| 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-a6 |
100.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
100.2 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{4} \) |
$0.56516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$6.423095656$ |
0.535257971 |
\( \frac{21296}{25} \) |
\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i - 1\) , \( -i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}-i$ |
| 2000.2-b6 |
2000.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2000.2 |
\( 2^{4} \cdot 5^{3} \) |
\( 2^{4} \cdot 5^{10} \) |
$1.19516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.872495702$ |
1.436247851 |
\( \frac{21296}{25} \) |
\( \bigl[i + 1\) , \( 1\) , \( i + 1\) , \( 3 i + 3\) , \( 5 i + 1\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(3i+3\right){x}+5i+1$ |
| 2000.3-b6 |
2000.3-b |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2000.3 |
\( 2^{4} \cdot 5^{3} \) |
\( 2^{4} \cdot 5^{10} \) |
$1.19516$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.872495702$ |
1.436247851 |
\( \frac{21296}{25} \) |
\( \bigl[i + 1\) , \( -1\) , \( i + 1\) , \( -5 i + 3\) , \( 5 i - 1\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(-5i+3\right){x}+5i-1$ |
| 2500.3-a6 |
2500.3-a |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2500.3 |
\( 2^{2} \cdot 5^{4} \) |
\( 2^{4} \cdot 5^{16} \) |
$1.26373$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.284619131$ |
1.284619131 |
\( \frac{21296}{25} \) |
\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( -23\) , \( 39 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-23{x}+39i$ |
| 6400.2-e6 |
6400.2-e |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
6400.2 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{4} \) |
$1.59850$ |
$(a+1), (-a-2), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$0.413436914$ |
$3.211547828$ |
2.655544846 |
\( \frac{21296}{25} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( -4\) , \( 4 i\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}-4{x}+4i$ |
| 8100.2-c6 |
8100.2-c |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8100.2 |
\( 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 5^{4} \) |
$1.69547$ |
$(a+1), (-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$1$ |
$2.141031885$ |
2.141031885 |
\( \frac{21296}{25} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -9\) , \( 5 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}-9{x}+5i$ |
| 25600.2-i6 |
25600.2-i |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
25600.2 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{22} \cdot 5^{4} \) |
$2.26063$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.270907247$ |
2.270907247 |
\( \frac{21296}{25} \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( 8 i\) , \( 8 i - 8\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}+8i{x}+8i-8$ |
| 25600.2-n6 |
25600.2-n |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
25600.2 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{22} \cdot 5^{4} \) |
$2.26063$ |
$(a+1), (-a-2), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.270907247$ |
2.270907247 |
\( \frac{21296}{25} \) |
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( -8 i\) , \( -8 i - 8\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}-8i{x}-8i-8$ |
| 28900.4-c6 |
28900.4-c |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28900.4 |
\( 2^{2} \cdot 5^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 5^{4} \cdot 17^{6} \) |
$2.33020$ |
$(a+1), (-a-2), (2a+1), (a+4)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1.179442562$ |
$1.557829519$ |
3.674740881 |
\( \frac{21296}{25} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( 7 i + 14\) , \( -16 i - 12\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(7i+14\right){x}-16i-12$ |
| 28900.6-c6 |
28900.6-c |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
28900.6 |
\( 2^{2} \cdot 5^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 5^{4} \cdot 17^{6} \) |
$2.33020$ |
$(a+1), (-a-2), (2a+1), (a-4)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1.179442562$ |
$1.557829519$ |
3.674740881 |
\( \frac{21296}{25} \) |
\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -7 i + 14\) , \( 16 i - 12\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-7i+14\right){x}+16i-12$ |
| 32000.2-e6 |
32000.2-e |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
32000.2 |
\( 2^{8} \cdot 5^{3} \) |
\( 2^{16} \cdot 5^{10} \) |
$2.39032$ |
$(a+1), (-a-2), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \) |
$0.641865234$ |
$1.436247851$ |
3.687510258 |
\( \frac{21296}{25} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( 14 i + 11\) , \( 29 i - 3\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(14i+11\right){x}+29i-3$ |
| 32000.3-d6 |
32000.3-d |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
32000.3 |
\( 2^{8} \cdot 5^{3} \) |
\( 2^{16} \cdot 5^{10} \) |
$2.39032$ |
$(a+1), (-a-2), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \) |
$0.641865234$ |
$1.436247851$ |
3.687510258 |
\( \frac{21296}{25} \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( -14 i + 11\) , \( 29 i + 3\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(-14i+11\right){x}+29i+3$ |
| 67600.4-f6 |
67600.4-f |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.4 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 5^{4} \cdot 13^{6} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.781446210$ |
1.781446210 |
\( \frac{21296}{25} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( 10 i - 5\) , \( -9 i + 12\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(10i-5\right){x}-9i+12$ |
| 67600.6-d6 |
67600.6-d |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.6 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 5^{4} \cdot 13^{6} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.781446210$ |
1.781446210 |
\( \frac{21296}{25} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( i + 1\) , \( -13 i - 5\) , \( 4 i + 23\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-13i-5\right){x}+4i+23$ |
| 84500.4-f6 |
84500.4-f |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
84500.4 |
\( 2^{2} \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{4} \cdot 5^{10} \cdot 13^{6} \) |
$3.04707$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$0.539016719$ |
$0.796686965$ |
5.153131129 |
\( \frac{21296}{25} \) |
\( \bigl[i + 1\) , \( -1\) , \( 0\) , \( -15 i + 58\) , \( 80 i - 184\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-15i+58\right){x}+80i-184$ |
| 84500.6-c6 |
84500.6-c |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
84500.6 |
\( 2^{2} \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{4} \cdot 5^{10} \cdot 13^{6} \) |
$3.04707$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.796686965$ |
1.593373930 |
\( \frac{21296}{25} \) |
\( \bigl[i + 1\) , \( -1\) , \( i + 1\) , \( 50 i - 30\) , \( -25 i - 178\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(50i-30\right){x}-25i-178$ |
| 84500.7-b6 |
84500.7-b |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
84500.7 |
\( 2^{2} \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{4} \cdot 5^{10} \cdot 13^{6} \) |
$3.04707$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.796686965$ |
1.593373930 |
\( \frac{21296}{25} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( -52 i - 30\) , \( 24 i - 178\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-52i-30\right){x}+24i-178$ |
| 84500.9-e6 |
84500.9-e |
$8$ |
$12$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
84500.9 |
\( 2^{2} \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{4} \cdot 5^{10} \cdot 13^{6} \) |
$3.04707$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$0.539016719$ |
$0.796686965$ |
5.153131129 |
\( \frac{21296}{25} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( 15 i + 58\) , \( -80 i - 184\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(15i+58\right){x}-80i-184$ |
*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.
