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Label Class Base field Conductor norm Rank Torsion CM Sato-Tate Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
2.1-a1 2.1-a 3.3.1957.1 \( 2 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.495277891$ 2.256230663 \( \frac{33745986016713176920902011495}{1024} a^{2} - \frac{136366334712767942392742270533}{1024} a + \frac{110971321644318487687509098267}{1024} \) \( \bigl[a^{2} + a - 6\) , \( a^{2} - a - 6\) , \( 0\) , \( -6506 a^{2} + 26575 a - 22213\) , \( -1035967 a^{2} + 4186759 a - 3408020\bigr] \) ${y}^2+\left(a^{2}+a-6\right){x}{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-6506a^{2}+26575a-22213\right){x}-1035967a^{2}+4186759a-3408020$
2.1-a2 2.1-a 3.3.1957.1 \( 2 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $19.96222313$ 2.256230663 \( \frac{1208201331713038647}{1048576} a^{2} - \frac{4882016462354803125}{1048576} a + \frac{3972767044836889003}{1048576} \) \( \bigl[a^{2} + a - 6\) , \( a^{2} - a - 6\) , \( 0\) , \( -371 a^{2} + 1665 a - 1693\) , \( -17120 a^{2} + 67995 a - 52840\bigr] \) ${y}^2+\left(a^{2}+a-6\right){x}{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-371a^{2}+1665a-1693\right){x}-17120a^{2}+67995a-52840$
2.1-a3 2.1-a 3.3.1957.1 \( 2 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $12.47638945$ 2.256230663 \( -\frac{303439985770557}{4} a^{2} - \frac{39283729367165}{4} a + \frac{2686590421306587}{4} \) \( \bigl[a^{2} + a - 6\) , \( a^{2} - a - 6\) , \( 0\) , \( 44 a^{2} + 50 a - 503\) , \( 271 a^{2} + 400 a - 3450\bigr] \) ${y}^2+\left(a^{2}+a-6\right){x}{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(44a^{2}+50a-503\right){x}+271a^{2}+400a-3450$
2.1-a4 2.1-a 3.3.1957.1 \( 2 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $99.81111565$ 2.256230663 \( -\frac{51088425}{16} a^{2} - \frac{6564357}{16} a + \frac{452504203}{16} \) \( \bigl[a^{2} + a - 6\) , \( a^{2} - a - 6\) , \( 0\) , \( 4 a^{2} + 5 a - 33\) , \( 3 a^{2} + 9 a - 40\bigr] \) ${y}^2+\left(a^{2}+a-6\right){x}{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(4a^{2}+5a-33\right){x}+3a^{2}+9a-40$
2.1-a5 2.1-a 3.3.1957.1 \( 2 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $39.92444626$ 2.256230663 \( \frac{22236981725625867673}{1024} a^{2} + \frac{42506064262246252101}{1024} a - \frac{76376288557509693211}{1024} \) \( \bigl[1\) , \( -a^{2} + a + 5\) , \( 1\) , \( -26 a^{2} + 100 a - 77\) , \( -198 a^{2} + 767 a - 549\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(-26a^{2}+100a-77\right){x}-198a^{2}+767a-549$
2.1-a6 2.1-a 3.3.1957.1 \( 2 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $199.6222313$ 2.256230663 \( \frac{58829}{4} a^{2} - \frac{219883}{4} a + \frac{156629}{4} \) \( \bigl[1\) , \( -a^{2} + a + 5\) , \( 1\) , \( -a^{2} + 8\) , \( 2 a^{2} - 9 a + 9\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(-a^{2}+8\right){x}+2a^{2}-9a+9$
