| 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-a3 |
1300.4-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1300.4 |
\( 2^{2} \cdot 5^{2} \cdot 13 \) |
\( 2^{8} \cdot 5^{4} \cdot 13^{12} \) |
$1.07314$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.397400652$ |
1.192201957 |
\( \frac{40605232846917732}{2912260640310125} a + \frac{15507117639303424}{2912260640310125} \) |
\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( 11 i - 63\) , \( 1356 i + 1607\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(11i-63\right){x}+1356i+1607$ |
| 26000.4-j3 |
26000.4-j |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{8} \cdot 5^{10} \cdot 13^{12} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1.250851713$ |
$0.177722974$ |
4.001491570 |
\( \frac{40605232846917732}{2912260640310125} a + \frac{15507117639303424}{2912260640310125} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( 219 i + 233\) , \( 11702 i + 20389\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(219i+233\right){x}+11702i+20389$ |
| 26000.6-b3 |
26000.6-b |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.6 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{8} \cdot 5^{10} \cdot 13^{12} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$10.03986057$ |
$0.177722974$ |
3.568627771 |
\( \frac{40605232846917732}{2912260640310125} a + \frac{15507117639303424}{2912260640310125} \) |
\( \bigl[i + 1\) , \( -1\) , \( 0\) , \( -285 i + 145\) , \( -18130 i - 14965\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-285i+145\right){x}-18130i-14965$ |
| 32500.6-c3 |
32500.6-c |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
32500.6 |
\( 2^{2} \cdot 5^{4} \cdot 13 \) |
\( 2^{8} \cdot 5^{16} \cdot 13^{12} \) |
$2.39960$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.079480130$ |
0.953761565 |
\( \frac{40605232846917732}{2912260640310125} a + \frac{15507117639303424}{2912260640310125} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( 274 i - 1573\) , \( -171074 i - 201150\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(274i-1573\right){x}-171074i-201150$ |
| 67600.6-i3 |
67600.6-i |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.6 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{4} \cdot 13^{18} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$6.999374845$ |
$0.110219109$ |
4.628789192 |
\( \frac{40605232846917732}{2912260640310125} a + \frac{15507117639303424}{2912260640310125} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( -701 i - 447\) , \( 61718 i - 76839\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-701i-447\right){x}+61718i-76839$ |
| 83200.4-g3 |
83200.4-g |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
83200.4 |
\( 2^{8} \cdot 5^{2} \cdot 13 \) |
\( 2^{20} \cdot 5^{4} \cdot 13^{12} \) |
$3.03528$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.198700326$ |
2.384403914 |
\( \frac{40605232846917732}{2912260640310125} a + \frac{15507117639303424}{2912260640310125} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 44 i - 252\) , \( 10848 i + 12856\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+\left(44i-252\right){x}+10848i+12856$ |
| 84500.6-b3 |
84500.6-b |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
84500.6 |
\( 2^{2} \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{10} \cdot 13^{18} \) |
$3.04707$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.049291484$ |
2.365991253 |
\( \frac{40605232846917732}{2912260640310125} a + \frac{15507117639303424}{2912260640310125} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( 3886 i - 1460\) , \( 835002 i - 727142\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(3886i-1460\right){x}+835002i-727142$ |
| 84500.9-b3 |
84500.9-b |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
84500.9 |
\( 2^{2} \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{10} \cdot 13^{18} \) |
$3.04707$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{4} \) |
$1$ |
$0.049291484$ |
1.774493439 |
\( \frac{40605232846917732}{2912260640310125} a + \frac{15507117639303424}{2912260640310125} \) |
\( \bigl[i + 1\) , \( 1\) , \( i + 1\) , \( 313 i + 4140\) , \( 524905 i - 972807\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(313i+4140\right){x}+524905i-972807$ |
*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.
