| 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 |
| 9408.2-b6 |
9408.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
9408.2 |
\( 2^{6} \cdot 3 \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{2} \cdot 7^{3} \) |
$1.52431$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.007296960$ |
1.163126343 |
\( \frac{34063884256}{147} a - \frac{4235820272}{49} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 336 a - 224\) , \( -1916 a + 88\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(336a-224\right){x}-1916a+88$ |
| 37632.2-n1 |
37632.2-n |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
37632.2 |
\( 2^{8} \cdot 3 \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{2} \cdot 7^{3} \) |
$2.15570$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.709575947$ |
$1.007296960$ |
3.976905641 |
\( \frac{34063884256}{147} a - \frac{4235820272}{49} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 336 a - 224\) , \( 1916 a - 88\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(336a-224\right){x}+1916a-88$ |
| 112896.2-e1 |
112896.2-e |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{8} \cdot 7^{3} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.581563171$ |
1.343062614 |
\( \frac{34063884256}{147} a - \frac{4235820272}{49} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -1008 a + 672\) , \( 5220 a - 11232\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-1008a+672\right){x}+5220a-11232$ |
| 112896.2-bg1 |
112896.2-bg |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{8} \cdot 7^{3} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.581563171$ |
2.686125229 |
\( \frac{34063884256}{147} a - \frac{4235820272}{49} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 673 a + 337\) , \( -6229 a + 11904\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(673a+337\right){x}-6229a+11904$ |
*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.
