| 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 |
| 1300.4-a1 |
1300.4-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1300.4 |
\( 2^{2} \cdot 5^{2} \cdot 13 \) |
\( 2^{8} \cdot 5^{4} \cdot 13^{4} \) |
$1.07314$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$1.192201957$ |
1.192201957 |
\( \frac{6278960157372}{3570125} a - \frac{12247085251904}{3570125} \) |
\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( -79 i + 107\) , \( 360 i + 495\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-79i+107\right){x}+360i+495$ |
| 26000.4-j1 |
26000.4-j |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{8} \cdot 5^{10} \cdot 13^{4} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$3.752555139$ |
$0.533168923$ |
4.001491570 |
\( \frac{6278960157372}{3570125} a - \frac{12247085251904}{3570125} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -191 i - 637\) , \( 2970 i + 6165\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-191i-637\right){x}+2970i+6165$ |
| 26000.6-b1 |
26000.6-b |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.6 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{8} \cdot 5^{10} \cdot 13^{4} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$3.346620191$ |
$0.533168923$ |
3.568627771 |
\( \frac{6278960157372}{3570125} a - \frac{12247085251904}{3570125} \) |
\( \bigl[i + 1\) , \( -1\) , \( 0\) , \( 665 i - 5\) , \( -4950 i - 4725\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-{x}^{2}+\left(665i-5\right){x}-4950i-4725$ |
| 32500.6-c1 |
32500.6-c |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
32500.6 |
\( 2^{2} \cdot 5^{4} \cdot 13 \) |
\( 2^{8} \cdot 5^{16} \cdot 13^{4} \) |
$2.39960$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.238440391$ |
0.953761565 |
\( \frac{6278960157372}{3570125} a - \frac{12247085251904}{3570125} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -1976 i + 2677\) , \( -42324 i - 59900\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-1976i+2677\right){x}-42324i-59900$ |
| 67600.6-i1 |
67600.6-i |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.6 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{4} \cdot 13^{10} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$2.333124948$ |
$0.330657329$ |
4.628789192 |
\( \frac{6278960157372}{3570125} a - \frac{12247085251904}{3570125} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( 889 i + 1483\) , \( 19530 i - 21015\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(889i+1483\right){x}+19530i-21015$ |
| 83200.4-g1 |
83200.4-g |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
83200.4 |
\( 2^{8} \cdot 5^{2} \cdot 13 \) |
\( 2^{20} \cdot 5^{4} \cdot 13^{4} \) |
$3.03528$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.596100978$ |
2.384403914 |
\( \frac{6278960157372}{3570125} a - \frac{12247085251904}{3570125} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( -316 i + 428\) , \( 2880 i + 3960\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+\left(-316i+428\right){x}+2880i+3960$ |
| 84500.6-b1 |
84500.6-b |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
84500.6 |
\( 2^{2} \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{10} \cdot 13^{10} \) |
$3.04707$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.147874453$ |
2.365991253 |
\( \frac{6278960157372}{3570125} a - \frac{12247085251904}{3570125} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( -8604 i - 890\) , \( 247366 i - 184394\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-8604i-890\right){x}+247366i-184394$ |
| 84500.9-b1 |
84500.9-b |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
84500.9 |
\( 2^{2} \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{10} \cdot 13^{10} \) |
$3.04707$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.147874453$ |
1.774493439 |
\( \frac{6278960157372}{3570125} a - \frac{12247085251904}{3570125} \) |
\( \bigl[i + 1\) , \( 1\) , \( i + 1\) , \( 3263 i - 8010\) , \( 169535 i - 262217\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(3263i-8010\right){x}+169535i-262217$ |
*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.
