| 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 |
| 4116.2-a2 |
4116.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
4116.2 |
\( 2^{2} \cdot 3 \cdot 7^{3} \) |
\( 2^{4} \cdot 3^{2} \cdot 7^{6} \) |
$1.23970$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.031964990$ |
$3.434541343$ |
1.521226697 |
\( -\frac{2016793}{4116} a - \frac{38862}{343} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -3 a + 2\) , \( -a + 4\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a+2\right){x}-a+4$ |
| 12348.2-c2 |
12348.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
12348.2 |
\( 2^{2} \cdot 3^{2} \cdot 7^{3} \) |
\( 2^{4} \cdot 3^{8} \cdot 7^{12} \) |
$1.63154$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.749478365$ |
1.730846145 |
\( -\frac{2016793}{4116} a - \frac{38862}{343} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 37 a + 28\) , \( 312 a - 315\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(37a+28\right){x}+312a-315$ |
| 28812.3-e2 |
28812.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
28812.3 |
\( 2^{2} \cdot 3 \cdot 7^{4} \) |
\( 2^{4} \cdot 3^{2} \cdot 7^{18} \) |
$2.01647$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.490648763$ |
2.266209564 |
\( -\frac{2016793}{4116} a - \frac{38862}{343} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 9 a - 138\) , \( 585 a - 1290\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(9a-138\right){x}+585a-1290$ |
| 86436.3-g2 |
86436.3-g |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
86436.3 |
\( 2^{2} \cdot 3^{2} \cdot 7^{4} \) |
\( 2^{4} \cdot 3^{8} \cdot 7^{12} \) |
$2.65383$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.331122644$ |
$0.749478365$ |
4.584978817 |
\( -\frac{2016793}{4116} a - \frac{38862}{343} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -43 a + 65\) , \( -58 a - 251\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-43a+65\right){x}-58a-251$ |
*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.
