| 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-a7 |
100.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{2} \) |
$0.56516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$6.423095656$ |
0.535257971 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-{x}$ |
| 2000.2-b7 |
2000.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2000.2 |
\( 2^{4} \cdot 5^{3} \) |
\( 2^{8} \cdot 5^{8} \) |
$1.19516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.872495702$ |
1.436247851 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( 6 i + 4\) , \( 4 i - 5\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(6i+4\right){x}+4i-5$ |
| 2000.3-b7 |
2000.3-b |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2000.3 |
\( 2^{4} \cdot 5^{3} \) |
\( 2^{8} \cdot 5^{8} \) |
$1.19516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.872495702$ |
1.436247851 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( -6 i + 4\) , \( -4 i - 5\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(-6i+4\right){x}-4i-5$ |
| 2500.3-a7 |
2500.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2500.3 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{8} \cdot 5^{14} \) |
$1.26373$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.284619131$ |
1.284619131 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -33\) , \( -62\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-33{x}-62$ |
| 6400.2-e7 |
6400.2-e |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6400.2 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{2} \) |
$1.59850$ |
$(a+1), (-a-2), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.826873828$ |
$6.423095656$ |
2.655544846 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+{x}$ |
| 8100.2-c7 |
8100.2-c |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8100.2 |
\( 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 5^{2} \) |
$1.69547$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$2.141031885$ |
2.141031885 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -12\) , \( -11\bigr] \) |
${y}^2={x}^{3}-12{x}-11$ |
| 25600.2-i7 |
25600.2-i |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
25600.2 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{2} \) |
$2.26063$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$4.541814495$ |
2.270907247 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( -2 i\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}-2i{x}$ |
| 25600.2-n7 |
25600.2-n |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
25600.2 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{2} \) |
$2.26063$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$4.541814495$ |
2.270907247 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 2 i\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+2i{x}$ |
| 28900.4-c7 |
28900.4-c |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28900.4 |
\( 2^{2} \cdot 5^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 5^{2} \cdot 17^{6} \) |
$2.33020$ |
$(a+1), (-a-2), (2a+1), (a+4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$2.358885124$ |
$1.557829519$ |
3.674740881 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 10 i + 20\) , \( 18 i - 9\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(10i+20\right){x}+18i-9$ |
| 28900.6-c7 |
28900.6-c |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28900.6 |
\( 2^{2} \cdot 5^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 5^{2} \cdot 17^{6} \) |
$2.33020$ |
$(a+1), (-a-2), (2a+1), (a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$2.358885124$ |
$1.557829519$ |
3.674740881 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( -10 i + 20\) , \( 18 i + 9\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(-10i+20\right){x}+18i+9$ |
| 32000.2-e7 |
32000.2-e |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
32000.2 |
\( 2^{8} \cdot 5^{3} \) |
\( 2^{8} \cdot 5^{8} \) |
$2.39032$ |
$(a+1), (-a-2), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1.283730469$ |
$2.872495702$ |
3.687510258 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( -6 i - 4\) , \( 5 i + 4\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(-6i-4\right){x}+5i+4$ |
| 32000.3-d7 |
32000.3-d |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
32000.3 |
\( 2^{8} \cdot 5^{3} \) |
\( 2^{8} \cdot 5^{8} \) |
$2.39032$ |
$(a+1), (-a-2), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1.283730469$ |
$2.872495702$ |
3.687510258 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( 6 i - 4\) , \( 5 i - 4\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(6i-4\right){x}+5i-4$ |
| 67600.4-f7 |
67600.4-f |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.4 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{2} \cdot 13^{6} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.781446210$ |
1.781446210 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 16 i - 7\) , \( -21 i - 9\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+\left(16i-7\right){x}-21i-9$ |
| 67600.6-d7 |
67600.6-d |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.6 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{2} \cdot 13^{6} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.781446210$ |
1.781446210 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( -16 i - 7\) , \( -21 i + 9\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+\left(-16i-7\right){x}-21i+9$ |
| 84500.4-f7 |
84500.4-f |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
84500.4 |
\( 2^{2} \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{8} \cdot 13^{6} \) |
$3.04707$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.078033438$ |
$0.796686965$ |
5.153131129 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( -22 i + 84\) , \( 234 i + 57\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(-22i+84\right){x}+234i+57$ |
| 84500.6-c7 |
84500.6-c |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
84500.6 |
\( 2^{2} \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{8} \cdot 13^{6} \) |
$3.04707$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.796686965$ |
1.593373930 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( 74 i - 44\) , \( 174 i - 13\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(74i-44\right){x}+174i-13$ |
| 84500.7-b7 |
84500.7-b |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
84500.7 |
\( 2^{2} \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{8} \cdot 13^{6} \) |
$3.04707$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.796686965$ |
1.593373930 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( -74 i - 44\) , \( 174 i + 13\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(-74i-44\right){x}+174i+13$ |
| 84500.9-e7 |
84500.9-e |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
84500.9 |
\( 2^{2} \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{8} \cdot 13^{6} \) |
$3.04707$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.078033438$ |
$0.796686965$ |
5.153131129 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( 22 i + 84\) , \( 234 i - 57\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(22i+84\right){x}+234i-57$ |
*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.
