| 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 |
| 100.2-a5 |
100.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{12} \) |
$0.56516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$2.141031885$ |
0.535257971 |
\( -\frac{20720464}{15625} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i + 9\) , \( 17 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+9\right){x}+17i$ |
| 2000.2-b5 |
2000.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2000.2 |
\( 2^{4} \cdot 5^{3} \) |
\( 2^{4} \cdot 5^{18} \) |
$1.19516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.957498567$ |
1.436247851 |
\( -\frac{20720464}{15625} \) |
\( \bigl[i + 1\) , \( 1\) , \( i + 1\) , \( -37 i - 27\) , \( -193 i - 35\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(-37i-27\right){x}-193i-35$ |
| 2000.3-b5 |
2000.3-b |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2000.3 |
\( 2^{4} \cdot 5^{3} \) |
\( 2^{4} \cdot 5^{18} \) |
$1.19516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.957498567$ |
1.436247851 |
\( -\frac{20720464}{15625} \) |
\( \bigl[i + 1\) , \( -1\) , \( i + 1\) , \( 35 i - 27\) , \( -193 i + 35\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(35i-27\right){x}-193i+35$ |
| 2500.3-a5 |
2500.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2500.3 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{4} \cdot 5^{24} \) |
$1.26373$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.428206377$ |
1.284619131 |
\( -\frac{20720464}{15625} \) |
\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( 227\) , \( -1961 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+227{x}-1961i$ |
| 6400.2-e5 |
6400.2-e |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6400.2 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{12} \) |
$1.59850$ |
$(a+1), (-a-2), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$0.137812304$ |
$1.070515942$ |
2.655544846 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 36\) , \( -140 i\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+36{x}-140i$ |
| 8100.2-c5 |
8100.2-c |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8100.2 |
\( 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{12} \) |
$1.69547$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{3} \) |
$1$ |
$0.713677295$ |
2.141031885 |
\( -\frac{20720464}{15625} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 81\) , \( -391 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+81{x}-391i$ |
| 25600.2-i5 |
25600.2-i |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
25600.2 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{22} \cdot 5^{12} \) |
$2.26063$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.756969082$ |
2.270907247 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( -72 i\) , \( -280 i + 280\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}-72i{x}-280i+280$ |
| 25600.2-n5 |
25600.2-n |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
25600.2 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{22} \cdot 5^{12} \) |
$2.26063$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.756969082$ |
2.270907247 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 72 i\) , \( 280 i + 280\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+72i{x}+280i+280$ |
| 28900.4-c5 |
28900.4-c |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28900.4 |
\( 2^{2} \cdot 5^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 5^{12} \cdot 17^{6} \) |
$2.33020$ |
$(a+1), (-a-2), (2a+1), (a+4)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$0.393147520$ |
$0.519276506$ |
3.674740881 |
\( -\frac{20720464}{15625} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( -73 i - 136\) , \( 750 i + 774\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(-73i-136\right){x}+750i+774$ |
| 28900.6-c5 |
28900.6-c |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28900.6 |
\( 2^{2} \cdot 5^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 5^{12} \cdot 17^{6} \) |
$2.33020$ |
$(a+1), (-a-2), (2a+1), (a-4)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$0.393147520$ |
$0.519276506$ |
3.674740881 |
\( -\frac{20720464}{15625} \) |
\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( 73 i - 136\) , \( -750 i + 774\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(73i-136\right){x}-750i+774$ |
| 32000.2-e5 |
32000.2-e |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
32000.2 |
\( 2^{8} \cdot 5^{3} \) |
\( 2^{16} \cdot 5^{18} \) |
$2.39032$ |
$(a+1), (-a-2), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \) |
$1.925595704$ |
$0.478749283$ |
3.687510258 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( -146 i - 109\) , \( -1395 i - 171\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(-146i-109\right){x}-1395i-171$ |
| 32000.3-d5 |
32000.3-d |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
32000.3 |
\( 2^{8} \cdot 5^{3} \) |
\( 2^{16} \cdot 5^{18} \) |
$2.39032$ |
$(a+1), (-a-2), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \) |
$1.925595704$ |
$0.478749283$ |
3.687510258 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( 146 i - 109\) , \( -1395 i + 171\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(146i-109\right){x}-1395i+171$ |
| 67600.4-f5 |
67600.4-f |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.4 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 5^{12} \cdot 13^{6} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.593815403$ |
1.781446210 |
\( -\frac{20720464}{15625} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( -110 i + 45\) , \( 203 i - 696\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-110i+45\right){x}+203i-696$ |
| 67600.6-d5 |
67600.6-d |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.6 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 5^{12} \cdot 13^{6} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.593815403$ |
1.781446210 |
\( -\frac{20720464}{15625} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( i + 1\) , \( 107 i + 45\) , \( -158 i - 805\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}^{2}+\left(107i+45\right){x}-158i-805$ |
| 84500.4-f5 |
84500.4-f |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
84500.4 |
\( 2^{2} \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{4} \cdot 5^{18} \cdot 13^{6} \) |
$3.04707$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$1.617050157$ |
$0.265562321$ |
5.153131129 |
\( -\frac{20720464}{15625} \) |
\( \bigl[i + 1\) , \( -1\) , \( 0\) , \( 145 i - 572\) , \( -3198 i + 7970\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-{x}^{2}+\left(145i-572\right){x}-3198i+7970$ |
| 84500.6-c5 |
84500.6-c |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
84500.6 |
\( 2^{2} \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{4} \cdot 5^{18} \cdot 13^{6} \) |
$3.04707$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.265562321$ |
1.593373930 |
\( -\frac{20720464}{15625} \) |
\( \bigl[i + 1\) , \( -1\) , \( i + 1\) , \( -510 i + 300\) , \( 331 i + 8364\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(-510i+300\right){x}+331i+8364$ |
| 84500.7-b5 |
84500.7-b |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
84500.7 |
\( 2^{2} \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{4} \cdot 5^{18} \cdot 13^{6} \) |
$3.04707$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.265562321$ |
1.593373930 |
\( -\frac{20720464}{15625} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( 508 i + 300\) , \( -332 i + 8364\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(508i+300\right){x}-332i+8364$ |
| 84500.9-e5 |
84500.9-e |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
84500.9 |
\( 2^{2} \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{4} \cdot 5^{18} \cdot 13^{6} \) |
$3.04707$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$1.617050157$ |
$0.265562321$ |
5.153131129 |
\( -\frac{20720464}{15625} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -145 i - 572\) , \( 3198 i + 7970\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-145i-572\right){x}+3198i+7970$ |
*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.