2.1-a7 2.1-a 3.3.1957.1 \( 2 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $9.981111565$ 2.256230663 \( -\frac{1844128704001587604521}{1099511627776} a^{2} - \frac{237751339073011253141}{1099511627776} a + \frac{16324643986414033240011}{1099511627776} \) \( \bigl[a + 1\) , \( a^{2} + a - 7\) , \( a^{2} + a - 5\) , \( 1076 a^{2} + 142 a - 9533\) , \( -38349 a^{2} - 4961 a + 339519\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(a^{2}+a-7\right){x}^{2}+\left(1076a^{2}+142a-9533\right){x}-38349a^{2}-4961a+339519$
2.1-a8 2.1-a 3.3.1957.1 \( 2 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $49.90555782$ 2.256230663 \( \frac{9117637591}{256} a^{2} + \frac{17428636011}{256} a - \frac{31314734389}{256} \) \( \bigl[a + 1\) , \( a^{2} + a - 7\) , \( a^{2} + a - 5\) , \( 6 a^{2} + 2 a - 48\) , \( 7 a^{2} + 2 a - 59\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+\left(a^{2}+a-7\right){x}^{2}+\left(6a^{2}+2a-48\right){x}+7a^{2}+2a-59$
2.1-b1 2.1-b 3.3.1957.1 \( 2 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.255681703$ $199.6222313$ 1.730630699 \( \frac{58829}{4} a^{2} - \frac{219883}{4} a + \frac{156629}{4} \) \( \bigl[a^{2} - 5\) , \( a^{2} + a - 5\) , \( a\) , \( -4 a^{2} + 19 a - 14\) , \( 12 a^{2} - 51 a + 42\bigr] \) ${y}^2+\left(a^{2}-5\right){x}{y}+a{y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(-4a^{2}+19a-14\right){x}+12a^{2}-51a+42$
2.1-b2 2.1-b 3.3.1957.1 \( 2 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.278408518$ $39.92444626$ 1.730630699 \( \frac{22236981725625867673}{1024} a^{2} + \frac{42506064262246252101}{1024} a - \frac{76376288557509693211}{1024} \) \( \bigl[a^{2} - 5\) , \( a^{2} + a - 5\) , \( a\) , \( -1114 a^{2} - 1016 a + 2571\) , \( 27300 a^{2} + 83651 a - 129307\bigr] \) ${y}^2+\left(a^{2}-5\right){x}{y}+a{y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(-1114a^{2}-1016a+2571\right){x}+27300a^{2}+83651a-129307$
2.1-b3 2.1-b 3.3.1957.1 \( 2 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $5.113634072$ $2.495277891$ 1.730630699 \( \frac{33745986016713176920902011495}{1024} a^{2} - \frac{136366334712767942392742270533}{1024} a + \frac{110971321644318487687509098267}{1024} \) \( \bigl[a\) , \( 1\) , \( a^{2} + a - 6\) , \( -48957 a^{2} + 192360 a - 154807\) , \( -20208669 a^{2} + 81872981 a - 66692514\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+{x}^{2}+\left(-48957a^{2}+192360a-154807\right){x}-20208669a^{2}+81872981a-66692514$
2.1-b4 2.1-b 3.3.1957.1 \( 2 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $2.556817036$ $19.96222313$ 1.730630699 \( \frac{1208201331713038647}{1048576} a^{2} - \frac{4882016462354803125}{1048576} a + \frac{3972767044836889003}{1048576} \) \( \bigl[a\) , \( 1\) , \( a^{2} + a - 6\) , \( -3932 a^{2} + 10355 a - 6677\) , \( -284267 a^{2} + 1354261 a - 1166954\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+{x}^{2}+\left(-3932a^{2}+10355a-6677\right){x}-284267a^{2}+1354261a-1166954$
2.1-b5 2.1-b 3.3.1957.1 \( 2 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.022726814$ $12.47638945$ 1.730630699 \( -\frac{303439985770557}{4} a^{2} - \frac{39283729367165}{4} a + \frac{2686590421306587}{4} \) \( \bigl[a\) , \( 1\) , \( a^{2} + a - 6\) , \( -72 a^{2} + 320 a - 267\) , \( -1499 a^{2} + 5315 a - 4094\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+{x}^{2}+\left(-72a^{2}+320a-267\right){x}-1499a^{2}+5315a-4094$
