| 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 |
| 256.6-a1 |
256.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
256.6 |
\( 2^{8} \) |
\( 2^{19} \) |
$0.94569$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.081235671$ |
1.164597616 |
\( 237572 a - 523524 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 11 a - 1\) , \( -8 a - 12\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(11a-1\right){x}-8a-12$ |
| 512.6-a1 |
512.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
512.6 |
\( 2^{9} \) |
\( 2^{19} \) |
$1.12462$ |
$(a), (-a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.081235671$ |
1.164597616 |
\( 237572 a - 523524 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 11 a - 1\) , \( 8 a + 12\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(11a-1\right){x}+8a+12$ |
| 512.7-a1 |
512.7-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
512.7 |
\( 2^{9} \) |
\( 2^{25} \) |
$1.12462$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.453077269$ |
$2.178762637$ |
1.492427233 |
\( 237572 a - 523524 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -21 a + 22\) , \( 17 a - 74\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-21a+22\right){x}+17a-74$ |
| 1024.7-b1 |
1024.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1024.7 |
\( 2^{10} \) |
\( 2^{25} \) |
$1.33740$ |
$(a), (-a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.178762637$ |
1.646989744 |
\( 237572 a - 523524 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -21 a + 22\) , \( -17 a + 74\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-21a+22\right){x}-17a+74$ |
| 2048.6-a1 |
2048.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2048.6 |
\( 2^{11} \) |
\( 2^{25} \) |
$1.59045$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.396505574$ |
$2.178762637$ |
2.300030359 |
\( 237572 a - 523524 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -10 a - 21\) , \( -47 a - 29\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-10a-21\right){x}-47a-29$ |
| 2048.6-e1 |
2048.6-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2048.6 |
\( 2^{11} \) |
\( 2^{25} \) |
$1.59045$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.178762637$ |
1.646989744 |
\( 237572 a - 523524 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -10 a - 21\) , \( 47 a + 29\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-10a-21\right){x}+47a+29$ |
| 4096.7-b1 |
4096.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{31} \) |
$1.89137$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.160998220$ |
$1.540617835$ |
2.704191521 |
\( 237572 a - 523524 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 43 a - 2\) , \( 23 a + 182\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(43a-2\right){x}+23a+182$ |
| 4096.7-h1 |
4096.7-h |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{31} \) |
$1.89137$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.540617835$ |
2.329195233 |
\( 237572 a - 523524 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 43 a - 2\) , \( -23 a - 182\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(43a-2\right){x}-23a-182$ |
| 12544.6-b1 |
12544.6-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
12544.6 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{19} \cdot 7^{6} \) |
$2.50205$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.225894401$ |
$1.164597616$ |
4.316879497 |
\( 237572 a - 523524 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -75 a + 2\) , \( -300 a + 312\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-75a+2\right){x}-300a+312$ |
| 20736.6-d1 |
20736.6-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20736.6 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{19} \cdot 3^{12} \) |
$2.83706$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.027078557$ |
3.105593645 |
\( 237572 a - 523524 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 96 a - 3\) , \( 124 a + 518\bigr] \) |
${y}^2={x}^{3}+\left(96a-3\right){x}+124a+518$ |
| 25088.6-f1 |
25088.6-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
25088.6 |
\( 2^{9} \cdot 7^{2} \) |
\( 2^{19} \cdot 7^{6} \) |
$2.97546$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.164597616$ |
1.760706098 |
\( 237572 a - 523524 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -75 a + 2\) , \( 300 a - 312\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-75a+2\right){x}+300a-312$ |
| 25088.7-e1 |
25088.7-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
25088.7 |
\( 2^{9} \cdot 7^{2} \) |
\( 2^{25} \cdot 7^{6} \) |
$2.97546$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.862501160$ |
$0.823494872$ |
4.637654791 |
\( 237572 a - 523524 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 148 a - 152\) , \( -912 a + 336\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(148a-152\right){x}-912a+336$ |
| 30976.16-a1 |
30976.16-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
30976.16 |
\( 2^{8} \cdot 11^{2} \) |
\( 2^{19} \cdot 11^{6} \) |
$3.13649$ |
$(a), (-a+1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.929027510$ |
1.404557573 |
\( 237572 a - 523524 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -71 a + 170\) , \( -362 a - 360\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-71a+170\right){x}-362a-360$ |
| 30976.18-g1 |
30976.18-g |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
30976.18 |
\( 2^{8} \cdot 11^{2} \) |
\( 2^{19} \cdot 11^{6} \) |
$3.13649$ |
$(a), (-a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.929027510$ |
2.809115146 |
\( 237572 a - 523524 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 8 a - 168\) , \( -56 a + 784\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(8a-168\right){x}-56a+784$ |
| 41472.6-a1 |
41472.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
41472.6 |
\( 2^{9} \cdot 3^{4} \) |
\( 2^{19} \cdot 3^{12} \) |
$3.37385$ |
$(a), (-a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.551496412$ |
$1.027078557$ |
3.425447505 |
\( 237572 a - 523524 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 96 a - 3\) , \( -124 a - 518\bigr] \) |
${y}^2={x}^{3}+\left(96a-3\right){x}-124a-518$ |
| 41472.7-a1 |
41472.7-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
41472.7 |
\( 2^{9} \cdot 3^{4} \) |
\( 2^{25} \cdot 3^{12} \) |
$3.37385$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.726254212$ |
2.195986326 |
\( 237572 a - 523524 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -189 a + 195\) , \( -270 a + 1802\bigr] \) |
${y}^2={x}^{3}+\left(-189a+195\right){x}-270a+1802$ |
*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.
