| 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-a2 |
1300.4-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1300.4 |
\( 2^{2} \cdot 5^{2} \cdot 13 \) |
\( 2^{8} \cdot 5^{7} \cdot 13 \) |
$1.07314$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$2.384403914$ |
1.192201957 |
\( \frac{109985792}{8125} a - \frac{102465536}{8125} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -4 i - 13\) , \( -8 i - 14\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-4i-13\right){x}-8i-14$ |
| 26000.4-j2 |
26000.4-j |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{8} \cdot 5^{13} \cdot 13 \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$0.938138784$ |
$1.066337847$ |
4.001491570 |
\( \frac{109985792}{8125} a - \frac{102465536}{8125} \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( 66 i + 24\) , \( -36 i - 235\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(66i+24\right){x}-36i-235$ |
| 26000.6-b2 |
26000.6-b |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.6 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{8} \cdot 5^{13} \cdot 13 \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.836655047$ |
$1.066337847$ |
3.568627771 |
\( \frac{109985792}{8125} a - \frac{102465536}{8125} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( -42 i + 56\) , \( 172 i + 179\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(-42i+56\right){x}+172i+179$ |
| 32500.6-c2 |
32500.6-c |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
32500.6 |
\( 2^{2} \cdot 5^{4} \cdot 13 \) |
\( 2^{8} \cdot 5^{19} \cdot 13 \) |
$2.39960$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.476880782$ |
0.953761565 |
\( \frac{109985792}{8125} a - \frac{102465536}{8125} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -100 i - 333\) , \( 1200 i + 2412\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-100i-333\right){x}+1200i+2412$ |
| 67600.6-i2 |
67600.6-i |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.6 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{7} \cdot 13^{7} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$0.583281237$ |
$0.661314659$ |
4.628789192 |
\( \frac{109985792}{8125} a - \frac{102465536}{8125} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( -180 i - 19\) , \( -769 i + 655\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+\left(-180i-19\right){x}-769i+655$ |
| 83200.4-g2 |
83200.4-g |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
83200.4 |
\( 2^{8} \cdot 5^{2} \cdot 13 \) |
\( 2^{8} \cdot 5^{7} \cdot 13 \) |
$3.03528$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.384403914$ |
2.384403914 |
\( \frac{109985792}{8125} a - \frac{102465536}{8125} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 4 i + 13\) , \( -14 i + 8\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+\left(4i+13\right){x}-14i+8$ |
| 84500.6-b2 |
84500.6-b |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
84500.6 |
\( 2^{2} \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{13} \cdot 13^{7} \) |
$3.04707$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.295748906$ |
2.365991253 |
\( \frac{109985792}{8125} a - \frac{102465536}{8125} \) |
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 614 i - 664\) , \( -9154 i + 5003\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(614i-664\right){x}-9154i+5003$ |
| 84500.9-b2 |
84500.9-b |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
84500.9 |
\( 2^{2} \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{13} \cdot 13^{7} \) |
$3.04707$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.295748906$ |
1.774493439 |
\( \frac{109985792}{8125} a - \frac{102465536}{8125} \) |
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( 466 i + 776\) , \( -7614 i + 7967\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(466i+776\right){x}-7614i+7967$ |
*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.
