| 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 |
| 4356.6-c1 |
4356.6-c |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4356.6 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 11^{9} \) |
$1.92070$ |
$(a), (-a+1), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.737347964$ |
2.229530679 |
\( -\frac{11528611}{576} a - \frac{43599055}{288} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 128 a - 203\) , \( -919 a + 895\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(128a-203\right){x}-919a+895$ |
| 34848.15-g1 |
34848.15-g |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
34848.15 |
\( 2^{5} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{20} \cdot 3^{4} \cdot 11^{3} \) |
$3.23022$ |
$(a), (-a+1), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.281924569$ |
$1.222753269$ |
4.169391889 |
\( -\frac{11528611}{576} a - \frac{43599055}{288} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 57 a - 51\) , \( 171 a - 9\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(57a-51\right){x}+171a-9$ |
| 34848.6-b1 |
34848.6-b |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
34848.6 |
\( 2^{5} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{20} \cdot 3^{4} \cdot 11^{3} \) |
$3.23022$ |
$(a), (-a+1), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.431747936$ |
$1.222753269$ |
3.192567334 |
\( -\frac{11528611}{576} a - \frac{43599055}{288} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -51 a + 66\) , \( 9 a + 234\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-51a+66\right){x}+9a+234$ |
| 39204.6-b1 |
39204.6-b |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39204.6 |
\( 2^{2} \cdot 3^{4} \cdot 11^{2} \) |
\( 2^{8} \cdot 3^{16} \cdot 11^{9} \) |
$3.32675$ |
$(a), (-a+1), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.245782654$ |
2.229530679 |
\( -\frac{11528611}{576} a - \frac{43599055}{288} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 1144 a - 1818\) , \( 24339 a - 20058\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(1144a-1818\right){x}+24339a-20058$ |
*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.
