| 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 |
| 9216.2-a1 |
9216.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{3} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.504669137$ |
$1.360046576$ |
3.882715037 |
\( -\frac{41803784}{9} a - \frac{21890312}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 64 a - 63\) , \( 292 a - 37\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(64a-63\right){x}+292a-37$ |
| 9216.2-a2 |
9216.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{3} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.504669137$ |
$1.360046576$ |
3.882715037 |
\( \frac{41803784}{9} a - \frac{21890312}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -64 a - 63\) , \( -292 a - 37\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-64a-63\right){x}-292a-37$ |
| 9216.2-a3 |
9216.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{9} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.504669137$ |
$1.360046576$ |
3.882715037 |
\( -\frac{27471928}{6561} a - \frac{56129704}{6561} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 24 a + 17\) , \( -12 a - 101\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(24a+17\right){x}-12a-101$ |
| 9216.2-a4 |
9216.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{9} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.504669137$ |
$1.360046576$ |
3.882715037 |
\( \frac{27471928}{6561} a - \frac{56129704}{6561} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -24 a + 17\) , \( 12 a - 101\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-24a+17\right){x}+12a-101$ |
| 9216.2-a5 |
9216.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{6} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.504669137$ |
$2.720093152$ |
3.882715037 |
\( -\frac{121088}{81} a - \frac{65728}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -4 a - 3\) , \( -4 a - 1\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-4a-3\right){x}-4a-1$ |
| 9216.2-a6 |
9216.2-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{6} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.504669137$ |
$2.720093152$ |
3.882715037 |
\( \frac{121088}{81} a - \frac{65728}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 4 a - 3\) , \( 4 a - 1\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(4a-3\right){x}+4a-1$ |
| 9216.2-b1 |
9216.2-b |
$8$ |
$20$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{20} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{4} \) |
$2.833291884$ |
$0.687971971$ |
2.756621001 |
\( -\frac{873722816}{59049} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -159\) , \( -765\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-159{x}-765$ |
| 9216.2-b2 |
9216.2-b |
$8$ |
$20$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{25} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$5.666583769$ |
$0.343985985$ |
2.756621001 |
\( -\frac{2514081593672}{3486784401} a - \frac{1943385699640}{3486784401} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 220 a - 139\) , \( -2304 a - 1593\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(220a-139\right){x}-2304a-1593$ |
| 9216.2-b3 |
9216.2-b |
$8$ |
$20$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{25} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$5.666583769$ |
$0.343985985$ |
2.756621001 |
\( \frac{2514081593672}{3486784401} a - \frac{1943385699640}{3486784401} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -220 a - 139\) , \( 2304 a - 1593\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-220a-139\right){x}+2304a-1593$ |
| 9216.2-b4 |
9216.2-b |
$8$ |
$20$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{4} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2Cs, 5B |
$1$ |
\( 2^{4} \) |
$0.566658376$ |
$3.439859856$ |
2.756621001 |
\( \frac{64}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 3\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+{x}+3$ |
| 9216.2-b5 |
9216.2-b |
$8$ |
$20$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{2} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \) |
$1.133316753$ |
$3.439859856$ |
2.756621001 |
\( \frac{85184}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -7\) , \( -5\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-7{x}-5$ |
| 9216.2-b6 |
9216.2-b |
$8$ |
$20$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{5} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$1.133316753$ |
$1.719929928$ |
2.756621001 |
\( -\frac{2400472}{81} a + \frac{4984520}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 20 a + 21\) , \( -16 a + 71\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(20a+21\right){x}-16a+71$ |
| 9216.2-b7 |
9216.2-b |
$8$ |
$20$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{5} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$1.133316753$ |
$1.719929928$ |
2.756621001 |
\( \frac{2400472}{81} a + \frac{4984520}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -20 a + 21\) , \( 16 a + 71\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-20a+21\right){x}+16a+71$ |
| 9216.2-b8 |
9216.2-b |
$8$ |
$20$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{10} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2 \) |
$5.666583769$ |
$0.687971971$ |
2.756621001 |
\( \frac{58591911104}{243} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -647\) , \( 6555\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-647{x}+6555$ |
| 9216.2-c1 |
9216.2-c |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{26} \cdot 3^{7} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.911404267$ |
1.288920275 |
\( -\frac{18202756}{81} a - \frac{253086988}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -44 a + 213\) , \( 832 a + 455\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-44a+213\right){x}+832a+455$ |
| 9216.2-c2 |
9216.2-c |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{26} \cdot 3^{7} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.911404267$ |
1.288920275 |
\( \frac{18202756}{81} a - \frac{253086988}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 44 a + 213\) , \( -832 a + 455\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(44a+213\right){x}-832a+455$ |
| 9216.2-c3 |
9216.2-c |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{4} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$3.645617069$ |
1.288920275 |
