| 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 |
| 650.3-a2 |
650.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
650.3 |
\( 2 \cdot 5^{2} \cdot 13 \) |
\( 2^{12} \cdot 5^{5} \cdot 13 \) |
$0.90240$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
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 |
\( -\frac{171697}{6500} a + \frac{2279159}{104000} \) |
\( \bigl[1\) , \( 0\) , \( i + 1\) , \( -2 i - 1\) , \( 3 i + 4\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-2i-1\right){x}+3i+4$ |
| 16250.5-a2 |
16250.5-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16250.5 |
\( 2 \cdot 5^{4} \cdot 13 \) |
\( 2^{12} \cdot 5^{17} \cdot 13 \) |
$2.01782$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.491363925$ |
$0.578569857$ |
2.274306853 |
\( -\frac{171697}{6500} a + \frac{2279159}{104000} \) |
\( \bigl[1\) , \( 1\) , \( i + 1\) , \( -38 i - 13\) , \( 437 i + 500\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(-38i-13\right){x}+437i+500$ |
| 26000.3-f2 |
26000.3-f |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.3 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{24} \cdot 5^{11} \cdot 13 \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.646860765$ |
2.587443063 |
\( -\frac{171697}{6500} a + \frac{2279159}{104000} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -26 i + 18\) , \( -408 i + 244\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-26i+18\right){x}-408i+244$ |
| 26000.5-f2 |
26000.5-f |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.5 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{24} \cdot 5^{11} \cdot 13 \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.646860765$ |
1.293721531 |
\( -\frac{171697}{6500} a + \frac{2279159}{104000} \) |
\( \bigl[i + 1\) , \( -1\) , \( 0\) , \( -10 i - 30\) , \( 296 i - 372\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-10i-30\right){x}+296i-372$ |
| 42250.4-i2 |
42250.4-i |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
42250.4 |
\( 2 \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{12} \cdot 5^{11} \cdot 13^{7} \) |
$2.56227$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{7} \cdot 3 \) |
$0.370672091$ |
$0.358813793$ |
6.384108451 |
\( -\frac{171697}{6500} a + \frac{2279159}{104000} \) |
\( \bigl[1\) , \( -i\) , \( 1\) , \( 86 i + 56\) , \( -2677 i + 1030\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-i{x}^{2}+\left(86i+56\right){x}-2677i+1030$ |
| 42250.7-e2 |
42250.7-e |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
42250.7 |
\( 2 \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{12} \cdot 5^{11} \cdot 13^{7} \) |
$2.56227$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.358813793$ |
2.152882762 |
\( -\frac{171697}{6500} a + \frac{2279159}{104000} \) |
\( \bigl[1\) , \( -i + 1\) , \( i\) , \( -80 i + 67\) , \( -2199 i + 1873\bigr] \) |
${y}^2+{x}{y}+i{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-80i+67\right){x}-2199i+1873$ |
| 52650.3-a2 |
52650.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52650.3 |
\( 2 \cdot 3^{4} \cdot 5^{2} \cdot 13 \) |
\( 2^{12} \cdot 3^{12} \cdot 5^{5} \cdot 13 \) |
$2.70719$ |
$(a+1), (-a-2), (2a+1), (-3a-2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$0.836000358$ |
$0.964283096$ |
3.224564057 |
\( -\frac{171697}{6500} a + \frac{2279159}{104000} \) |
\( \bigl[1\) , \( -1\) , \( i + 1\) , \( -14 i - 5\) , \( -95 i - 108\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(-14i-5\right){x}-95i-108$ |
| 67600.4-a2 |
67600.4-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.4 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{24} \cdot 5^{5} \cdot 13^{7} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1.059422156$ |
$0.401166016$ |
3.400033334 |
\( -\frac{171697}{6500} a + \frac{2279159}{104000} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( i + 1\) , \( 3 i + 82\) , \( 1082 i + 1719\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}^{2}+\left(3i+82\right){x}+1082i+1719$ |
| 83200.3-e2 |
83200.3-e |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
83200.3 |
\( 2^{8} \cdot 5^{2} \cdot 13 \) |
\( 2^{36} \cdot 5^{5} \cdot 13 \) |
$3.03528$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
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.
