| 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 |
| 450.2-a8 |
450.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
450.2 |
\( 2 \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{8} \cdot 5^{6} \) |
$1.16409$ |
$(a), (-a-1), (a-1), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.323572535$ |
1.372802002 |
\( \frac{16778985534208729}{81000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -5334\) , \( -150368\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-5334{x}-150368$ |
| 3600.2-b8 |
3600.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3600.2 |
\( 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{18} \cdot 3^{8} \cdot 5^{6} \) |
$1.95776$ |
$(a), (-a-1), (a-1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.161786267$ |
1.372802002 |
\( \frac{16778985534208729}{81000} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -21334\) , \( -1202942\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-21334{x}-1202942$ |
| 4050.3-c8 |
4050.3-c |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
4050.3 |
\( 2 \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{20} \cdot 5^{6} \) |
$2.01626$ |
$(a), (-a-1), (a-1), (5)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$3.762559272$ |
$0.107857511$ |
4.591332359 |
\( \frac{16778985534208729}{81000} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -48002\) , \( 4059929\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-48002{x}+4059929$ |
| 11250.2-b8 |
11250.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
11250.2 |
\( 2 \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{6} \cdot 3^{8} \cdot 5^{18} \) |
$2.60299$ |
$(a), (-a-1), (a-1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.064714507$ |
1.098241602 |
\( \frac{16778985534208729}{81000} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -133338\) , \( -18795969\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-133338{x}-18795969$ |
| 32400.3-g8 |
32400.3-g |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
32400.3 |
\( 2^{4} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{18} \cdot 3^{20} \cdot 5^{6} \) |
$3.39094$ |
$(a), (-a-1), (a-1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{6} \cdot 3 \) |
$1$ |
$0.053928755$ |
1.830402670 |
\( \frac{16778985534208729}{81000} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -192006\) , \( 32479434\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-192006{x}+32479434$ |
*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.
