| 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 |
| 9.1-a1 |
9.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{2} \) |
$0.63815$ |
$(3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$15.98892188$ |
0.969470791 |
\( -\frac{396321250}{3} a + 338397375 \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 48 a - 123\) , \( 291 a - 749\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(48a-123\right){x}+291a-749$ |
| 9.1-a2 |
9.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{2} \) |
$0.63815$ |
$(3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$15.98892188$ |
0.969470791 |
\( -\frac{31564213125250}{3} a + \frac{80853398915125}{3} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 32 a - 79\) , \( -131 a + 330\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(32a-79\right){x}-131a+330$ |
| 9.1-a3 |
9.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{16} \) |
$0.63815$ |
$(3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$7.994460944$ |
0.969470791 |
\( \frac{5359375}{6561} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 58 a + 92\) , \( 322 a + 503\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(58a+92\right){x}+322a+503$ |
| 9.1-a4 |
9.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$0.63815$ |
$(3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$31.97784377$ |
0.969470791 |
\( \frac{274625}{81} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -22 a - 33\) , \( 71 a + 111\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-22a-33\right){x}+71a+111$ |
| 9.1-a5 |
9.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$0.63815$ |
$(3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$31.97784377$ |
0.969470791 |
\( -\frac{14326000}{9} a + \frac{36913625}{9} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 2 a - 4\) , \( -2 a + 3\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a-4\right){x}-2a+3$ |
| 9.1-a6 |
9.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$0.63815$ |
$(3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$31.97784377$ |
0.969470791 |
\( \frac{14326000}{9} a + \frac{22587625}{9} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -a - 2\) , \( -1\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-a-2\right){x}-1$ |
| 9.1-a7 |
9.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{2} \) |
$0.63815$ |
$(3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$15.98892188$ |
0.969470791 |
\( \frac{396321250}{3} a + \frac{618870875}{3} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -49 a - 74\) , \( -292 a - 457\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-49a-74\right){x}-292a-457$ |
| 9.1-a8 |
9.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{2} \) |
$0.63815$ |
$(3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$15.98892188$ |
0.969470791 |
\( \frac{31564213125250}{3} a + 16429728596625 \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -31 a - 47\) , \( 99 a + 152\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-31a-47\right){x}+99a+152$ |
| 9.1-b1 |
9.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{10} \) |
$0.63815$ |
$(3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$0.808547756$ |
0.196101635 |
\( -\frac{13549359104}{243} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( 795 a - 2035\) , \( 17928 a - 45924\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(795a-2035\right){x}+17928a-45924$ |
| 9.1-b2 |
9.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{2} \) |
$0.63815$ |
$(3)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$20.21369391$ |
0.196101635 |
\( \frac{4096}{3} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( -5 a + 15\) , \( 2 a - 6\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-5a+15\right){x}+2a-6$ |
*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.
