Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
2.1-a1 |
2.1-a |
$8$ |
$20$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{22} \) |
$4.43717$ |
$(2,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$16$ |
\( 2 \cdot 5 \) |
$1$ |
$2.495277891$ |
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 |
$8$ |
$20$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{32} \) |
$4.43717$ |
$(2,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B |
$4$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$19.96222313$ |
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 |
$8$ |
$20$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{14} \) |
$4.43717$ |
$(2,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$16$ |
\( 2 \) |
$1$ |
$12.47638945$ |
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 |
$8$ |
$20$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{16} \) |
$4.43717$ |
$(2,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B |
$4$ |
\( 2^{2} \) |
$1$ |
$99.81111565$ |
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 |
$8$ |
$20$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{10} \) |
$4.43717$ |
$(2,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$4$ |
\( 2 \cdot 5 \) |
$1$ |
$39.92444626$ |
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 |
$8$ |
$20$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{2} \) |
$4.43717$ |
$(2,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$4$ |
\( 2 \) |
$1$ |
$199.6222313$ |
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 |
$8$ |
$20$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{40} \) |
$4.43717$ |
$(2,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$9.981111565$ |
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 |
$8$ |
$20$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{8} \) |
$4.43717$ |
$(2,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$1$ |
$49.90555782$ |
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 |
$8$ |
$20$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{2} \) |
$4.43717$ |
$(2,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \) |
$0.255681703$ |
$199.6222313$ |
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 |
$8$ |
$20$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{10} \) |
$4.43717$ |
$(2,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \) |
$1.278408518$ |
$39.92444626$ |
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 |
$8$ |
$20$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{22} \) |
$4.43717$ |
$(2,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$4$ |
\( 2 \) |
$5.113634072$ |
$2.495277891$ |
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 |
$8$ |
$20$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{32} \) |
$4.43717$ |
$(2,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B |
$4$ |
\( 2 \) |
$2.556817036$ |
$19.96222313$ |
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 |
$8$ |
$20$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{14} \) |
$4.43717$ |
$(2,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$4$ |
\( 2 \) |
$1.022726814$ |
$12.47638945$ |
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 |
$8$ |
$20$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{16} \) |
$4.43717$ |
$(2,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B |
$4$ |
\( 2 \) |
$0.511363407$ |
$99.81111565$ |
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 |
$8$ |
$20$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{8} \) |
$4.43717$ |
$(2,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \) |
$1.022726814$ |
$49.90555782$ |
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 |
$8$ |
$20$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{40} \) |
$4.43717$ |
$(2,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \) |
$5.113634072$ |
$9.981111565$ |
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 |
$6$ |
$8$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{2} \cdot 5^{16} \) |
$5.80231$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$5.510505719$ |
$1.909854987$ |
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 |
$6$ |
$8$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{4} \cdot 5^{8} \) |
$5.80231$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$2.755252859$ |
$15.27883989$ |
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 |
$6$ |
$8$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{8} \cdot 5^{4} \) |
$5.80231$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.377626429$ |
$122.2307191$ |
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 |
$6$ |
$8$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{2} \cdot 5^{4} \) |
$5.80231$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$5.510505719$ |
$1.909854987$ |
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 |
$6$ |
$8$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{28} \cdot 5^{2} \) |
$5.80231$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.688813214$ |
$244.4614383$ |
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 |
$6$ |
$8$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{28} \cdot 5^{2} \) |
$5.80231$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$2.755252859$ |
$61.11535959$ |
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 |
$6$ |
$8$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{28} \cdot 5^{2} \) |
$5.80231$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.542246724$ |
$61.11535959$ |
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 |
$6$ |
$8$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{28} \cdot 5^{2} \) |
$5.80231$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.135561681$ |
$244.4614383$ |
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 |
$6$ |
$8$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{8} \cdot 5^{4} \) |
$5.80231$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$0.271123362$ |
$122.2307191$ |
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 |
$6$ |
$8$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{2} \cdot 5^{16} \) |
$5.80231$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1.084493449$ |
$1.909854987$ |
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 |
$6$ |
$8$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{4} \cdot 5^{8} \) |
