| 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 |
| 92928.1-o4 |
92928.1-o |
$4$ |
$4$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
92928.1 |
\( 2^{8} \cdot 3 \cdot 11^{2} \) |
\( 2^{24} \cdot 3^{6} \cdot 11^{8} \) |
$2.70231$ |
$(-2a+1), (2), (11)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 3 \) |
$0.966388507$ |
$0.256396494$ |
3.433321346 |
\( \frac{347873904937}{395307} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -2344\) , \( -44428\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-2344{x}-44428$ |
| 9801.1-b4 |
9801.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
9801.1 |
\( 3^{4} \cdot 11^{2} \) |
\( 3^{18} \cdot 11^{8} \) |
$1.77822$ |
$(3), (11)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.341861992$ |
1.367447969 |
\( \frac{347873904937}{395307} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -1318\) , \( 18084\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-1318{x}+18084$ |
| 363.2-d4 |
363.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-21}) \) |
$2$ |
$[0, 1]$ |
363.2 |
\( 3 \cdot 11^{2} \) |
\( 3^{18} \cdot 11^{8} \) |
$3.57483$ |
$(3,a), (11,a+1), (11,a+10)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$1.025585977$ |
5.371228996 |
\( \frac{347873904937}{395307} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -1299\) , \( 20721\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-1299{x}+20721$ |
| 33.1-d4 |
33.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
33.1 |
\( 3 \cdot 11 \) |
\( 3^{18} \cdot 11^{8} \) |
$2.46067$ |
$(3,a), (11,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$1.025585977$ |
0.714126411 |
\( \frac{347873904937}{395307} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -1296\) , \( 22019\bigr] \) |
${y}^2+a{x}{y}={x}^3-1296{x}+22019$ |
| 33.1-h4 |
33.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
33.1 |
\( 3 \cdot 11 \) |
\( 3^{18} \cdot 11^{8} \) |
$5.50223$ |
$(3,a), (11,a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \cdot 3 \) |
$6.147048426$ |
$2.051171954$ |
11.77898796 |
\( \frac{347873904937}{395307} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -669\) , \( 33987\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-669{x}+33987$ |
| 363.1-a5 |
363.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
363.1 |
\( 3 \cdot 11^{2} \) |
\( 3^{6} \cdot 11^{8} \) |
$1.35116$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$8.936252827$ |
1.289836993 |
\( \frac{347873904937}{395307} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -146\) , \( 621\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-146{x}+621$ |
*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.
