| 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-a2 |
900.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
900.2 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \) |
$1.29494$ |
$(a), (-a+1), (3), (5)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.542111717$ |
$3.882870421$ |
1.060794864 |
\( \frac{357911}{2160} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 1\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}+2$ |
| 8100.2-b2 |
8100.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8100.2 |
\( 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{18} \cdot 5^{2} \) |
$2.24289$ |
$(a), (-a+1), (3), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{6} \) |
$1$ |
$1.294290140$ |
3.913565526 |
\( \frac{357911}{2160} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 13\) , \( -61\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+13{x}-61$ |
| 22500.2-c2 |
22500.2-c |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
22500.2 |
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{14} \) |
$2.89556$ |
$(a), (-a+1), (3), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{6} \cdot 3 \) |
$1$ |
$0.776574084$ |
7.044417947 |
\( \frac{357911}{2160} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 37\) , \( 281\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+37{x}+281$ |
| 28800.2-p2 |
28800.2-p |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28800.2 |
\( 2^{7} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{26} \cdot 3^{6} \cdot 5^{2} \) |
$3.07989$ |
$(a), (-a+1), (3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.372802002$ |
4.150963083 |
\( \frac{357911}{2160} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 7 a + 4\) , \( 38 a - 13\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(7a+4\right){x}+38a-13$ |
| 28800.7-p2 |
28800.7-p |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28800.7 |
\( 2^{7} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{26} \cdot 3^{6} \cdot 5^{2} \) |
$3.07989$ |
$(a), (-a+1), (3), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.372802002$ |
4.150963083 |
\( \frac{357911}{2160} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -9 a + 11\) , \( -39 a + 25\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-9a+11\right){x}-39a+25$ |
*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.
