| 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 |
| 1800.2-b4 |
1800.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
1800.2 |
\( 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{8} \cdot 5^{2} \) |
$1.64627$ |
$(a), (-a-1), (a-1), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.740793442$ |
2.461853696 |
\( \frac{546718898}{405} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -54\) , \( 162\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-54{x}+162$ |
| 3600.2-a4 |
3600.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3600.2 |
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{8} \cdot 5^{2} \) |
$1.95776$ |
$(a), (-a-1), (a-1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.222905284$ |
$1.740793442$ |
2.195040798 |
\( \frac{546718898}{405} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -54\) , \( -162\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-54{x}-162$ |
| 16200.3-e4 |
16200.3-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
16200.3 |
\( 2^{3} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{20} \cdot 5^{2} \) |
$2.85143$ |
$(a), (-a-1), (a-1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.721777306$ |
$0.580264480$ |
4.738427010 |
\( \frac{546718898}{405} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -485\) , \( -3887\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-485{x}-3887$ |
| 32400.3-h4 |
32400.3-h |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
32400.3 |
\( 2^{4} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{10} \cdot 3^{20} \cdot 5^{2} \) |
$3.39094$ |
$(a), (-a-1), (a-1), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.374384071$ |
$0.580264480$ |
4.915620320 |
\( \frac{546718898}{405} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -486\) , \( 4374\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-486{x}+4374$ |
| 45000.2-c4 |
45000.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
45000.2 |
\( 2^{3} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{10} \cdot 3^{8} \cdot 5^{14} \) |
$3.68118$ |
$(a), (-a-1), (a-1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.348158688$ |
1.969482956 |
\( \frac{546718898}{405} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -1351\) , \( 18899\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-1351{x}+18899$ |
*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.