\( -\frac{372736}{27} a - \frac{352256}{27} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -4 a + 3\) , \( 2 a - 7\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-4a+3\right){x}+2a-7$ |
| 9216.2-c4 |
9216.2-c |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{4} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$3.645617069$ |
1.288920275 |
\( \frac{372736}{27} a - \frac{352256}{27} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 4 a + 3\) , \( -2 a - 7\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(4a+3\right){x}-2a-7$ |
| 9216.2-c5 |
9216.2-c |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{8} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.822808534$ |
1.288920275 |
\( -\frac{855712}{729} a + \frac{467888}{729} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 4 a + 13\) , \( -16 a - 1\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(4a+13\right){x}-16a-1$ |
| 9216.2-c6 |
9216.2-c |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{8} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.822808534$ |
1.288920275 |
\( \frac{855712}{729} a + \frac{467888}{729} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -4 a + 13\) , \( 16 a - 1\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-4a+13\right){x}+16a-1$ |
| 9216.2-c7 |
9216.2-c |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{26} \cdot 3^{13} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.911404267$ |
1.288920275 |
\( -\frac{715706108}{531441} a + \frac{421307996}{531441} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 36 a - 27\) , \( 96 a + 87\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(36a-27\right){x}+96a+87$ |
| 9216.2-c8 |
9216.2-c |
$8$ |
$12$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{26} \cdot 3^{13} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.911404267$ |
1.288920275 |
\( \frac{715706108}{531441} a + \frac{421307996}{531441} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -36 a - 27\) , \( -96 a + 87\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-36a-27\right){x}-96a+87$ |
| 9216.2-d1 |
9216.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{23} \cdot 3^{2} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.046050378$ |
$1.884597082$ |
2.787957272 |
\( \frac{110584}{3} a - 1178880 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 32 a + 1\) , \( -68 a - 85\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(32a+1\right){x}-68a-85$ |
| 9216.2-d2 |
9216.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{23} \cdot 3^{5} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.046050378$ |
$1.884597082$ |
2.787957272 |
\( -\frac{1862600}{81} a - \frac{2730832}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 12 a + 21\) , \( -24 a + 39\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(12a+21\right){x}-24a+39$ |
| 9216.2-d3 |
9216.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{4} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.523025189$ |
$3.769194165$ |
2.787957272 |
\( 640 a + \frac{6784}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 2 a + 1\) , \( -2 a - 1\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(2a+1\right){x}-2a-1$ |
| 9216.2-d4 |
9216.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{5} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.046050378$ |
$3.769194165$ |
2.787957272 |
\( -\frac{109408}{81} a + \frac{158240}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -2 a - 2\) , \( 2 a + 2\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-2a-2\right){x}+2a+2$ |
| 9216.2-e1 |
9216.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{23} \cdot 3^{14} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.020976159$ |
1.443878331 |
\( -\frac{105306568}{531441} a + \frac{136151936}{531441} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -4 a - 27\) , \( 56 a - 73\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-4a-27\right){x}+56a-73$ |
| 9216.2-e2 |
9216.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{10} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.041952319$ |
1.443878331 |
\( \frac{1668992}{729} a + \frac{3939968}{729} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 6 a + 13\) , \( 6 a - 21\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(6a+13\right){x}+6a-21$ |
| 9216.2-e3 |
9216.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{11} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.041952319$ |
1.443878331 |
\( -\frac{24685856}{6561} a + \frac{51528992}{6561} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 4 a + 16\) , \( 14 a - 16\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(4a+16\right){x}+14a-16$ |
| 9216.2-e4 |
9216.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{23} \cdot 3^{5} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$1.020976159$ |
1.443878331 |
\( \frac{576294904}{27} a + \frac{292647184}{27} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 96 a + 193\) , \( 564 a - 1173\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(96a+193\right){x}+564a-1173$ |
| 9216.2-f1 |
9216.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{23} \cdot 3^{14} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.020976159$ |
1.443878331 |
\( \frac{105306568}{531441} a + \frac{136151936}{531441} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 4 a - 27\) , \( -56 a - 73\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(4a-27\right){x}-56a-73$ |
| 9216.2-f2 |
9216.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{10} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.041952319$ |
1.443878331 |
\( -\frac{1668992}{729} a + \frac{3939968}{729} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -6 a + 13\) , \( -6 a - 21\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-6a+13\right){x}-6a-21$ |
| 9216.2-f3 |
9216.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{11} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.041952319$ |
1.443878331 |
\( \frac{24685856}{6561} a + \frac{51528992}{6561} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -4 a + 16\) , \( -14 a - 16\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-4a+16\right){x}-14a-16$ |
| 9216.2-f4 |
9216.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{23} \cdot 3^{5} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$1.020976159$ |
1.443878331 |
