| 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 |
| 4464.2-a2 |
4464.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
4464.2 |
\( 2^{4} \cdot 3^{2} \cdot 31 \) |
\( 2^{8} \cdot 3^{9} \cdot 31 \) |
$1.26512$ |
$(-2a+1), (6a-5), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2.721357765$ |
1.571176638 |
\( -\frac{63744}{31} a + \frac{157440}{31} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3 a - 6\) , \( 3 a + 5\bigr] \) |
${y}^2={x}^{3}+\left(-3a-6\right){x}+3a+5$ |
| 71424.2-a2 |
71424.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
71424.2 |
\( 2^{8} \cdot 3^{2} \cdot 31 \) |
\( 2^{8} \cdot 3^{3} \cdot 31 \) |
$2.53023$ |
$(-2a+1), (6a-5), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.592114760$ |
$4.713529915$ |
3.222712205 |
\( -\frac{63744}{31} a + \frac{157440}{31} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 2 a + 2\) , \( -3 a + 1\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a+2\right){x}-3a+1$ |
| 71424.2-b2 |
71424.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
71424.2 |
\( 2^{8} \cdot 3^{2} \cdot 31 \) |
\( 2^{8} \cdot 3^{9} \cdot 31 \) |
$2.53023$ |
$(-2a+1), (6a-5), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.081212031$ |
$2.721357765$ |
3.397550170 |
\( -\frac{63744}{31} a + \frac{157440}{31} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 9 a - 3\) , \( -3 a - 5\bigr] \) |
${y}^2={x}^{3}+\left(9a-3\right){x}-3a-5$ |
| 71424.2-h2 |
71424.2-h |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
71424.2 |
\( 2^{8} \cdot 3^{2} \cdot 31 \) |
\( 2^{8} \cdot 3^{3} \cdot 31 \) |
$2.53023$ |
$(-2a+1), (6a-5), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4.713529915$ |
2.721357765 |
\( -\frac{63744}{31} a + \frac{157440}{31} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2 a + 2\) , \( 3 a - 1\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+2\right){x}+3a-1$ |
| 138384.3-b2 |
138384.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
138384.3 |
\( 2^{4} \cdot 3^{2} \cdot 31^{2} \) |
\( 2^{8} \cdot 3^{3} \cdot 31^{7} \) |
$2.98518$ |
$(-2a+1), (6a-5), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.846574964$ |
2.932621700 |
\( -\frac{63744}{31} a + \frac{157440}{31} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 3 a + 81\) , \( 296 a - 87\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(3a+81\right){x}+296a-87$ |
*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.
