2} - 19692 a - 157999\) , \( 5562481 a^{2} - 2944283 a - 23635709\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(37178a^{2}-19692a-157999\right){x}+5562481a^{2}-2944283a-23635709$
16.2-a2 16.2-a 3.3.316.1 \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $23.39817653$ 1.316250266 \( 103101005876 a^{2} - 290083733531 a + 113696309796 \) \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -6407 a^{2} + 3208 a + 26891\) , \( 17854891 a^{2} - 9448825 a - 75864197\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6407a^{2}+3208a+26891\right){x}+17854891a^{2}-9448825a-75864197$
16.2-a3 16.2-a 3.3.316.1 \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $23.39817653$ 1.316250266 \( -343127540 a^{2} + 181623451 a + 1457997356 \) \( \bigl[a\) , \( -a^{2} - a + 2\) , \( a^{2} - 2\) , \( 5718326614 a^{2} - 3026804944 a - 24297973164\) , \( 344200023976745 a^{2} - 182190779570766 a - 1462554275103174\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(5718326614a^{2}-3026804944a-24297973164\right){x}+344200023976745a^{2}-182190779570766a-1462554275103174$
16.2-a4 16.2-a 3.3.316.1 \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $93.59270615$ 1.316250266 \( -97 a^{2} - 314 a + 1270 \) \( \bigl[a\) , \( -a^{2} - a + 2\) , \( a\) , \( -710 a^{2} + 377 a + 3018\) , \( -11698 a^{2} + 6191 a + 49704\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(-710a^{2}+377a+3018\right){x}-11698a^{2}+6191a+49704$
16.2-a5 16.2-a 3.3.316.1 \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $46.79635307$ 1.316250266 \( -2320978186626 a^{2} + 1226457049213 a + 9867024470514 \) \( \bigl[a\) , \( -a^{2} + a + 3\) , \( a^{2} + a - 2\) , \( 108 a^{2} - 82 a - 507\) , \( -1006 a^{2} + 425 a + 4083\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(108a^{2}-82a-507\right){x}-1006a^{2}+425a+4083$
16.2-a6 16.2-a 3.3.316.1 \( 2^{4} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $93.59270615$ 1.316250266 \( 155385857 a^{2} + 210010108 a - 130120956 \) \( \bigl[a\) , \( -a^{2} + a + 3\) , \( a^{2} + a - 2\) , \( -7 a^{2} - 22 a - 17\) , \( -65 a^{2} - 71 a + 85\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-7a^{2}-22a-17\right){x}-65a^{2}-71a+85$
16.2-a7 16.2-a 3.3.316.1 \( 2^{4} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $187.1854123$ 1.316250266 \( 4165 a^{2} + 5890 a - 1058 \) \( \bigl[a\) , \( -a^{2} + a + 3\) , \( a^{2} + a - 2\) , \( -2 a^{2} - 2 a + 3\) , \( -2 a^{2} - 3 a + 1\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-2a^{2}-2a+3\right){x}-2a^{2}-3a+1$
16.2-a8 16.2-a 3.3.316.1 \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $11.69908826$ 1.316250266 \( 189657446701367682 a^{2} + 254695362995847043 a - 161898141766190114 \) \( \bigl[a\) , \( -a^{2} + a + 3\) , \( a^{2} + a - 2\) , \( -202 a^{2} - 282 a + 153\) , \( -3296 a^{2} - 4399 a + 2863\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-202a^{2}-282a+153\right){x}-3296a^{2}-4399a+2863$
16.4-a1 16.4-a 3.3.316.1 \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $14.52078800$ 1.633716289 \( \frac{118715864416425}{2} a^{2} + \frac{159426274721303}{2} a - 50669979335827 \) \( \bigl[a^{2} - 3\) , \( 1\) , \( a + 1\) , \( 623 a^{2} - 449 a - 2863\) , \( 14329 a^{2} - 8700 a - 62909\bigr] \) ${y}^2+\left(a^{2}-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(623a^{2}-449a-2863\right){x}+14329a^{2}-8700a-62909$
16.4-a2 16.4-a 3.3.316.1 \( 2^{4} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $116.1663040$ 1.633716289 \( 2838366 a^{2} + \frac{6985779}{2} a - \frac{4542013}{2} \) \( \bigl[a^{2} - 3\) , \( 1\) , \( a + 1\) , \( 68 a^{2} - 44 a - 303\) , \( -73 a^{2} + 16 a + 269\bigr] \) ${y}^2+\left(a^{2}-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(68a^{2}-44a-303\right){x}-73a^{2}+16a+269$
16.4-a3 16.4-a 3.3.316.1 \( 2^{4} \) $0$ $\Z/4\Z$ $1$ $58.08315201$ 1.633716289 \( -\frac{3655}{4} a^{2} - \frac{775}{2} a + \frac{7961}{4} \) \( \bigl[a + 1\) , \( a^{2} + a - 2\) , \( 0\) , \( a^{2} + 4 a + 4\) , \( 0\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(a^{2}+4a+4\right){x}$
16.4-a4 16.4-a 3.3.316.1 \( 2^{4} \) $0$ $\Z/4\Z$ $1$ $232.3326080$ 1.633716289 \( \frac{112062878879}{2} a^{2} - \frac{315301616071}{2} a + 61790982411 \) \( \bigl[a + 1\) , \( -a^{2} + a + 4\) , \( 0\) , \( 11635 a^{2} - 6160 a - 49441\) , \( -979527 a^{2} + 518475 a + 4162139\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(11635a^{2}-6160a-49441\right){x}-979527a^{2}+518475a+4162139$
16.5-a1 16.5-a 3.3.316.1 \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $152.8488957$ 2.149605541 \( 510768 a^{2} - 1452320 a + 597920 \) \( \bigl[a^{2} + a - 2\) , \( a^{2} - a - 3\) , \( a + 1\) , \( 29 a^{2} - 12 a - 116\) , \( -136 a^{2} + 77 a + 587\bigr] \) ${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(29a^{2}-12a-116\right){x}-136a^{2}+77a+587$
16.5-a2 16.5-a 3.3.316.1 \( 2^{4} \) $0$ $\Z/2\Z$ $1$ $152.8488957$ 2.149605541 \( 342336 a^{2} + 460416 a - 292544 \) \( \bigl[a^{2} + a - 2\) , \( -a + 1\) , \( a + 1\) , \( -2775 a^{2} + 1470 a + 11796\) , \( -1678490 a^{2} + 888455 a + 7132145\bigr] \) ${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2775a^{2}+1470a+11796\right){x}-1678490a^{2}+888455a+7132145$
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  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.