\( -\frac{576294904}{27} a + \frac{292647184}{27} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -96 a + 193\) , \( -564 a - 1173\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-96a+193\right){x}-564a-1173$ |
| 9216.2-g1 |
9216.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{23} \cdot 3^{2} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.046050378$ |
$1.884597082$ |
2.787957272 |
\( -\frac{110584}{3} a - 1178880 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -32 a + 1\) , \( 68 a - 85\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-32a+1\right){x}+68a-85$ |
| 9216.2-g2 |
9216.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{23} \cdot 3^{5} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.046050378$ |
$1.884597082$ |
2.787957272 |
\( \frac{1862600}{81} a - \frac{2730832}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -12 a + 21\) , \( 24 a + 39\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-12a+21\right){x}+24a+39$ |
| 9216.2-g3 |
9216.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{4} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.523025189$ |
$3.769194165$ |
2.787957272 |
\( -640 a + \frac{6784}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -2 a + 1\) , \( 2 a - 1\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-2a+1\right){x}+2a-1$ |
| 9216.2-g4 |
9216.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{5} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.046050378$ |
$3.769194165$ |
2.787957272 |
\( \frac{109408}{81} a + \frac{158240}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 2 a - 2\) , \( -2 a + 2\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(2a-2\right){x}-2a+2$ |
| 9216.2-h1 |
9216.2-h |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{27} \cdot 3^{5} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.514366890$ |
$0.592819380$ |
2.946351043 |
\( -\frac{15347957750}{81} a - \frac{35138997500}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -640 a + 257\) , \( 3060 a - 10437\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-640a+257\right){x}+3060a-10437$ |
| 9216.2-h2 |
9216.2-h |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{27} \cdot 3^{5} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.514366890$ |
$0.592819380$ |
2.946351043 |
\( \frac{15347957750}{81} a - \frac{35138997500}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 640 a + 257\) , \( -3060 a - 10437\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(640a+257\right){x}-3060a-10437$ |
| 9216.2-h3 |
9216.2-h |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{8} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.878591722$ |
$2.371277522$ |
2.946351043 |
\( -\frac{8000}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -3\) , \( -9\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-3{x}-9$ |
| 9216.2-h4 |
9216.2-h |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{27} \cdot 3^{17} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.514366890$ |
$0.592819380$ |
2.946351043 |
\( -\frac{56997401750}{43046721} a + \frac{87757407500}{43046721} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 80 a + 97\) , \( -260 a + 443\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(80a+97\right){x}-260a+443$ |
| 9216.2-h5 |
9216.2-h |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{27} \cdot 3^{17} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.514366890$ |
$0.592819380$ |
2.946351043 |
\( \frac{56997401750}{43046721} a + \frac{87757407500}{43046721} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -80 a + 97\) , \( 260 a + 443\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-80a+97\right){x}+260a+443$ |
| 9216.2-h6 |
9216.2-h |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{10} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.757183445$ |
$1.185638761$ |
2.946351043 |
\( -\frac{100738000}{6561} a + \frac{45365000}{6561} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -40 a + 17\) , \( 60 a - 165\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-40a+17\right){x}+60a-165$ |
| 9216.2-h7 |
9216.2-h |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{10} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.757183445$ |
$1.185638761$ |
2.946351043 |
\( \frac{100738000}{6561} a + \frac{45365000}{6561} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 40 a + 17\) , \( -60 a - 165\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(40a+17\right){x}-60a-165$ |
| 9216.2-h8 |
9216.2-h |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{4} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.439295861$ |
$2.371277522$ |
2.946351043 |
\( \frac{2744000}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -23\) , \( 51\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-23{x}+51$ |
| 9216.2-i1 |
9216.2-i |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{3} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.845367848$ |
$3.155152462$ |
3.772081557 |
\( -\frac{2820064}{9} a - \frac{1154272}{9} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 8 a - 9\) , \( -17 a - 2\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(8a-9\right){x}-17a-2$ |
| 9216.2-i2 |
9216.2-i |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{23} \cdot 3^{6} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.845367848$ |
$1.577576231$ |
3.772081557 |
\( \frac{8113672}{81} a - \frac{1280704}{81} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 12 a - 44\) , \( -60 a + 96\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(12a-44\right){x}-60a+96$ |
| 9216.2-i3 |
9216.2-i |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{6} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.422683924$ |
$3.155152462$ |
3.772081557 |
\( -\frac{15232}{81} a + \frac{106112}{81} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 2 a - 4\) , \( 0\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(2a-4\right){x}$ |
| 9216.2-i4 |
9216.2-i |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9216.2 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{23} \cdot 3^{9} \) |
$2.47639$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.845367848$ |
$1.577576231$ |
3.772081557 |
\( \frac{1905752}{6561} a + \frac{14345072}{6561} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -8 a + 16\) , \( 16 a + 16\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-8a+16\right){x}+16a+16$ |
*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.