2.1-b6 2.1-b 3.3.1957.1 \( 2 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.511363407$ $99.81111565$ 1.730630699 \( -\frac{51088425}{16} a^{2} - \frac{6564357}{16} a + \frac{452504203}{16} \) \( \bigl[a\) , \( 1\) , \( a^{2} + a - 6\) , \( -17 a^{2} + 10 a + 13\) , \( -49 a^{2} - 59 a + 126\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+{x}^{2}+\left(-17a^{2}+10a+13\right){x}-49a^{2}-59a+126$
2.1-b7 2.1-b 3.3.1957.1 \( 2 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.022726814$ $49.90555782$ 1.730630699 \( \frac{9117637591}{256} a^{2} + \frac{17428636011}{256} a - \frac{31314734389}{256} \) \( \bigl[1\) , \( -a^{2} + a + 7\) , \( a\) , \( -212 a^{2} - 404 a + 743\) , \( -3941 a^{2} - 7528 a + 13543\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+7\right){x}^{2}+\left(-212a^{2}-404a+743\right){x}-3941a^{2}-7528a+13543$
2.1-b8 2.1-b 3.3.1957.1 \( 2 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $5.113634072$ $9.981111565$ 1.730630699 \( -\frac{1844128704001587604521}{1099511627776} a^{2} - \frac{237751339073011253141}{1099511627776} a + \frac{16324643986414033240011}{1099511627776} \) \( \bigl[1\) , \( -a^{2} + a + 7\) , \( a\) , \( -1367 a^{2} - 2584 a + 4678\) , \( 59691 a^{2} + 114172 a - 205088\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+7\right){x}^{2}+\left(-1367a^{2}-2584a+4678\right){x}+59691a^{2}+114172a-205088$
10.1-a1 10.1-a 3.3.1957.1 \( 2 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $5.510505719$ $1.909854987$ 5.709626238 \( -\frac{2981793872800340768201}{610351562500} a^{2} - \frac{386027265671168228289}{610351562500} a + \frac{26400141019045592285199}{610351562500} \) \( \bigl[a^{2} - 5\) , \( -a - 1\) , \( 1\) , \( 140 a^{2} - 9 a - 1310\) , \( 2000 a^{2} + 127 a - 18099\bigr] \) ${y}^2+\left(a^{2}-5\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(140a^{2}-9a-1310\right){x}+2000a^{2}+127a-18099$
10.1-a2 10.1-a 3.3.1957.1 \( 2 \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $2.755252859$ $15.27883989$ 5.709626238 \( \frac{15046168718351}{6250000} a^{2} + \frac{27908855989139}{6250000} a - \frac{49520546907549}{6250000} \) \( \bigl[a^{2} - 5\) , \( -a - 1\) , \( 1\) , \( -5 a^{2} - 29 a - 30\) , \( -30 a^{2} - 123 a - 87\bigr] \) ${y}^2+\left(a^{2}-5\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-5a^{2}-29a-30\right){x}-30a^{2}-123a-87$
10.1-a3 10.1-a 3.3.1957.1 \( 2 \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1.377626429$ $122.2307191$ 5.709626238 \( \frac{62236119}{160000} a^{2} + \frac{114531691}{160000} a + \frac{72099019}{160000} \) \( \bigl[a^{2} - 5\) , \( -a - 1\) , \( 1\) , \( -4 a\) , \( -3 a + 1\bigr] \) ${y}^2+\left(a^{2}-5\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}-4a{x}-3a+1$
10.1-a4 10.1-a 3.3.1957.1 \( 2 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $5.510505719$ $1.909854987$ 5.709626238 \( \frac{153118770135195129}{2500} a^{2} + \frac{292341679554580081}{2500} a - \frac{525519586917853471}{2500} \) \( \bigl[a^{2} - 5\) , \( -a - 1\) , \( 1\) , \( -230 a^{2} - 449 a + 770\) , \( -4360 a^{2} - 8453 a + 14613\bigr] \) ${y}^2+\left(a^{2}-5\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-230a^{2}-449a+770\right){x}-4360a^{2}-8453a+14613$
