| 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 |
| 400.3-a4 |
400.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
400.3 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$1.05731$ |
$(a), (-a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$2.141031885$ |
1.213850982 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -116\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-41{x}-116$ |
| 6400.3-a4 |
6400.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6400.3 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{6} \) |
$2.11462$ |
$(a), (-a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$1.513938165$ |
1.716644522 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -41 a + 82\) , \( -116 a - 232\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-41a+82\right){x}-116a-232$ |
| 6400.5-a4 |
6400.5-a |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6400.5 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$2.11462$ |
$(a), (-a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$2.141031885$ |
1.213850982 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -41\) , \( 116\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-41{x}+116$ |
| 6400.7-a4 |
6400.7-a |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6400.7 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{6} \) |
$2.11462$ |
$(a), (-a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$1.513938165$ |
1.716644522 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 41 a + 41\) , \( 116 a - 348\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(41a+41\right){x}+116a-348$ |
| 10000.3-a4 |
10000.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
10000.3 |
\( 2^{4} \cdot 5^{4} \) |
\( 2^{8} \cdot 5^{18} \) |
$2.36422$ |
$(a), (-a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.564791727$ |
$0.428206377$ |
3.290750365 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -1033\) , \( -12438\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-1033{x}-12438$ |
| 25600.5-n4 |
25600.5-n |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
25600.5 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{6} \) |
$2.99053$ |
$(a), (-a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$4.470594188$ |
$1.513938165$ |
5.116280683 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -41 a + 82\) , \( 116 a + 232\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-41a+82\right){x}+116a+232$ |
| 25600.7-n4 |
25600.7-n |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
25600.7 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{6} \) |
$2.99053$ |
$(a), (-a+1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$4.470594188$ |
$1.513938165$ |
5.116280683 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 41 a + 41\) , \( -116 a + 348\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(41a+41\right){x}-116a+348$ |
| 32400.3-a4 |
32400.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
32400.3 |
\( 2^{4} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 5^{6} \) |
$3.17193$ |
$(a), (-a+1), (3), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$1$ |
$0.713677295$ |
1.618467976 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -372\) , \( 2761\bigr] \) |
${y}^2={x}^{3}-372{x}+2761$ |
*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.
