| 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 |
| 650.4-a2 |
650.4-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
650.4 |
\( 2 \cdot 5^{2} \cdot 13 \) |
\( 2^{12} \cdot 5^{5} \cdot 13 \) |
$0.90240$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$2.892849288$ |
1.446424644 |
\( \frac{171697}{6500} a + \frac{2279159}{104000} \) |
\( \bigl[1\) , \( 0\) , \( i + 1\) , \( i - 1\) , \( -4 i + 4\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}-4i+4$ |
| 16250.6-a2 |
16250.6-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.6 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{12} \cdot 5^{17} \cdot 13 \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.491363925$ |
$0.578569857$ |
2.274306853 |
\( \frac{171697}{6500} a + \frac{2279159}{104000} \) |
\( \bigl[1\) , \( 1\) , \( i + 1\) , \( 37 i - 13\) , \( -438 i + 500\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(37i-13\right){x}-438i+500$ |
| 26000.4-f2 |
26000.4-f |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{24} \cdot 5^{11} \cdot 13 \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.646860765$ |
1.293721531 |
\( \frac{171697}{6500} a + \frac{2279159}{104000} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( 10 i - 30\) , \( -296 i - 372\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(10i-30\right){x}-296i-372$ |
| 26000.6-f2 |
26000.6-f |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.6 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{24} \cdot 5^{11} \cdot 13 \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.646860765$ |
2.587443063 |
\( \frac{171697}{6500} a + \frac{2279159}{104000} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( 26 i + 18\) , \( -408 i - 244\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(26i+18\right){x}-408i-244$ |
| 42250.6-e2 |
42250.6-e |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
42250.6 |
\( 2 \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{12} \cdot 5^{11} \cdot 13^{7} \) |
$2.56227$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.358813793$ |
2.152882762 |
\( \frac{171697}{6500} a + \frac{2279159}{104000} \) |
\( \bigl[1\) , \( i + 1\) , \( i\) , \( 79 i + 67\) , \( 2199 i + 1873\bigr] \) |
${y}^2+{x}{y}+i{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(79i+67\right){x}+2199i+1873$ |
| 42250.9-i2 |
42250.9-i |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
42250.9 |
\( 2 \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{12} \cdot 5^{11} \cdot 13^{7} \) |
$2.56227$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{7} \cdot 3 \) |
$0.370672091$ |
$0.358813793$ |
6.384108451 |
\( \frac{171697}{6500} a + \frac{2279159}{104000} \) |
\( \bigl[1\) , \( i\) , \( 1\) , \( -86 i + 56\) , \( 2677 i + 1030\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+i{x}^{2}+\left(-86i+56\right){x}+2677i+1030$ |
| 52650.4-a2 |
52650.4-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52650.4 |
\( 2 \cdot 3^{4} \cdot 5^{2} \cdot 13 \) |
\( 2^{12} \cdot 3^{12} \cdot 5^{5} \cdot 13 \) |
$2.70719$ |
$(a+1), (-a-2), (2a+1), (2a+3), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$0.836000358$ |
$0.964283096$ |
3.224564057 |
\( \frac{171697}{6500} a + \frac{2279159}{104000} \) |
\( \bigl[i\) , \( 1\) , \( i + 1\) , \( 13 i - 4\) , \( -95 i + 108\bigr] \) |
${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(13i-4\right){x}-95i+108$ |
| 67600.6-a2 |
67600.6-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.6 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{24} \cdot 5^{5} \cdot 13^{7} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1.059422156$ |
$0.401166016$ |
3.400033334 |
\( \frac{171697}{6500} a + \frac{2279159}{104000} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( i + 1\) , \( -5 i + 82\) , \( 1082 i - 1719\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-5i+82\right){x}+1082i-1719$ |
| 83200.4-n2 |
83200.4-n |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
83200.4 |
\( 2^{8} \cdot 5^{2} \cdot 13 \) |
\( 2^{36} \cdot 5^{5} \cdot 13 \) |
$3.03528$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.723212322$ |
1.446424644 |
\( \frac{171697}{6500} a + \frac{2279159}{104000} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( -24 i + 8\) , \( -256 i - 224\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+\left(-24i+8\right){x}-256i-224$ |
*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.
