| 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 |
| 9522.1-a1 |
9522.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
9522.1 |
\( 2 \cdot 3^{2} \cdot 23^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 23^{2} \) |
$1.76543$ |
$(a+1), (3), (23)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.177368191$ |
$4.491787368$ |
1.593400402 |
\( -\frac{389017}{828} \) |
\( \bigl[i\) , \( -1\) , \( 0\) , \( -1\) , \( -1\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-{x}^{2}-{x}-1$ |
| 9522.1-a2 |
9522.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
9522.1 |
\( 2 \cdot 3^{2} \cdot 23^{2} \) |
\( 2^{2} \cdot 3^{2} \cdot 23^{4} \) |
$1.76543$ |
$(a+1), (3), (23)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.354736382$ |
$2.245893684$ |
1.593400402 |
\( \frac{3463512697}{3174} \) |
\( \bigl[i\) , \( -1\) , \( 0\) , \( -31\) , \( -55\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-{x}^{2}-31{x}-55$ |
| 9522.1-b1 |
9522.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
9522.1 |
\( 2 \cdot 3^{2} \cdot 23^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 23^{2} \) |
$1.76543$ |
$(a+1), (3), (23)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$2.218580474$ |
$1.491436144$ |
2.205914071 |
\( -\frac{4956477625}{268272} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( -35\) , \( -82\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-35{x}-82$ |
| 9522.1-b2 |
9522.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
9522.1 |
\( 2 \cdot 3^{2} \cdot 23^{2} \) |
\( 2^{24} \cdot 3^{4} \cdot 23^{6} \) |
$1.76543$ |
$(a+1), (3), (23)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.739526824$ |
$0.497145381$ |
2.205914071 |
\( \frac{752329532375}{448524288} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( 190\) , \( -190\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+190{x}-190$ |
| 9522.1-b3 |
9522.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
9522.1 |
\( 2 \cdot 3^{2} \cdot 23^{2} \) |
\( 2^{12} \cdot 3^{2} \cdot 23^{12} \) |
$1.76543$ |
$(a+1), (3), (23)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.479053649$ |
$0.248572690$ |
2.205914071 |
\( \frac{50591419971625}{28422890688} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( -770\) , \( -1342\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-770{x}-1342$ |
| 9522.1-b4 |
9522.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
9522.1 |
\( 2 \cdot 3^{2} \cdot 23^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 23^{4} \) |
$1.76543$ |
$(a+1), (3), (23)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$4.437160948$ |
$0.745718072$ |
2.205914071 |
\( \frac{21081759765625}{57132} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( -575\) , \( -5266\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-575{x}-5266$ |
| 9522.1-c1 |
9522.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
9522.1 |
\( 2 \cdot 3^{2} \cdot 23^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 23^{2} \) |
$1.76543$ |
$(a+1), (3), (23)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$3.583234393$ |
3.583234393 |
\( \frac{2924207}{3312} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+3{x}+3$ |
| 9522.1-c2 |
9522.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
9522.1 |
\( 2 \cdot 3^{2} \cdot 23^{2} \) |
\( 2^{4} \cdot 3^{8} \cdot 23^{4} \) |
$1.76543$ |
$(a+1), (3), (23)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.791617196$ |
3.583234393 |
\( \frac{545338513}{171396} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -17\) , \( 11\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-17{x}+11$ |
| 9522.1-c3 |
9522.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
9522.1 |
\( 2 \cdot 3^{2} \cdot 23^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 23^{8} \) |
$1.76543$ |
$(a+1), (3), (23)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.895808598$ |
3.583234393 |
\( \frac{135559106353}{5037138} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -107\) , \( -457\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-107{x}-457$ |
| 9522.1-c4 |
9522.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
9522.1 |
\( 2 \cdot 3^{2} \cdot 23^{2} \) |
\( 2^{2} \cdot 3^{16} \cdot 23^{2} \) |
$1.76543$ |
$(a+1), (3), (23)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.895808598$ |
3.583234393 |
\( \frac{1666957239793}{301806} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -247\) , \( 1391\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-247{x}+1391$ |
*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.
