| 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-a2 |
4464.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
4464.1 |
\( 2^{4} \cdot 3^{2} \cdot 31 \) |
\( 2^{8} \cdot 3^{9} \cdot 31 \) |
$1.26512$ |
$(-2a+1), (-6a+1), (2)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2.721357765$ |
1.571176638 |
\( \frac{63744}{31} a + \frac{93696}{31} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 3 a - 9\) , \( -3 a + 8\bigr] \) |
${y}^2={x}^{3}+\left(3a-9\right){x}-3a+8$ |
| 71424.1-b2 |
71424.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
71424.1 |
\( 2^{8} \cdot 3^{2} \cdot 31 \) |
\( 2^{8} \cdot 3^{3} \cdot 31 \) |
$2.53023$ |
$(-2a+1), (-6a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.592114760$ |
$4.713529915$ |
3.222712205 |
\( \frac{63744}{31} a + \frac{93696}{31} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -a - 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-a-1\right){x}$ |
| 71424.1-c2 |
71424.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
71424.1 |
\( 2^{8} \cdot 3^{2} \cdot 31 \) |
\( 2^{8} \cdot 3^{9} \cdot 31 \) |
$2.53023$ |
$(-2a+1), (-6a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.081212031$ |
$2.721357765$ |
3.397550170 |
\( \frac{63744}{31} a + \frac{93696}{31} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -9 a + 6\) , \( 3 a - 8\bigr] \) |
${y}^2={x}^{3}+\left(-9a+6\right){x}+3a-8$ |
| 71424.1-e2 |
71424.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
71424.1 |
\( 2^{8} \cdot 3^{2} \cdot 31 \) |
\( 2^{8} \cdot 3^{3} \cdot 31 \) |
$2.53023$ |
$(-2a+1), (-6a+1), (2)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4.713529915$ |
2.721357765 |
\( \frac{63744}{31} a + \frac{93696}{31} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -a - 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-1\right){x}$ |
| 138384.1-b2 |
138384.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
138384.1 |
\( 2^{4} \cdot 3^{2} \cdot 31^{2} \) |
\( 2^{8} \cdot 3^{3} \cdot 31^{7} \) |
$2.98518$ |
$(-2a+1), (-6a+1), (2)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.846574964$ |
2.932621700 |
\( \frac{63744}{31} a + \frac{93696}{31} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -80 a - 2\) , \( -213 a + 128\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-80a-2\right){x}-213a+128$ |
*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.