10.1-a5 10.1-a 3.3.1957.1 \( 2 \cdot 5 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.688813214$ $244.4614383$ 5.709626238 \( \frac{2217577}{400} a^{2} - \frac{6813147}{400} a + \frac{5546677}{400} \) \( \bigl[a^{2} + a - 5\) , \( 1\) , \( a^{2} + a - 5\) , \( -6 a^{2} - 5 a + 40\) , \( -6 a^{2} - 4 a + 43\bigr] \) ${y}^2+\left(a^{2}+a-5\right){x}{y}+\left(a^{2}+a-5\right){y}={x}^{3}+{x}^{2}+\left(-6a^{2}-5a+40\right){x}-6a^{2}-4a+43$
10.1-a6 10.1-a 3.3.1957.1 \( 2 \cdot 5 \) $1$ $\Z/8\Z$ $\mathrm{SU}(2)$ $2.755252859$ $61.11535959$ 5.709626238 \( -\frac{96448750817}{1638400} a^{2} - \frac{12818175213}{1638400} a + \frac{855539380083}{1638400} \) \( \bigl[a\) , \( -a^{2} + a + 5\) , \( a^{2} + a - 6\) , \( 11 a^{2} + 2 a - 87\) , \( -25 a^{2} - 12 a + 190\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(11a^{2}+2a-87\right){x}-25a^{2}-12a+190$
10.1-b1 10.1-b 3.3.1957.1 \( 2 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.542246724$ $61.11535959$ 2.247362609 \( -\frac{96448750817}{1638400} a^{2} - \frac{12818175213}{1638400} a + \frac{855539380083}{1638400} \) \( \bigl[a^{2} + a - 6\) , \( a^{2} - a - 7\) , \( a\) , \( 233 a^{2} + 439 a - 810\) , \( -7674 a^{2} - 14653 a + 26409\bigr] \) ${y}^2+\left(a^{2}+a-6\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-7\right){x}^{2}+\left(233a^{2}+439a-810\right){x}-7674a^{2}-14653a+26409$
10.1-b2 10.1-b 3.3.1957.1 \( 2 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.135561681$ $244.4614383$ 2.247362609 \( \frac{2217577}{400} a^{2} - \frac{6813147}{400} a + \frac{5546677}{400} \) \( \bigl[a^{2} + a - 5\) , \( -a^{2} + 7\) , \( 0\) , \( -565 a^{2} - 1074 a + 1960\) , \( 13804 a^{2} + 26395 a - 47386\bigr] \) ${y}^2+\left(a^{2}+a-5\right){x}{y}={x}^{3}+\left(-a^{2}+7\right){x}^{2}+\left(-565a^{2}-1074a+1960\right){x}+13804a^{2}+26395a-47386$
10.1-b3 10.1-b 3.3.1957.1 \( 2 \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.271123362$ $122.2307191$ 2.247362609 \( \frac{62236119}{160000} a^{2} + \frac{114531691}{160000} a + \frac{72099019}{160000} \) \( \bigl[1\) , \( -a^{2} + a + 7\) , \( a\) , \( -124 a^{2} - 236 a + 439\) , \( -1495 a^{2} - 2854 a + 5139\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+7\right){x}^{2}+\left(-124a^{2}-236a+439\right){x}-1495a^{2}-2854a+5139$
10.1-b4 10.1-b 3.3.1957.1 \( 2 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.084493449$ $1.909854987$ 2.247362609 \( -\frac{2981793872800340768201}{610351562500} a^{2} - \frac{386027265671168228289}{610351562500} a + \frac{26400141019045592285199}{610351562500} \) \( \bigl[1\) , \( -a^{2} + a + 7\) , \( a\) , \( -1739 a^{2} - 3401 a + 5749\) , \( -112010 a^{2} - 214834 a + 382499\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+7\right){x}^{2}+\left(-1739a^{2}-3401a+5749\right){x}-112010a^{2}-214834a+382499$
