| 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 |
| 32448.2-f3 |
32448.2-f |
$6$ |
$8$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
32448.2 |
\( 2^{6} \cdot 3 \cdot 13^{2} \) |
\( 2^{16} \cdot 3^{4} \cdot 13^{4} \) |
$2.07729$ |
$(-2a+1), (-4a+1), (4a-3), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1.290496608$ |
$1.332286356$ |
3.970578733 |
\( \frac{61918288}{1521} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -52\) , \( -160\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-52{x}-160$ |
| 12168.2-e3 |
12168.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
12168.2 |
\( 2^{3} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 13^{4} \) |
$1.87704$ |
$(a+1), (-3a-2), (2a+3), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.664572713$ |
2.664572713 |
\( \frac{61918288}{1521} \) |
\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 13\) , \( -20 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}+13{x}-20i$ |
| 12168.2-g3 |
12168.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
12168.2 |
\( 2^{3} \cdot 3^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 13^{4} \) |
$2.65453$ |
$(a), (-a-1), (a-1), (13)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.600891747$ |
$2.664572713$ |
6.032600140 |
\( \frac{61918288}{1521} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -13\) , \( 20\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-13{x}+20$ |
| 936.1-f3 |
936.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{-13}) \) |
$2$ |
$[0, 1]$ |
936.1 |
\( 2^{3} \cdot 3^{2} \cdot 13 \) |
\( 2^{16} \cdot 3^{4} \cdot 13^{4} \) |
$3.56418$ |
$(2,a+1), (a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$3.637012422$ |
$2.664572713$ |
5.375646230 |
\( \frac{61918288}{1521} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -52\) , \( -160\bigr] \) |
${y}^2={x}^3+{x}^2-52{x}-160$ |
| 936.2-i3 |
936.2-i |
$4$ |
$4$ |
\(\Q(\sqrt{-26}) \) |
$2$ |
$[0, 1]$ |
936.2 |
\( 2^{3} \cdot 3^{2} \cdot 13 \) |
\( 2^{16} \cdot 3^{4} \cdot 13^{4} \) |
$5.04051$ |
$(2,a), (3,a+1), (3,a+2), (13,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$7.042501251$ |
$2.664572713$ |
14.72067845 |
\( \frac{61918288}{1521} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -52\) , \( -160\bigr] \) |
${y}^2={x}^3+{x}^2-52{x}-160$ |
| 4056.1-j3 |
4056.1-j |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4056.1 |
\( 2^{3} \cdot 3 \cdot 13^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 13^{4} \) |
$2.47032$ |
$(a+1), (a), (a+4), (a-4)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.659745188$ |
$6.320340634$ |
4.814886846 |
\( \frac{61918288}{1521} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 52 a - 91\) , \( 300 a - 520\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(52a-91\right){x}+300a-520$ |
*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.
