| 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 |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
289.1 |
\( 17^{2} \) |
\( 17^{8} \) |
$1.27630$ |
$(17)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.036297434$ |
$7.539083304$ |
2.215843774 |
\( -\frac{35937}{83521} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -2\) , \( 13\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-2{x}+13$ |
| 289.1-a2 |
289.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
289.1 |
\( 17^{2} \) |
\( 17^{2} \) |
$1.27630$ |
$(17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.509074358$ |
$30.15633321$ |
2.215843774 |
\( \frac{35937}{17} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 7469 a - 12938\) , \( 199451 a - 345460\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(7469a-12938\right){x}+199451a-345460$ |
| 289.1-a3 |
289.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
289.1 |
\( 17^{2} \) |
\( 17^{4} \) |
$1.27630$ |
$(17)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1.018148717$ |
$30.15633321$ |
2.215843774 |
\( \frac{20346417}{289} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 318 a - 552\) , \( -4102 a + 7103\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(318a-552\right){x}-4102a+7103$ |
| 289.1-a4 |
289.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
289.1 |
\( 17^{2} \) |
\( 17^{2} \) |
$1.27630$ |
$(17)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$2.036297434$ |
$30.15633321$ |
2.215843774 |
\( \frac{82483294977}{17} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 5078 a - 8797\) , \( -260547 a + 451279\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(5078a-8797\right){x}-260547a+451279$ |
| 289.1-b1 |
289.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
289.1 |
\( 17^{2} \) |
\( 17^{8} \) |
$1.27630$ |
$(17)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.624239889$ |
$2.393455763$ |
1.252050144 |
\( -\frac{35937}{83521} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( -14\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-{x}-14$ |
| 289.1-b2 |
289.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
289.1 |
\( 17^{2} \) |
\( 17^{2} \) |
$1.27630$ |
$(17)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.906059972$ |
$38.29529222$ |
1.252050144 |
\( \frac{35937}{17} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 7469 a - 12937\) , \( -199451 a + 345459\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(7469a-12937\right){x}-199451a+345459$ |
| 289.1-b3 |
289.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
289.1 |
\( 17^{2} \) |
\( 17^{4} \) |
$1.27630$ |
$(17)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1.812119944$ |
$9.573823055$ |
1.252050144 |
\( \frac{20346417}{289} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 318 a - 553\) , \( 4101 a - 7105\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(318a-553\right){x}+4101a-7105$ |
| 289.1-b4 |
289.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
289.1 |
\( 17^{2} \) |
\( 17^{2} \) |
$1.27630$ |
$(17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$3.624239889$ |
$2.393455763$ |
1.252050144 |
\( \frac{82483294977}{17} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 5078 a - 8798\) , \( 260546 a - 451281\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(5078a-8798\right){x}+260546a-451281$ |
*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.
