| 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 |
| 9522.2-a1 |
9522.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9522.2 |
\( 2 \cdot 3^{2} \cdot 23^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 23^{2} \) |
$2.49670$ |
$(a), (-a-1), (a-1), (23)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.113812930$ |
$4.491787368$ |
2.891916725 |
\( -\frac{389017}{828} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -1\) , \( 1\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-{x}+1$ |
| 9522.2-a2 |
9522.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9522.2 |
\( 2 \cdot 3^{2} \cdot 23^{2} \) |
\( 2^{2} \cdot 3^{2} \cdot 23^{4} \) |
$2.49670$ |
$(a), (-a-1), (a-1), (23)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.455251720$ |
$2.245893684$ |
2.891916725 |
\( \frac{3463512697}{3174} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -31\) , \( 55\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-31{x}+55$ |
| 9522.2-b1 |
9522.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9522.2 |
\( 2 \cdot 3^{2} \cdot 23^{2} \) |
\( 2^{4} \cdot 3^{18} \cdot 23^{2} \) |
$2.49670$ |
$(a), (-a-1), (a-1), (23)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.493497679$ |
$1.242212315$ |
1.733907557 |
\( -\frac{1201765573}{2716254} a + \frac{6953457961}{5432508} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( 19 a + 8\) , \( -6 a + 42\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(19a+8\right){x}-6a+42$ |
| 9522.2-b2 |
9522.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9522.2 |
\( 2 \cdot 3^{2} \cdot 23^{2} \) |
\( 2^{2} \cdot 3^{21} \cdot 23^{4} \) |
$2.49670$ |
$(a), (-a-1), (a-1), (23)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.986995359$ |
$0.621106157$ |
1.733907557 |
\( \frac{28657073203607}{45543430818} a + \frac{88833484644931}{45543430818} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( -91 a - 2\) , \( -130 a + 340\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-91a-2\right){x}-130a+340$ |
| 9522.2-c1 |
9522.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9522.2 |
\( 2 \cdot 3^{2} \cdot 23^{2} \) |
\( 2^{4} \cdot 3^{18} \cdot 23^{2} \) |
$2.49670$ |
$(a), (-a-1), (a-1), (23)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.493497679$ |
$1.242212315$ |
1.733907557 |
\( \frac{1201765573}{2716254} a + \frac{6953457961}{5432508} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( -20 a + 8\) , \( 6 a + 42\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-20a+8\right){x}+6a+42$ |
| 9522.2-c2 |
9522.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9522.2 |
\( 2 \cdot 3^{2} \cdot 23^{2} \) |
\( 2^{2} \cdot 3^{21} \cdot 23^{4} \) |
$2.49670$ |
$(a), (-a-1), (a-1), (23)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.986995359$ |
$0.621106157$ |
1.733907557 |
\( -\frac{28657073203607}{45543430818} a + \frac{88833484644931}{45543430818} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( 90 a - 2\) , \( 130 a + 340\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(90a-2\right){x}+130a+340$ |
| 9522.2-d1 |
9522.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9522.2 |
\( 2 \cdot 3^{2} \cdot 23^{2} \) |
\( 2 \cdot 3^{11} \cdot 23^{4} \) |
$2.49670$ |
$(a), (-a-1), (a-1), (23)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.164832972$ |
$1.450779499$ |
4.058277544 |
\( -\frac{43654702391}{6941538} a - \frac{57596930017}{3470769} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -26 a - 15\) , \( -61 a + 49\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-26a-15\right){x}-61a+49$ |
| 9522.2-d2 |
9522.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9522.2 |
\( 2 \cdot 3^{2} \cdot 23^{2} \) |
\( 2^{2} \cdot 3^{10} \cdot 23^{2} \) |
$2.49670$ |
$(a), (-a-1), (a-1), (23)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.082416486$ |
$2.901558998$ |
4.058277544 |
\( -\frac{6353551}{16767} a - \frac{12372337}{33534} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -a - 5\) , \( -4 a + 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a-5\right){x}-4a+7$ |
| 9522.2-e1 |
9522.2-e |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9522.2 |
\( 2 \cdot 3^{2} \cdot 23^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 23^{2} \) |
$2.49670$ |
$(a), (-a-1), (a-1), (23)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$1.491436144$ |
2.109209222 |
