| 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 |
| 289.1-a1 |
289.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
289.1 |
\( 17^{2} \) |
\( - 17^{7} \) |
$1.51910$ |
$(-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$64$ |
\( 2^{2} \) |
$1$ |
$0.145124572$ |
2.252664248 |
\( -\frac{97064067741644382786}{17} a + \frac{248634735746274843273}{17} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -24497 a - 38627\) , \( -3044003 a - 4756060\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-24497a-38627\right){x}-3044003a-4756060$ |
| 289.1-a2 |
289.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
289.1 |
\( 17^{2} \) |
\( 17^{14} \) |
$1.51910$ |
$(-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.580498289$ |
2.252664248 |
\( -\frac{35937}{83521} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -187 a - 292\) , \( -126667 a - 197799\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-187a-292\right){x}-126667a-197799$ |
| 289.1-a3 |
289.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
289.1 |
\( 17^{2} \) |
\( - 17^{7} \) |
$1.51910$ |
$(-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$9.287972634$ |
2.252664248 |
\( -\frac{5821794}{17} a + \frac{14936697}{17} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 17 a - 37\) , \( -51 a + 132\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(17a-37\right){x}-51a+132$ |
| 289.1-a4 |
289.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
289.1 |
\( 17^{2} \) |
\( 17^{8} \) |
$1.51910$ |
$(-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$9.287972634$ |
2.252664248 |
\( \frac{35937}{17} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -187 a - 292\) , \( 901 a + 1407\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-187a-292\right){x}+901a+1407$ |
| 289.1-a5 |
289.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
289.1 |
\( 17^{2} \) |
\( 17^{10} \) |
$1.51910$ |
$(-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$1$ |
$2.321993158$ |
2.252664248 |
\( \frac{20346417}{289} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -1547 a - 2417\) , \( -46597 a - 72764\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-1547a-2417\right){x}-46597a-72764$ |
| 289.1-a6 |
289.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
289.1 |
\( 17^{2} \) |
\( - 17^{7} \) |
$1.51910$ |
$(-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$9.287972634$ |
2.252664248 |
\( \frac{5821794}{17} a + \frac{9114903}{17} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -17 a - 20\) , \( 51 a + 81\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-17a-20\right){x}+51a+81$ |
| 289.1-a7 |
289.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
289.1 |
\( 17^{2} \) |
\( 17^{8} \) |
$1.51910$ |
$(-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$64$ |
\( 2^{2} \) |
$1$ |
$0.580498289$ |
2.252664248 |
\( \frac{82483294977}{17} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -24667 a - 38542\) , \( -3022719 a - 4720173\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-24667a-38542\right){x}-3022719a-4720173$ |
| 289.1-a8 |
289.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
289.1 |
\( 17^{2} \) |
\( - 17^{7} \) |
$1.51910$ |
$(-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$64$ |
\( 2^{2} \) |
$1$ |
$0.145124572$ |
2.252664248 |
\( \frac{97064067741644382786}{17} a + \frac{151570668004630460487}{17} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 24497 a - 63124\) , \( 3044003 a - 7800063\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(24497a-63124\right){x}+3044003a-7800063$ |
*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.
