| 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 |
| 88.4-a2 |
88.4-a |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
88.4 |
\( 2^{3} \cdot 11 \) |
\( 2^{13} \cdot 11^{6} \) |
$0.72412$ |
$(a), (-a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$1.676496384$ |
0.633656072 |
\( -\frac{2638880885903}{907039232} a - \frac{10019801056547}{453519616} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( 3 a - 31\) , \( -2 a + 74\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(3a-31\right){x}-2a+74$ |
| 1408.4-c2 |
1408.4-c |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1408.4 |
\( 2^{7} \cdot 11 \) |
\( 2^{19} \cdot 11^{6} \) |
$1.44823$ |
$(a), (-a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$0.059629436$ |
$1.185461961$ |
2.885513208 |
\( -\frac{2638880885903}{907039232} a - \frac{10019801056547}{453519616} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -34 a + 56\) , \( 68 a + 152\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-34a+56\right){x}+68a+152$ |
| 2816.10-b2 |
2816.10-b |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2816.10 |
\( 2^{8} \cdot 11 \) |
\( 2^{25} \cdot 11^{6} \) |
$1.72225$ |
$(a), (-a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.838248192$ |
1.900968216 |
\( -\frac{2638880885903}{907039232} a - \frac{10019801056547}{453519616} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -86 a + 15\) , \( 302 a - 324\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-86a+15\right){x}+302a-324$ |
| 2816.14-a2 |
2816.14-a |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2816.14 |
\( 2^{8} \cdot 11 \) |
\( 2^{31} \cdot 11^{6} \) |
$1.72225$ |
$(a), (-a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.592730980$ |
1.344187517 |
\( -\frac{2638880885903}{907039232} a - \frac{10019801056547}{453519616} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 159 a - 190\) , \( -1086 a + 557\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(159a-190\right){x}-1086a+557$ |
| 3872.6-a2 |
3872.6-a |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.6 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{13} \cdot 11^{12} \) |
$1.86497$ |
$(a), (-a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$2.731457337$ |
$0.505482678$ |
2.087428802 |
\( -\frac{2638880885903}{907039232} a - \frac{10019801056547}{453519616} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -243 a + 174\) , \( -970 a + 2531\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-243a+174\right){x}-970a+2531$ |
| 7128.4-a2 |
7128.4-a |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7128.4 |
\( 2^{3} \cdot 3^{4} \cdot 11 \) |
\( 2^{13} \cdot 3^{12} \cdot 11^{6} \) |
$2.17235$ |
$(a), (-a+1), (2a+1), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{4} \) |
$1$ |
$0.558832128$ |
3.801936433 |
\( -\frac{2638880885903}{907039232} a - \frac{10019801056547}{453519616} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 24 a - 276\) , \( 283 a - 1673\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(24a-276\right){x}+283a-1673$ |
| 7744.15-a2 |
7744.15-a |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7744.15 |
\( 2^{6} \cdot 11^{2} \) |
\( 2^{25} \cdot 11^{12} \) |
$2.21783$ |
$(a), (-a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.252741339$ |
1.146326966 |
\( -\frac{2638880885903}{907039232} a - \frac{10019801056547}{453519616} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 36 a + 1284\) , \( 14595 a - 8017\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(36a+1284\right){x}+14595a-8017$ |
| 11264.10-g2 |
11264.10-g |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
11264.10 |
\( 2^{10} \cdot 11 \) |
\( 2^{31} \cdot 11^{6} \) |
$2.43563$ |
$(a), (-a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1.136501097$ |
$0.592730980$ |
4.073788236 |
\( -\frac{2638880885903}{907039232} a - \frac{10019801056547}{453519616} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 102 a + 143\) , \( 725 a - 1599\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(102a+143\right){x}+725a-1599$ |
| 11264.14-h2 |
11264.14-h |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
11264.14 |
\( 2^{10} \cdot 11 \) |
\( 2^{31} \cdot 11^{6} \) |
$2.43563$ |
$(a), (-a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.592730980$ |
1.344187517 |