$5.80231$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$0.542246724$ |
$15.27883989$ |
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 |
$6$ |
$8$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{2} \cdot 5^{4} \) |
$5.80231$ |
$(2,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1.084493449$ |
$1.909854987$ |
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 |
$6$ |
$8$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
11.1 |
\( 11 \) |
\( 2^{12} \cdot 11^{2} \) |
$5.89521$ |
$(11,a-4)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$88.49109675$ |
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 |
$6$ |
$8$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
11.1 |
\( 11 \) |
\( - 5^{24} \cdot 11^{2} \) |
$5.89521$ |
$(11,a-4)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$353.9643870$ |
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 |
$6$ |
$8$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{16} \) |
$5.89521$ |
$(11,a-4)$ |
$0 \le r \le 2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 2^{4} \) |
$1$ |
$2.765346773$ |
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 |
$6$ |
$8$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
11.1 |
\( 11 \) |
\( 11^{4} \) |
$5.89521$ |
$(11,a-4)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$176.9821935$ |
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 |
$6$ |
$8$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
11.1 |
\( 11 \) |
\( 11^{8} \) |
$5.89521$ |
$(11,a-4)$ |
$0 \le r \le 2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{3} \) |
$1$ |
$22.12277418$ |
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 |
$6$ |
$8$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
11.1 |
\( 11 \) |
\( 11^{4} \) |
$5.89521$ |
$(11,a-4)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 2^{2} \) |
$1$ |
$2.765346773$ |
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 |
$6$ |
$8$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
11.1 |
\( 11 \) |
\( 2^{12} \cdot 11^{2} \) |
$5.89521$ |
$(11,a-4)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.541909224$ |
$88.49109675$ |
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 |
$6$ |
$8$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{16} \) |
$5.89521$ |
$(11,a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$3.083818448$ |
$2.765346773$ |
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 |
$6$ |
$8$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
11.1 |
\( 11 \) |
\( 11^{4} \) |
$5.89521$ |
$(11,a-4)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$0.770954612$ |
$176.9821935$ |
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 |
$6$ |
$8$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
11.1 |
\( 11 \) |
\( 11^{8} \) |
$5.89521$ |
$(11,a-4)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1.541909224$ |
$22.12277418$ |
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 |
$6$ |
$8$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
11.1 |
\( 11 \) |
\( 11^{4} \) |
$5.89521$ |
$(11,a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$3.083818448$ |
$2.765346773$ |
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 |
$6$ |
$8$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
11.1 |
\( 11 \) |
\( - 5^{24} \cdot 11^{2} \) |
$5.89521$ |
$(11,a-4)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.541909224$ |
$353.9643870$ |
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 |
$8$ |
$20$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{20} \) |
$6.27510$ |
$(2,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$4$ |
\( 2^{2} \) |
$1$ |
$33.72247828$ |
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 |
$8$ |
$20$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{52} \) |
$6.27510$ |
$(2,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$100$ |
\( 2^{2} \) |
$1$ |
$1.348899131$ |
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 |
$8$ |
$20$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{26} \) |
$6.27510$ |
$(2,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$4$ |
\( 2^{2} \) |
$1$ |
$33.72247828$ |
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 |
$8$ |
$20$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{14} \) |
$6.27510$ |
$(2,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$4$ |
\( 2 \) |
$1$ |
$269.7798262$ |
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 |
$8$ |
$20$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{28} \) |
$6.27510$ |
$(2,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2Cs, 5B |
$4$ |
\( 2^{2} \) |
$1$ |
$134.8899131$ |
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 |
$8$ |
$20$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{34} \) |
$6.27510$ |
$(2,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$100$ |
\( 2^{2} \) |
$1$ |
$1.348899131$ |
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 |
$8$ |
$20$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{44} \) |
$6.27510$ |
$(2,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2Cs, 5B |
$100$ |
\( 2^{2} \) |
$1$ |
$5.395596525$ |
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 |
$8$ |
$20$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{22} \) |
$6.27510$ |
$(2,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$100$ |
\( 2 \) |
$1$ |
$10.79119305$ |
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 |
$8$ |
$20$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{34} \) |
$6.27510$ |
$(2,a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$16.20666373$ |
$1.348899131$ |
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 |
$8$ |
$20$ |
3.3.1957.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{44} \) |
$6.27510$ |
$(2,a)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{2} \) |
$16.20666373$ |
$5.395596525$ |
4.447543380 |
\( \frac{1208201331713038647}{1048576} a^{2} - \frac{4882016462354803125}{1048576} a + \frac{3972767044836889003}{1048576} \) |
\( \bigl[a^{2} - 6\) , \( a^{2} + a - 6\) , \( 0\) , \( -17202 a^{2} + 95091 a - 131023\) , \( -6354008 a^{2} + 27777935 a - 27013555\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}={x}^{3}+\left(a^{2}+a-6\right){x}^{2}+\left(-17202a^{2}+95091a-131023\right){x}-6354008a^{2}+27777935a-27013555$ |
*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.