| 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 |
| 396.2-e1 |
396.2-e |
$4$ |
$6$ |
\(\Q(\sqrt{-55}) \) |
$2$ |
$[0, 1]$ |
396.2 |
\( 2^{2} \cdot 3^{2} \cdot 11 \) |
\( 2^{6} \cdot 3^{4} \cdot 5^{12} \cdot 11^{12} \) |
$2.95627$ |
$(2,a), (2,a+1), (11,a+5), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.623134288$ |
6.049685541 |
\( -\frac{7357983625}{127552392} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -1013\) , \( -69469\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-1013{x}-69469$ |
| 726.2-g1 |
726.2-g |
$4$ |
$6$ |
\(\Q(\sqrt{-30}) \) |
$2$ |
$[0, 1]$ |
726.2 |
\( 2 \cdot 3 \cdot 11^{2} \) |
\( 2^{6} \cdot 3^{4} \cdot 5^{12} \cdot 11^{12} \) |
$5.08117$ |
$(2,a), (3,a), (11,a+5), (11,a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.623134288$ |
5.460875297 |
\( -\frac{7357983625}{127552392} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -1013\) , \( -69469\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-1013{x}-69469$ |
| 66.1-o1 |
66.1-o |
$4$ |
$6$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
66.1 |
\( 2 \cdot 3 \cdot 11 \) |
\( 2^{6} \cdot 3^{4} \cdot 5^{12} \cdot 11^{12} \) |
$6.54330$ |
$(2,a+1), (3,a), (11,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$16$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.246268576$ |
4.657050101 |
\( -\frac{7357983625}{127552392} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -1013\) , \( -69469\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-1013{x}-69469$ |
| 4356.1-d1 |
4356.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4356.1 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{6} \cdot 3^{4} \cdot 11^{12} \) |
$1.62329$ |
$(-3a+2), (-3a+1), (2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.635354791$ |
1.704835804 |
\( -\frac{7357983625}{127552392} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -41\) , \( -556\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-41{x}-556$ |
*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.
