| 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-a4 |
256.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
256.6 |
\( 2^{8} \) |
\( 2^{13} \) |
$0.94569$ |
$(a), (-a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.162471343$ |
1.164597616 |
\( 2056 a + 2768 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+{x}$ |
| 512.6-a4 |
512.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
512.6 |
\( 2^{9} \) |
\( 2^{13} \) |
$1.12462$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$6.162471343$ |
1.164597616 |
\( 2056 a + 2768 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+{x}$ |
| 512.7-a4 |
512.7-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
512.7 |
\( 2^{9} \) |
\( 2^{19} \) |
$1.12462$ |
$(a), (-a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.453077269$ |
$4.357525275$ |
1.492427233 |
\( 2056 a + 2768 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -a - 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-a-1\right){x}$ |
| 1024.7-b4 |
1024.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1024.7 |
\( 2^{10} \) |
\( 2^{19} \) |
$1.33740$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4.357525275$ |
1.646989744 |
\( 2056 a + 2768 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -a - 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-1\right){x}$ |
| 2048.6-a4 |
2048.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2048.6 |
\( 2^{11} \) |
\( 2^{19} \) |
$1.59045$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.349126393$ |
$4.357525275$ |
2.300030359 |
\( 2056 a + 2768 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( a - 3\) , \( a - 3\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(a-3\right){x}+a-3$ |
| 2048.6-e4 |
2048.6-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2048.6 |
\( 2^{11} \) |
\( 2^{19} \) |
$1.59045$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4.357525275$ |
1.646989744 |
\( 2056 a + 2768 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( a - 3\) , \( -a + 3\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(a-3\right){x}-a+3$ |
| 4096.7-b4 |
4096.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{25} \) |
$1.89137$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.290249555$ |
$3.081235671$ |
2.704191521 |
\( 2056 a + 2768 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( a + 5\) , \( -5 a + 7\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(a+5\right){x}-5a+7$ |
| 4096.7-h4 |
4096.7-h |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4096.7 |
\( 2^{12} \) |
\( 2^{25} \) |
$1.89137$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.081235671$ |
2.329195233 |
\( 2056 a + 2768 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( a + 5\) , \( 5 a - 7\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(a+5\right){x}+5a-7$ |
| 12544.6-b4 |
12544.6-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
12544.6 |
\( 2^{8} \cdot 7^{2} \) |
\( 2^{13} \cdot 7^{6} \) |
$2.50205$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.225894401$ |
$2.329195233$ |
4.316879497 |
\( 2056 a + 2768 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -2 a - 10\) , \( -a - 9\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-2a-10\right){x}-a-9$ |
| 20736.6-d4 |
20736.6-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20736.6 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{13} \cdot 3^{12} \) |
$2.83706$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.054157114$ |
3.105593645 |
\( 2056 a + 2768 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 3 a + 12\) , \( -11 a + 15\bigr] \) |
${y}^2={x}^{3}+\left(3a+12\right){x}-11a+15$ |
| 25088.6-f4 |
25088.6-f |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
25088.6 |
\( 2^{9} \cdot 7^{2} \) |
\( 2^{13} \cdot 7^{6} \) |
$2.97546$ |
$(a), (-a+1), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.329195233$ |
1.760706098 |
\( 2056 a + 2768 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -2 a - 10\) , \( a + 9\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-2a-10\right){x}+a+9$ |
| 25088.7-e4 |
25088.7-e |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
25088.7 |
\( 2^{9} \cdot 7^{2} \) |
\( 2^{19} \cdot 7^{6} \) |
$2.97546$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.465625290$ |
$1.646989744$ |
4.637654791 |
\( 2056 a + 2768 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 14 a + 5\) , \( -7 a - 34\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(14a+5\right){x}-7a-34$ |
| 30976.16-a4 |
30976.16-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
30976.16 |
\( 2^{8} \cdot 11^{2} \) |
\( 2^{13} \cdot 11^{6} \) |
$3.13649$ |
$(a), (-a+1), (-2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.858055020$ |
1.404557573 |
\( 2056 a + 2768 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -13 a + 7\) , \( 6 a - 22\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-13a+7\right){x}+6a-22$ |
| 30976.18-g4 |
30976.18-g |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
30976.18 |
\( 2^{8} \cdot 11^{2} \) |
\( 2^{13} \cdot 11^{6} \) |
$3.13649$ |
$(a), (-a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.858055020$ |
2.809115146 |
\( 2056 a + 2768 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 12 a - 15\) , \( -20 a + 26\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(12a-15\right){x}-20a+26$ |
| 41472.6-a4 |
41472.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
41472.6 |
\( 2^{9} \cdot 3^{4} \) |
\( 2^{13} \cdot 3^{12} \) |
$3.37385$ |
$(a), (-a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$2.205985648$ |
$2.054157114$ |
3.425447505 |
\( 2056 a + 2768 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 3 a + 12\) , \( 11 a - 15\bigr] \) |
${y}^2={x}^{3}+\left(3a+12\right){x}+11a-15$ |
| 41472.7-a4 |
41472.7-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
41472.7 |
\( 2^{9} \cdot 3^{4} \) |
\( 2^{19} \cdot 3^{12} \) |
$3.37385$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.452508425$ |
2.195986326 |
\( 2056 a + 2768 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -18 a - 6\) , \( -37 a + 23\bigr] \) |
${y}^2={x}^{3}+\left(-18a-6\right){x}-37a+23$ |
*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.
