| 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 |
| 900.2-a4 |
900.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
900.2 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{24} \cdot 5^{2} \) |
$1.29494$ |
$(a), (-a+1), (3), (5)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$2.168446869$ |
$0.970717605$ |
1.060794864 |
\( \frac{35578826569}{5314410} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -69\) , \( -194\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-69{x}-194$ |
| 8100.2-b4 |
8100.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8100.2 |
\( 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{2} \cdot 3^{36} \cdot 5^{2} \) |
$2.24289$ |
$(a), (-a+1), (3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$16$ |
\( 2^{2} \) |
$1$ |
$0.323572535$ |
3.913565526 |
\( \frac{35578826569}{5314410} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -617\) , \( 5231\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-617{x}+5231$ |
| 22500.2-c4 |
22500.2-c |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
22500.2 |
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{2} \cdot 3^{24} \cdot 5^{14} \) |
$2.89556$ |
$(a), (-a+1), (3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.194143521$ |
7.044417947 |
\( \frac{35578826569}{5314410} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -1713\) , \( -24219\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-1713{x}-24219$ |
| 28800.2-p4 |
28800.2-p |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28800.2 |
\( 2^{7} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{24} \cdot 5^{2} \) |
$3.07989$ |
$(a), (-a+1), (3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.343200500$ |
4.150963083 |
\( \frac{35578826569}{5314410} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -343 a - 136\) , \( -3294 a + 1163\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-343a-136\right){x}-3294a+1163$ |
| 28800.7-p4 |
28800.7-p |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28800.7 |
\( 2^{7} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{20} \cdot 3^{24} \cdot 5^{2} \) |
$3.07989$ |
$(a), (-a+1), (3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.343200500$ |
4.150963083 |
\( \frac{35578826569}{5314410} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 341 a - 479\) , \( 3293 a - 2131\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(341a-479\right){x}+3293a-2131$ |
*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.