\( -\frac{4956477625}{268272} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( 82\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-36{x}+82$ |
| 9522.2-e2 |
9522.2-e |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9522.2 |
\( 2 \cdot 3^{2} \cdot 23^{2} \) |
\( 2^{24} \cdot 3^{4} \cdot 23^{6} \) |
$2.49670$ |
$(a), (-a-1), (a-1), (23)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.497145381$ |
2.109209222 |
\( \frac{752329532375}{448524288} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 189\) , \( 190\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+189{x}+190$ |
| 9522.2-e3 |
9522.2-e |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9522.2 |
\( 2 \cdot 3^{2} \cdot 23^{2} \) |
\( 2^{12} \cdot 3^{2} \cdot 23^{12} \) |
$2.49670$ |
$(a), (-a-1), (a-1), (23)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.248572690$ |
2.109209222 |
\( \frac{50591419971625}{28422890688} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -771\) , \( 1342\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-771{x}+1342$ |
| 9522.2-e4 |
9522.2-e |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9522.2 |
\( 2 \cdot 3^{2} \cdot 23^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 23^{4} \) |
$2.49670$ |
$(a), (-a-1), (a-1), (23)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.745718072$ |
2.109209222 |
\( \frac{21081759765625}{57132} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -576\) , \( 5266\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-576{x}+5266$ |
| 9522.2-f1 |
9522.2-f |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9522.2 |
\( 2 \cdot 3^{2} \cdot 23^{2} \) |
\( 2 \cdot 3^{11} \cdot 23^{4} \) |
$2.49670$ |
$(a), (-a-1), (a-1), (23)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.164832972$ |
$1.450779499$ |
4.058277544 |
\( \frac{43654702391}{6941538} a - \frac{57596930017}{3470769} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 23 a - 14\) , \( 47 a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(23a-14\right){x}+47a$ |
| 9522.2-f2 |
9522.2-f |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9522.2 |
\( 2 \cdot 3^{2} \cdot 23^{2} \) |
\( 2^{2} \cdot 3^{10} \cdot 23^{2} \) |
$2.49670$ |
$(a), (-a-1), (a-1), (23)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.082416486$ |
$2.901558998$ |
4.058277544 |
\( \frac{6353551}{16767} a - \frac{12372337}{33534} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -2 a - 4\) , \( 8\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a-4\right){x}+8$ |
| 9522.2-g1 |
9522.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9522.2 |
\( 2 \cdot 3^{2} \cdot 23^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 23^{2} \) |
$2.49670$ |
$(a), (-a-1), (a-1), (23)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.404422894$ |
$3.583234393$ |
4.098792611 |
\( \frac{2924207}{3312} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+3{x}+3$ |
| 9522.2-g2 |
9522.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9522.2 |
\( 2 \cdot 3^{2} \cdot 23^{2} \) |
\( 2^{4} \cdot 3^{8} \cdot 23^{4} \) |
$2.49670$ |
$(a), (-a-1), (a-1), (23)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.808845789$ |
$1.791617196$ |
4.098792611 |
\( \frac{545338513}{171396} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -17\) , \( 11\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-17{x}+11$ |
| 9522.2-g3 |
9522.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9522.2 |
\( 2 \cdot 3^{2} \cdot 23^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 23^{8} \) |
$2.49670$ |
$(a), (-a-1), (a-1), (23)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.617691578$ |
$0.895808598$ |
4.098792611 |
\( \frac{135559106353}{5037138} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -107\) , \( -457\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-107{x}-457$ |
| 9522.2-g4 |
9522.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9522.2 |
\( 2 \cdot 3^{2} \cdot 23^{2} \) |
\( 2^{2} \cdot 3^{16} \cdot 23^{2} \) |
$2.49670$ |
$(a), (-a-1), (a-1), (23)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.617691578$ |
$0.895808598$ |
4.098792611 |
\( \frac{1666957239793}{301806} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -247\) , \( 1391\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-247{x}+1391$ |
*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.
