| 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 |
| 4464.1-a1 |
4464.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
4464.1 |
\( 2^{4} \cdot 3^{2} \cdot 31 \) |
\( 2^{16} \cdot 3^{9} \cdot 31^{2} \) |
$1.26512$ |
$(-2a+1), (-6a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.360678882$ |
1.571176638 |
\( -\frac{355344}{961} a + \frac{669360}{961} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -12 a + 21\) , \( -24 a + 50\bigr] \) |
${y}^2={x}^{3}+\left(-12a+21\right){x}-24a+50$ |
| 71424.1-b1 |
71424.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
71424.1 |
\( 2^{8} \cdot 3^{2} \cdot 31 \) |
\( 2^{16} \cdot 3^{3} \cdot 31^{2} \) |
$2.53023$ |
$(-2a+1), (-6a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.296057380$ |
$2.356764957$ |
3.222712205 |
\( -\frac{355344}{961} a + \frac{669360}{961} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4 a + 4\) , \( 12 a\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(4a+4\right){x}+12a$ |
| 71424.1-c1 |
71424.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
71424.1 |
\( 2^{8} \cdot 3^{2} \cdot 31 \) |
\( 2^{16} \cdot 3^{9} \cdot 31^{2} \) |
$2.53023$ |
$(-2a+1), (-6a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.540606015$ |
$1.360678882$ |
3.397550170 |
\( -\frac{355344}{961} a + \frac{669360}{961} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 21 a - 9\) , \( 24 a - 50\bigr] \) |
${y}^2={x}^{3}+\left(21a-9\right){x}+24a-50$ |
| 71424.1-e1 |
71424.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
71424.1 |
\( 2^{8} \cdot 3^{2} \cdot 31 \) |
\( 2^{16} \cdot 3^{3} \cdot 31^{2} \) |
$2.53023$ |
$(-2a+1), (-6a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.356764957$ |
2.721357765 |
\( -\frac{355344}{961} a + \frac{669360}{961} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 4 a + 4\) , \( -12 a\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(4a+4\right){x}-12a$ |
| 138384.1-b1 |
138384.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
138384.1 |
\( 2^{4} \cdot 3^{2} \cdot 31^{2} \) |
\( 2^{16} \cdot 3^{3} \cdot 31^{8} \) |
$2.98518$ |
$(-2a+1), (-6a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.423287482$ |
2.932621700 |
\( -\frac{355344}{961} a + \frac{669360}{961} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 150 a + 63\) , \( -1781 a + 813\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(150a+63\right){x}-1781a+813$ |
*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.