10.1-b5 10.1-b 3.3.1957.1 \( 2 \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.542246724$ $15.27883989$ 2.247362609 \( \frac{15046168718351}{6250000} a^{2} + \frac{27908855989139}{6250000} a - \frac{49520546907549}{6250000} \) \( \bigl[1\) , \( -a^{2} + a + 7\) , \( a\) , \( -1869 a^{2} - 3576 a + 6419\) , \( -102403 a^{2} - 195759 a + 351665\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+7\right){x}^{2}+\left(-1869a^{2}-3576a+6419\right){x}-102403a^{2}-195759a+351665$
10.1-b6 10.1-b 3.3.1957.1 \( 2 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.084493449$ $1.909854987$ 2.247362609 \( \frac{153118770135195129}{2500} a^{2} + \frac{292341679554580081}{2500} a - \frac{525519586917853471}{2500} \) \( \bigl[1\) , \( -a^{2} + a + 7\) , \( a\) , \( -29919 a^{2} - 57191 a + 102769\) , \( -6504088 a^{2} - 12432604 a + 22339215\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+7\right){x}^{2}+\left(-29919a^{2}-57191a+102769\right){x}-6504088a^{2}-12432604a+22339215$
11.1-a1 11.1-a 3.3.1957.1 \( 11 \) $0 \le r \le 2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $88.49109675$ 4.000683182 \( -\frac{94367604927778}{121} a^{2} - \frac{12216950994706}{121} a + \frac{835509871243821}{121} \) \( \bigl[a^{2} + a - 6\) , \( a^{2} - 7\) , \( a^{2} + a - 6\) , \( 51895 a^{2} + 99196 a - 178244\) , \( 33758168 a^{2} + 64528849 a - 115947554\bigr] \) ${y}^2+\left(a^{2}+a-6\right){x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(a^{2}-7\right){x}^{2}+\left(51895a^{2}+99196a-178244\right){x}+33758168a^{2}+64528849a-115947554$
11.1-a2 11.1-a 3.3.1957.1 \( 11 \) $0 \le r \le 2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $353.9643870$ 4.000683182 \( \frac{464727434}{121} a^{2} + \frac{888207074}{121} a - \frac{1596152309}{121} \) \( \bigl[1\) , \( -a^{2} + a + 6\) , \( a + 1\) , \( -185636 a^{2} - 354832 a + 637593\) , \( 100217800 a^{2} + 191566613 a - 344213187\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(-185636a^{2}-354832a+637593\right){x}+100217800a^{2}+191566613a-344213187$
11.1-a3 11.1-a 3.3.1957.1 \( 11 \) $0 \le r \le 2$ $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $2.765346773$ 4.000683182 \( -\frac{52028892561854339324}{45949729863572161} a^{2} + \frac{184047527372651237376}{45949729863572161} a - \frac{86097660316480487429}{45949729863572161} \) \( \bigl[1\) , \( -a^{2} - a + 7\) , \( a^{2} - 6\) , \( 182617 a^{2} + 349076 a - 627219\) , \( -278846719 a^{2} - 533016427 a + 957741374\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(-a^{2}-a+7\right){x}^{2}+\left(182617a^{2}+349076a-627219\right){x}-278846719a^{2}-533016427a+957741374$
11.1-a4 11.1-a 3.3.1957.1 \( 11 \) $0 \le r \le 2$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $176.9821935$ 4.000683182 \( -\frac{4719104528}{14641} a^{2} - \frac{657318240}{14641} a + \frac{42021732273}{14641} \) \( \bigl[1\) , \( -a^{2} - a + 7\) , \( a^{2} - 6\) , \( -32083 a^{2} - 61324 a + 110201\) , \( 6318353 a^{2} + 12077553 a - 21701344\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(-a^{2}-a+7\right){x}^{2}+\left(-32083a^{2}-61324a+110201\right){x}+6318353a^{2}+12077553a-21701344$
