| 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 |
| 14308.2-a2 |
14308.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
14308.2 |
\( 2^{2} \cdot 7^{2} \cdot 73 \) |
\( 2^{4} \cdot 7^{8} \cdot 73 \) |
$1.69275$ |
$(-3a+1), (9a-8), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.060039140$ |
2.378728304 |
\( \frac{20198991}{14308} a - \frac{3200392}{3577} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 3 a - 12\) , \( -6 a + 14\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(3a-12\right){x}-6a+14$ |
| 18396.2-c2 |
18396.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
18396.2 |
\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 73 \) |
\( 2^{4} \cdot 3^{6} \cdot 7^{2} \cdot 73 \) |
$1.80252$ |
$(-2a+1), (-3a+1), (9a-8), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.209103646$ |
$3.146761764$ |
3.039168860 |
\( \frac{20198991}{14308} a - \frac{3200392}{3577} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -a - 4\) , \( 3\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-a-4\right){x}+3$ |
| 100156.6-b2 |
100156.6-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
100156.6 |
\( 2^{2} \cdot 7^{3} \cdot 73 \) |
\( 2^{4} \cdot 7^{8} \cdot 73 \) |
$2.75339$ |
$(-3a+1), (3a-2), (9a-8), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.105806884$ |
$2.060039140$ |
4.026973283 |
\( \frac{20198991}{14308} a - \frac{3200392}{3577} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -7 a + 10\) , \( 21 a - 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-7a+10\right){x}+21a-1$ |
| 130816.2-a2 |
130816.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
130816.2 |
\( 2^{8} \cdot 7 \cdot 73 \) |
\( 2^{28} \cdot 7^{2} \cdot 73 \) |
$2.94350$ |
$(-3a+1), (9a-8), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.499940384$ |
$1.362587813$ |
3.146386573 |
\( \frac{20198991}{14308} a - \frac{3200392}{3577} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 2 a + 21\) , \( 47 a - 54\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(2a+21\right){x}+47a-54$ |
| 130816.2-b2 |
130816.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
130816.2 |
\( 2^{8} \cdot 7 \cdot 73 \) |
\( 2^{28} \cdot 7^{2} \cdot 73 \) |
$2.94350$ |
$(-3a+1), (9a-8), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.362587813$ |
3.146761764 |
\( \frac{20198991}{14308} a - \frac{3200392}{3577} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 21 a - 23\) , \( -47 a + 54\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(21a-23\right){x}-47a+54$ |
*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.
