| 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-a6 |
900.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
900.2 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{12} \) |
$1.29494$ |
$(a), (-a+1), (3), (5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.361407811$ |
$0.647145070$ |
1.060794864 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -334\) , \( -2368\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-334{x}-2368$ |
| 8100.2-b6 |
8100.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
8100.2 |
\( 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{16} \cdot 5^{12} \) |
$2.24289$ |
$(a), (-a+1), (3), (5)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B.1.1 |
$4$ |
\( 2^{5} \cdot 3^{3} \) |
$1$ |
$0.215715023$ |
3.913565526 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3002\) , \( 63929\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-3002{x}+63929$ |
| 22500.2-c6 |
22500.2-c |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
22500.2 |
\( 2^{2} \cdot 3^{2} \cdot 5^{4} \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{24} \) |
$2.89556$ |
$(a), (-a+1), (3), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B |
$4$ |
\( 2^{5} \cdot 3^{2} \) |
$1$ |
$0.129429014$ |
7.044417947 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -8338\) , \( -295969\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-8338{x}-295969$ |
| 28800.2-p6 |
28800.2-p |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28800.2 |
\( 2^{7} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{30} \cdot 3^{4} \cdot 5^{12} \) |
$3.07989$ |
$(a), (-a+1), (3), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$4$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.228800333$ |
4.150963083 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -1668 a - 666\) , \( -40252 a + 14207\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-1668a-666\right){x}-40252a+14207$ |
| 28800.7-p6 |
28800.7-p |
$8$ |
$12$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28800.7 |
\( 2^{7} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{30} \cdot 3^{4} \cdot 5^{12} \) |
$3.07989$ |
$(a), (-a+1), (3), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$4$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.228800333$ |
4.150963083 |
\( \frac{4102915888729}{9000000} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 1666 a - 2334\) , \( 40251 a - 26045\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(1666a-2334\right){x}+40251a-26045$ |
*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.