11.1-a5 11.1-a 3.3.1957.1 \( 11 \) $0 \le r \le 2$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $22.12277418$ 4.000683182 \( \frac{5510373784198200}{214358881} a^{2} - \frac{22266438999717392}{214358881} a + \frac{18120112986554473}{214358881} \) \( \bigl[1\) , \( -a^{2} - a + 7\) , \( a^{2} - 6\) , \( -134683 a^{2} - 257444 a + 462596\) , \( -55487530 a^{2} - 106064597 a + 190580341\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(-a^{2}-a+7\right){x}^{2}+\left(-134683a^{2}-257444a+462596\right){x}-55487530a^{2}-106064597a+190580341$
11.1-a6 11.1-a 3.3.1957.1 \( 11 \) $0 \le r \le 2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.765346773$ 4.000683182 \( \frac{240164514761676644156}{14641} a^{2} - \frac{970496300545716785152}{14641} a + \frac{789764257620111667461}{14641} \) \( \bigl[1\) , \( -a^{2} - a + 7\) , \( a^{2} - 6\) , \( -2093583 a^{2} - 4001884 a + 7190731\) , \( -3794498373 a^{2} - 7253196207 a + 13032780528\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(-a^{2}-a+7\right){x}^{2}+\left(-2093583a^{2}-4001884a+7190731\right){x}-3794498373a^{2}-7253196207a+13032780528$
11.1-b1 11.1-b 3.3.1957.1 \( 11 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $1.541909224$ $88.49109675$ 1.156629431 \( -\frac{94367604927778}{121} a^{2} - \frac{12216950994706}{121} a + \frac{835509871243821}{121} \) \( \bigl[a^{2} - 6\) , \( a^{2} - 7\) , \( 0\) , \( 6626091 a^{2} + 12665793 a - 22758313\) , \( 48496352729 a^{2} + 92700938961 a - 166568083554\bigr] \) ${y}^2+\left(a^{2}-6\right){x}{y}={x}^{3}+\left(a^{2}-7\right){x}^{2}+\left(6626091a^{2}+12665793a-22758313\right){x}+48496352729a^{2}+92700938961a-166568083554$
11.1-b2 11.1-b 3.3.1957.1 \( 11 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $3.083818448$ $2.765346773$ 1.156629431 \( -\frac{52028892561854339324}{45949729863572161} a^{2} + \frac{184047527372651237376}{45949729863572161} a - \frac{86097660316480487429}{45949729863572161} \) \( \bigl[a + 1\) , \( a^{2} - 6\) , \( a\) , \( 23317913 a^{2} + 44572268 a - 80088908\) , \( -401919492463 a^{2} - 768270441835 a + 1380453494659\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(23317913a^{2}+44572268a-80088908\right){x}-401919492463a^{2}-768270441835a+1380453494659$
11.1-b3 11.1-b 3.3.1957.1 \( 11 \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $0.770954612$ $176.9821935$ 1.156629431 \( -\frac{4719104528}{14641} a^{2} - \frac{657318240}{14641} a + \frac{42021732273}{14641} \) \( \bigl[a + 1\) , \( a^{2} - 6\) , \( a\) , \( -4096447 a^{2} - 7830372 a + 14069872\) , \( 9043930945 a^{2} + 17287503973 a - 31062753395\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(-4096447a^{2}-7830372a+14069872\right){x}+9043930945a^{2}+17287503973a-31062753395$
11.1-b4 11.1-b 3.3.1957.1 \( 11 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.541909224$ $22.12277418$ 1.156629431 \( \frac{5510373784198200}{214358881} a^{2} - \frac{22266438999717392}{214358881} a + \frac{18120112986554473}{214358881} \) \( \bigl[a + 1\) , \( a^{2} - 6\) , \( a\) , \( -17197107 a^{2} - 32872327 a + 59066077\) , \( -80363961659 a^{2} - 153615979044 a + 276022222850\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(-17197107a^{2}-32872327a+59066077\right){x}-80363961659a^{2}-153615979044a+276022222850$