\( -\frac{2638880885903}{907039232} a - \frac{10019801056547}{453519616} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 159 a - 190\) , \( 1086 a - 557\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(159a-190\right){x}+1086a-557$ |
| 15488.6-f2 |
15488.6-f |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.6 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{19} \cdot 11^{12} \) |
$2.63746$ |
$(a), (-a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.357430230$ |
4.863453427 |
\( -\frac{2638880885903}{907039232} a - \frac{10019801056547}{453519616} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 417 a + 138\) , \( -379 a + 7002\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(417a+138\right){x}-379a+7002$ |
| 17248.4-d2 |
17248.4-d |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
17248.4 |
\( 2^{5} \cdot 7^{2} \cdot 11 \) |
\( 2^{13} \cdot 7^{6} \cdot 11^{6} \) |
$2.70939$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.633656072$ |
4.310990701 |
\( -\frac{2638880885903}{907039232} a - \frac{10019801056547}{453519616} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -17 a + 214\) , \( -806 a + 283\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-17a+214\right){x}-806a+283$ |
| 30976.21-d2 |
30976.21-d |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
30976.21 |
\( 2^{8} \cdot 11^{2} \) |
\( 2^{31} \cdot 11^{12} \) |
$3.13649$ |
$(a), (-a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{3} \) |
$1$ |
$0.178715115$ |
2.431726713 |
\( -\frac{2638880885903}{907039232} a - \frac{10019801056547}{453519616} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1356 a - 1213\) , \( 35851 a + 3926\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-1356a-1213\right){x}+35851a+3926$ |
| 34496.10-c2 |
34496.10-c |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
34496.10 |
\( 2^{6} \cdot 7^{2} \cdot 11 \) |
\( 2^{25} \cdot 7^{6} \cdot 11^{6} \) |
$3.22203$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$0.287316091$ |
$0.316828036$ |
4.954467994 |
\( -\frac{2638880885903}{907039232} a - \frac{10019801056547}{453519616} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 609 a - 107\) , \( 3136 a + 7188\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(609a-107\right){x}+3136a+7188$ |
| 42592.6-e2 |
42592.6-e |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
42592.6 |
\( 2^{5} \cdot 11^{3} \) |
\( 2^{13} \cdot 11^{12} \) |
$3.39641$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.505482678$ |
3.438980898 |
\( -\frac{2638880885903}{907039232} a - \frac{10019801056547}{453519616} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 227 a + 12\) , \( -435 a - 2172\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(227a+12\right){x}-435a-2172$ |
| 45056.14-j2 |
45056.14-j |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
45056.14 |
\( 2^{12} \cdot 11 \) |
\( 2^{37} \cdot 11^{6} \) |
$3.44450$ |
$(a), (-a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1.767169879$ |
$0.419124096$ |
4.479111698 |
\( -\frac{2638880885903}{907039232} a - \frac{10019801056547}{453519616} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -347 a + 61\) , \( 3049 a - 3347\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-347a+61\right){x}+3049a-3347$ |
| 45056.14-y2 |
45056.14-y |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
45056.14 |
\( 2^{12} \cdot 11 \) |
\( 2^{37} \cdot 11^{6} \) |
$3.44450$ |
$(a), (-a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.419124096$ |
3.801936433 |
\( -\frac{2638880885903}{907039232} a - \frac{10019801056547}{453519616} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -347 a + 61\) , \( -3049 a + 3347\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-347a+61\right){x}-3049a+3347$ |
| 47432.6-d2 |
47432.6-d |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
47432.6 |
\( 2^{3} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{13} \cdot 7^{6} \cdot 11^{12} \) |
$3.48904$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1.233590842$ |
$0.191054494$ |
6.413747696 |
\( -\frac{2638880885903}{907039232} a - \frac{10019801056547}{453519616} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 1701 a - 1218\) , \( -28644 a - 9443\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(1701a-1218\right){x}-28644a-9443$ |
*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.
