| 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 |
| 14336.9-b1 |
14336.9-b |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14336.9 |
\( 2^{11} \cdot 7 \) |
\( 2^{17} \cdot 7 \) |
$2.58699$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.299194391$ |
$4.423751828$ |
4.002074513 |
\( -\frac{1072}{7} a + \frac{3280}{7} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 2 a\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+2a{x}$ |
| 14336.9-c1 |
14336.9-c |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
14336.9 |
\( 2^{11} \cdot 7 \) |
\( 2^{23} \cdot 7 \) |
$2.58699$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.741219377$ |
$3.128064916$ |
3.505366995 |
\( -\frac{1072}{7} a + \frac{3280}{7} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -2 a + 1\) , \( 3 a - 2\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-2a+1\right){x}+3a-2$ |
| 28672.9-c1 |
28672.9-c |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.9 |
\( 2^{12} \cdot 7 \) |
\( 2^{23} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.949735186$ |
$3.128064916$ |
4.491477793 |
\( -\frac{1072}{7} a + \frac{3280}{7} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -2 a + 1\) , \( -3 a + 2\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-2a+1\right){x}-3a+2$ |
| 28672.9-n1 |
28672.9-n |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28672.9 |
\( 2^{12} \cdot 7 \) |
\( 2^{17} \cdot 7 \) |
$3.07647$ |
$(a), (-a+1), (-2a+1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.423751828$ |
3.344042057 |
\( -\frac{1072}{7} a + \frac{3280}{7} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2 a\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+2a{x}$ |
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*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.
