| 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 |
| 9248.2-a1 |
9248.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9248.2 |
\( 2^{5} \cdot 17^{2} \) |
\( 2^{6} \cdot 17^{4} \) |
$2.47854$ |
$(a), (-2a+3), (2a+3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.132916407$ |
$3.667735283$ |
2.757728886 |
\( \frac{941192}{289} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -3\) , \( -1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-3{x}-1$ |
| 9248.2-a2 |
9248.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9248.2 |
\( 2^{5} \cdot 17^{2} \) |
\( 2^{12} \cdot 17^{2} \) |
$2.47854$ |
$(a), (-2a+3), (2a+3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.531665631$ |
$3.667735283$ |
2.757728886 |
\( \frac{438976}{17} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -6\) , \( -8\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-6{x}-8$ |
| 9248.2-b1 |
9248.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9248.2 |
\( 2^{5} \cdot 17^{2} \) |
\( 2^{12} \cdot 17^{4} \) |
$2.47854$ |
$(a), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.261429677$ |
$2.675241266$ |
1.978166466 |
\( -\frac{140608}{289} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -4\) , \( 6\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-4{x}+6$ |
| 9248.2-b2 |
9248.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9248.2 |
\( 2^{5} \cdot 17^{2} \) |
\( 2^{12} \cdot 17^{2} \) |
$2.47854$ |
$(a), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.522859354$ |
$2.675241266$ |
1.978166466 |
\( \frac{19248832}{17} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -22\) , \( -48\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-22{x}-48$ |
| 9248.2-c1 |
9248.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9248.2 |
\( 2^{5} \cdot 17^{2} \) |
\( 2^{6} \cdot 17^{4} \) |
$2.47854$ |
$(a), (-2a+3), (2a+3)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.882333163$ |
$3.845689929$ |
4.798680836 |
\( \frac{27000}{289} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 2\) , \( -3\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+2{x}-3$ |
| 9248.2-c2 |
9248.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9248.2 |
\( 2^{5} \cdot 17^{2} \) |
\( 2^{9} \cdot 17^{5} \) |
$2.47854$ |
$(a), (-2a+3), (2a+3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.882333163$ |
$1.922844964$ |
4.798680836 |
\( -\frac{6533480250}{83521} a + \frac{793665000}{83521} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 15 a + 22\) , \( 10 a - 69\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(15a+22\right){x}+10a-69$ |
| 9248.2-c3 |
9248.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9248.2 |
\( 2^{5} \cdot 17^{2} \) |
\( 2^{9} \cdot 17^{5} \) |
$2.47854$ |
$(a), (-2a+3), (2a+3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.882333163$ |
$1.922844964$ |
4.798680836 |
\( \frac{6533480250}{83521} a + \frac{793665000}{83521} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -15 a + 22\) , \( -10 a - 69\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-15a+22\right){x}-10a-69$ |
| 9248.2-c4 |
9248.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9248.2 |
\( 2^{5} \cdot 17^{2} \) |
\( 2^{12} \cdot 17^{2} \) |
$2.47854$ |
$(a), (-2a+3), (2a+3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.882333163$ |
$3.845689929$ |
4.798680836 |
\( \frac{216000}{17} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -5\) , \( 4\bigr] \) |
${y}^2={x}^{3}-5{x}+4$ |
| 9248.2-d1 |
9248.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9248.2 |
\( 2^{5} \cdot 17^{2} \) |
\( 2^{12} \cdot 17^{8} \) |
$2.47854$ |
$(a), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.908129645$ |
1.284289260 |
\( -\frac{1481544000}{83521} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 95\) , \( 264 a\bigr] \) |
${y}^2={x}^{3}+95{x}+264a$ |
| 9248.2-d2 |
9248.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9248.2 |
\( 2^{5} \cdot 17^{2} \) |
\( 2^{6} \cdot 17^{10} \) |
$2.47854$ |
$(a), (-2a+3), (2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.908129645$ |
1.284289260 |
\( -\frac{4812114420000}{6975757441} a - \frac{2517713739000}{6975757441} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -30 a + 23\) , \( -46 a + 156\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-30a+23\right){x}-46a+156$ |
| 9248.2-d3 |
9248.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9248.2 |
\( 2^{5} \cdot 17^{2} \) |
\( 2^{6} \cdot 17^{10} \) |
$2.47854$ |
$(a), (-2a+3), (2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.908129645$ |
1.284289260 |
\( \frac{4812114420000}{6975757441} a - \frac{2517713739000}{6975757441} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 30 a + 22\) , \( -76 a - 177\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(30a+22\right){x}-76a-177$ |
| 9248.2-d4 |
9248.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9248.2 |
\( 2^{5} \cdot 17^{2} \) |
\( 2^{12} \cdot 17^{4} \) |
$2.47854$ |
$(a), (-2a+3), (2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.908129645$ |
1.284289260 |
\( \frac{98611128000}{289} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 385\) , \( -2056 a\bigr] \) |
