| 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-a1 |
9408.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
9408.2 |
\( 2^{6} \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3 \cdot 7^{3} \) |
$1.52431$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.025954500$ |
$3.469791130$ |
2.055279100 |
\( \frac{23709440}{147} a - \frac{43353088}{147} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -3 a - 9\) , \( -2 a - 14\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a-9\right){x}-2a-14$ |
| 37632.2-o1 |
37632.2-o |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
37632.2 |
\( 2^{8} \cdot 3 \cdot 7^{2} \) |
\( 2^{8} \cdot 3 \cdot 7^{3} \) |
$2.15570$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.469791130$ |
2.003284843 |
\( \frac{23709440}{147} a - \frac{43353088}{147} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 12 a - 3\) , \( 2 a + 14\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(12a-3\right){x}+2a+14$ |
| 112896.2-g1 |
112896.2-g |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{7} \cdot 7^{3} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.003284843$ |
2.313194086 |
\( \frac{23709440}{147} a - \frac{43353088}{147} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 28 a - 35\) , \( 82 a - 81\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(28a-35\right){x}+82a-81$ |
| 112896.2-bf1 |
112896.2-bf |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
112896.2 |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{7} \cdot 7^{3} \) |
$2.83706$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.526205340$ |
$2.003284843$ |
4.868860331 |
\( \frac{23709440}{147} a - \frac{43353088}{147} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 9 a + 27\) , \( -90 a + 54\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(9a+27\right){x}-90a+54$ |
*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.