11.1-b5 11.1-b 3.3.1957.1 \( 11 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $3.083818448$ $2.765346773$ 1.156629431 \( \frac{240164514761676644156}{14641} a^{2} - \frac{970496300545716785152}{14641} a + \frac{789764257620111667461}{14641} \) \( \bigl[a + 1\) , \( a^{2} - 6\) , \( a\) , \( -267322687 a^{2} - 510988202 a + 918160342\) , \( -5479592630311 a^{2} - 10474259472621 a + 18820492505781\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(-267322687a^{2}-510988202a+918160342\right){x}-5479592630311a^{2}-10474259472621a+18820492505781$
11.1-b6 11.1-b 3.3.1957.1 \( 11 \) $1$ $\Z/8\Z$ $\mathrm{SU}(2)$ $1.541909224$ $353.9643870$ 1.156629431 \( \frac{464727434}{121} a^{2} + \frac{888207074}{121} a - \frac{1596152309}{121} \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -23702853 a^{2} - 45308081 a + 81411046\) , \( 144598509236 a^{2} + 276400529615 a - 496645525138\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-23702853a^{2}-45308081a+81411046\right){x}+144598509236a^{2}+276400529615a-496645525138$
16.3-a1 16.3-a 3.3.1957.1 \( 2^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $33.72247828$ 3.049187018 \( \frac{9117637591}{256} a^{2} + \frac{17428636011}{256} a - \frac{31314734389}{256} \) \( \bigl[a^{2} + a - 6\) , \( a^{2} + a - 5\) , \( a^{2} + a - 6\) , \( -6098 a^{2} - 11658 a + 20940\) , \( -625490 a^{2} - 1195627 a + 2148338\bigr] \) ${y}^2+\left(a^{2}+a-6\right){x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(-6098a^{2}-11658a+20940\right){x}-625490a^{2}-1195627a+2148338$
16.3-a2 16.3-a 3.3.1957.1 \( 2^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.348899131$ 3.049187018 \( -\frac{1844128704001587604521}{1099511627776} a^{2} - \frac{237751339073011253141}{1099511627776} a + \frac{16324643986414033240011}{1099511627776} \) \( \bigl[a^{2} + a - 6\) , \( a^{2} + a - 5\) , \( a^{2} + a - 6\) , \( -39498 a^{2} - 75503 a + 135650\) , \( 9280450 a^{2} + 17739609 a - 31875126\bigr] \) ${y}^2+\left(a^{2}+a-6\right){x}{y}+\left(a^{2}+a-6\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(-39498a^{2}-75503a+135650\right){x}+9280450a^{2}+17739609a-31875126$
16.3-a3 16.3-a 3.3.1957.1 \( 2^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $33.72247828$ 3.049187018 \( -\frac{303439985770557}{4} a^{2} - \frac{39283729367165}{4} a + \frac{2686590421306587}{4} \) \( \bigl[a\) , \( -a^{2} + 7\) , \( a^{2} - 6\) , \( 156 a^{2} + 320 a - 546\) , \( -20350 a^{2} - 38830 a + 69819\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(-a^{2}+7\right){x}^{2}+\left(156a^{2}+320a-546\right){x}-20350a^{2}-38830a+69819$
16.3-a4 16.3-a 3.3.1957.1 \( 2^{4} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $269.7798262$ 3.049187018 \( \frac{58829}{4} a^{2} - \frac{219883}{4} a + \frac{156629}{4} \) \( \bigl[a\) , \( -a^{2} + 7\) , \( a^{2} - 6\) , \( -49 a^{2} - 90 a + 179\) , \( 284 a^{2} + 543 a - 973\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(-a^{2}+7\right){x}^{2}+\left(-49a^{2}-90a+179\right){x}+284a^{2}+543a-973$