${y}^2={x}^{3}+385{x}-2056a$ |
| 9248.2-e1 |
9248.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9248.2 |
\( 2^{5} \cdot 17^{2} \) |
\( 2^{12} \cdot 17^{8} \) |
$2.47854$ |
$(a), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.908129645$ |
1.284289260 |
\( -\frac{1481544000}{83521} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 95\) , \( -264 a\bigr] \) |
${y}^2={x}^{3}+95{x}-264a$ |
| 9248.2-e2 |
9248.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9248.2 |
\( 2^{5} \cdot 17^{2} \) |
\( 2^{6} \cdot 17^{10} \) |
$2.47854$ |
$(a), (-2a+3), (2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.908129645$ |
1.284289260 |
\( -\frac{4812114420000}{6975757441} a - \frac{2517713739000}{6975757441} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -30 a + 22\) , \( 76 a - 177\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-30a+22\right){x}+76a-177$ |
| 9248.2-e3 |
9248.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9248.2 |
\( 2^{5} \cdot 17^{2} \) |
\( 2^{6} \cdot 17^{10} \) |
$2.47854$ |
$(a), (-2a+3), (2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.908129645$ |
1.284289260 |
\( \frac{4812114420000}{6975757441} a - \frac{2517713739000}{6975757441} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 30 a + 23\) , \( 46 a + 156\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(30a+23\right){x}+46a+156$ |
| 9248.2-e4 |
9248.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9248.2 |
\( 2^{5} \cdot 17^{2} \) |
\( 2^{12} \cdot 17^{4} \) |
$2.47854$ |
$(a), (-2a+3), (2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.908129645$ |
1.284289260 |
\( \frac{98611128000}{289} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 385\) , \( 2056 a\bigr] \) |
${y}^2={x}^{3}+385{x}+2056a$ |
| 9248.2-f1 |
9248.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9248.2 |
\( 2^{5} \cdot 17^{2} \) |
\( 2^{6} \cdot 17^{4} \) |
$2.47854$ |
$(a), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.431093428$ |
$3.845689929$ |
3.891591577 |
\( \frac{27000}{289} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 3\) , \( 2\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+3{x}+2$ |
| 9248.2-f2 |
9248.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9248.2 |
\( 2^{5} \cdot 17^{2} \) |
\( 2^{9} \cdot 17^{5} \) |
$2.47854$ |
$(a), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.862186857$ |
$1.922844964$ |
3.891591577 |
\( -\frac{6533480250}{83521} a + \frac{793665000}{83521} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 15 a + 23\) , \( -25 a + 48\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(15a+23\right){x}-25a+48$ |
| 9248.2-f3 |
9248.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9248.2 |
\( 2^{5} \cdot 17^{2} \) |
\( 2^{9} \cdot 17^{5} \) |
$2.47854$ |
$(a), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.862186857$ |
$1.922844964$ |
3.891591577 |
\( \frac{6533480250}{83521} a + \frac{793665000}{83521} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -15 a + 23\) , \( 25 a + 48\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-15a+23\right){x}+25a+48$ |
| 9248.2-f4 |
9248.2-f |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9248.2 |
\( 2^{5} \cdot 17^{2} \) |
\( 2^{12} \cdot 17^{2} \) |
$2.47854$ |
$(a), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.715546714$ |
$3.845689929$ |
3.891591577 |
\( \frac{216000}{17} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -5\) , \( -4\bigr] \) |
${y}^2={x}^{3}-5{x}-4$ |
| 9248.2-g1 |
9248.2-g |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9248.2 |
\( 2^{5} \cdot 17^{2} \) |
\( 2^{12} \cdot 17^{4} \) |
$2.47854$ |
$(a), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.928721300$ |
$2.675241266$ |
7.027378645 |
\( -\frac{140608}{289} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -4\) , \( -6\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-4{x}-6$ |
| 9248.2-g2 |
9248.2-g |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9248.2 |
\( 2^{5} \cdot 17^{2} \) |
\( 2^{12} \cdot 17^{2} \) |
$2.47854$ |
$(a), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.857442600$ |
$2.675241266$ |
7.027378645 |
\( \frac{19248832}{17} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -22\) , \( 48\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-22{x}+48$ |
| 9248.2-h1 |
9248.2-h |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9248.2 |
\( 2^{5} \cdot 17^{2} \) |
\( 2^{6} \cdot 17^{4} \) |
$2.47854$ |
$(a), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.667735283$ |
5.186960980 |
\( \frac{941192}{289} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -3\) , \( 2\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-3{x}+2$ |
| 9248.2-h2 |
9248.2-h |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
9248.2 |
\( 2^{5} \cdot 17^{2} \) |
\( 2^{12} \cdot 17^{2} \) |
$2.47854$ |
$(a), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$3.667735283$ |
5.186960980 |
\( \frac{438976}{17} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -6\) , \( 8\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-6{x}+8$ |
*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.
