| 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 |
| 20808.2-a1 |
20808.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
20808.2 |
\( 2^{3} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{10} \cdot 17^{2} \) |
$2.14648$ |
$(a+1), (a+4), (a-4), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2 \cdot 5 \) |
$0.035837594$ |
$2.721420930$ |
1.950583574 |
\( -\frac{2249728}{4131} \) |
\( \bigl[0\) , \( i\) , \( i + 1\) , \( 4\) , \( 8 i\bigr] \) |
${y}^2+\left(i+1\right){y}={x}^{3}+i{x}^{2}+4{x}+8i$ |
| 20808.2-b1 |
20808.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
20808.2 |
\( 2^{3} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{10} \cdot 3^{8} \cdot 17^{4} \) |
$2.14648$ |
$(a+1), (a+4), (a-4), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.152359192$ |
$1.473245113$ |
3.591398975 |
\( -\frac{31250}{23409} \) |
\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 2\) , \( -42 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}+2{x}-42i$ |
| 20808.2-b2 |
20808.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
20808.2 |
\( 2^{3} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 17^{2} \) |
$2.14648$ |
$(a+1), (a+4), (a-4), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.304718385$ |
$2.946490226$ |
3.591398975 |
\( \frac{12194500}{153} \) |
\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 12\) , \( -18 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}+12{x}-18i$ |
| 20808.2-c1 |
20808.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
20808.2 |
\( 2^{3} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{10} \cdot 3^{4} \cdot 17^{8} \) |
$2.14648$ |
$(a+1), (a+4), (a-4), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.809400023$ |
3.237600092 |
\( \frac{1285471294}{751689} \) |
\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( -72\) , \( -36 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-72{x}-36i$ |
| 20808.2-c2 |
20808.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
20808.2 |
\( 2^{3} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 17^{4} \) |
$2.14648$ |
$(a+1), (a+4), (a-4), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.618800046$ |
3.237600092 |
\( \frac{40873252}{23409} \) |
\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( 18\) , \( 0\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+18{x}$ |
| 20808.2-c3 |
20808.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
20808.2 |
\( 2^{3} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{10} \cdot 3^{16} \cdot 17^{2} \) |
$2.14648$ |
$(a+1), (a+4), (a-4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.809400023$ |
3.237600092 |
\( \frac{22994537186}{111537} \) |
\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( 188\) , \( 1020 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+188{x}+1020i$ |
| 20808.2-c4 |
20808.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
20808.2 |
\( 2^{3} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 17^{2} \) |
$2.14648$ |
$(a+1), (a+4), (a-4), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$3.237600092$ |
3.237600092 |
\( \frac{61918288}{153} \) |
\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( 13\) , \( -16 i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+13{x}-16i$ |
| 20808.2-d1 |
20808.2-d |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
20808.2 |
\( 2^{3} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 17^{10} \) |
$2.14648$ |
$(a+1), (a+4), (a-4), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$0.595188230$ |
3.571129383 |
\( \frac{57530252288}{38336139} \) |
\( \bigl[0\) , \( i\) , \( i + 1\) , \( -128\) , \( 173 i\bigr] \) |
${y}^2+\left(i+1\right){y}={x}^{3}+i{x}^{2}-128{x}+173i$ |
*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.