16.3-a5 16.3-a 3.3.1957.1 \( 2^{4} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $134.8899131$ 3.049187018 \( -\frac{51088425}{16} a^{2} - \frac{6564357}{16} a + \frac{452504203}{16} \) \( \bigl[a\) , \( -a^{2} + 7\) , \( a^{2} - 6\) , \( -269 a^{2} - 510 a + 934\) , \( -5275 a^{2} - 10082 a + 18119\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(-a^{2}+7\right){x}^{2}+\left(-269a^{2}-510a+934\right){x}-5275a^{2}-10082a+18119$
16.3-a6 16.3-a 3.3.1957.1 \( 2^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.348899131$ 3.049187018 \( \frac{33745986016713176920902011495}{1024} a^{2} - \frac{136366334712767942392742270533}{1024} a + \frac{110971321644318487687509098267}{1024} \) \( \bigl[a\) , \( -a^{2} + 7\) , \( a^{2} - 6\) , \( -28729 a^{2} - 42720 a + 84914\) , \( 5497565 a^{2} + 11567208 a - 20077861\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(-a^{2}+7\right){x}^{2}+\left(-28729a^{2}-42720a+84914\right){x}+5497565a^{2}+11567208a-20077861$
16.3-a7 16.3-a 3.3.1957.1 \( 2^{4} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.395596525$ 3.049187018 \( \frac{1208201331713038647}{1048576} a^{2} - \frac{4882016462354803125}{1048576} a + \frac{3972767044836889003}{1048576} \) \( \bigl[a\) , \( -a^{2} + 7\) , \( a^{2} - 6\) , \( -27104 a^{2} - 51045 a + 92244\) , \( 5544986 a^{2} + 10615813 a - 19063791\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(-a^{2}+7\right){x}^{2}+\left(-27104a^{2}-51045a+92244\right){x}+5544986a^{2}+10615813a-19063791$
16.3-a8 16.3-a 3.3.1957.1 \( 2^{4} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $10.79119305$ 3.049187018 \( \frac{22236981725625867673}{1024} a^{2} + \frac{42506064262246252101}{1024} a - \frac{76376288557509693211}{1024} \) \( \bigl[a\) , \( -a^{2} + 7\) , \( a^{2} - 6\) , \( -26984 a^{2} - 51530 a + 92639\) , \( 5547729 a^{2} + 10604763 a - 19054809\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(-a^{2}+7\right){x}^{2}+\left(-26984a^{2}-51530a+92639\right){x}+5547729a^{2}+10604763a-19054809$
16.3-b1 16.3-b 3.3.1957.1 \( 2^{4} \) $2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $16.20666373$ $1.348899131$ 4.447543380 \( \frac{33745986016713176920902011495}{1024} a^{2} - \frac{136366334712767942392742270533}{1024} a + \frac{110971321644318487687509098267}{1024} \) \( \bigl[a^{2} - 6\) , \( a^{2} + a - 6\) , \( 0\) , \( -362722 a^{2} + 1510096 a - 1321893\) , \( -438171465 a^{2} + 1769281039 a - 1436953135\bigr] \) ${y}^2+\left(a^{2}-6\right){x}{y}={x}^{3}+\left(a^{2}+a-6\right){x}^{2}+\left(-362722a^{2}+1510096a-1321893\right){x}-438171465a^{2}+1769281039a-1436953135$
16.3-b2 16.3-b 3.3.1957.1 \( 2^{4} \) $2$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $16.20666373$ $5.395596525$ 4.447543380 \( \frac{1208201331713038647}{1048576} a^{2} - \frac{4882016462354803125}{1048576} a + \frac{3972767044836889003}{1048576} \) \( \bigl[a^{2} - 6\) , \( a^{2} + a - 6\) , \( 0\) , \( -17202 a^{2} + 95091 a - 131023\) , \( -6354008 a^{2} + 27777935 a - 27013555\bigr] \) ${y}^2+\left(a^{2}-6\right){x}{y}={x}^{3}+\left(a^{2}+a-6\right){x}^{2}+\left(-17202a^{2}+95091a-131023\right){x}-6354008a^{2}+27777935a-27013555$
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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.