| 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 |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
289.1 |
\( 17^{2} \) |
\( 17^{4} \) |
$1.80496$ |
$(17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.530583116$ |
$21.22287761$ |
2.298540050 |
\( \frac{592704}{289} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 3 a - 8\) , \( 4 a - 10\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(3a-8\right){x}+4a-10$ |
| 289.1-a2 |
289.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
289.1 |
\( 17^{2} \) |
\( 17^{2} \) |
$1.80496$ |
$(17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.061166233$ |
$21.22287761$ |
2.298540050 |
\( \frac{21024576}{17} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( -12 a - 28\) , \( 28 a + 68\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-12a-28\right){x}+28a+68$ |
| 289.1-b1 |
289.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
289.1 |
\( 17^{2} \) |
\( 17^{8} \) |
$1.80496$ |
$(17)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$4.990329480$ |
$2.393455763$ |
1.219042955 |
\( -\frac{35937}{83521} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( -14\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-{x}-14$ |
| 289.1-b2 |
289.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
289.1 |
\( 17^{2} \) |
\( 17^{2} \) |
$1.80496$ |
$(17)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.247582370$ |
$38.29529222$ |
1.219042955 |
\( \frac{35937}{17} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-{x}$ |
| 289.1-b3 |
289.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
289.1 |
\( 17^{2} \) |
\( 17^{4} \) |
$1.80496$ |
$(17)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$2.495164740$ |
$9.573823055$ |
1.219042955 |
\( \frac{20346417}{289} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -6\) , \( -4\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-6{x}-4$ |
| 289.1-b4 |
289.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
289.1 |
\( 17^{2} \) |
\( 17^{2} \) |
$1.80496$ |
$(17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$4.990329480$ |
$2.393455763$ |
1.219042955 |
\( \frac{82483294977}{17} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -91\) , \( -310\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-91{x}-310$ |
| 289.1-c1 |
289.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
289.1 |
\( 17^{2} \) |
\( 17^{4} \) |
$1.80496$ |
$(17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.530583116$ |
$21.22287761$ |
2.298540050 |
\( \frac{592704}{289} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( -4 a - 8\) , \( -4 a - 10\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-4a-8\right){x}-4a-10$ |
| 289.1-c2 |
289.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
289.1 |
\( 17^{2} \) |
\( 17^{2} \) |
$1.80496$ |
$(17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.061166233$ |
$21.22287761$ |
2.298540050 |
\( \frac{21024576}{17} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 11 a - 28\) , \( -28 a + 68\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(11a-28\right){x}-28a+68$ |
| 289.1-d1 |
289.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
289.1 |
\( 17^{2} \) |
\( 17^{8} \) |
$1.80496$ |
$(17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.300533693$ |
$7.539083304$ |
4.002805844 |
\( -\frac{35937}{83521} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 14 a - 32\) , \( -2766 a + 6777\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(14a-32\right){x}-2766a+6777$ |
| 289.1-d2 |
289.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
289.1 |
\( 17^{2} \) |
\( 17^{2} \) |
$1.80496$ |
$(17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.300533693$ |
$30.15633321$ |
4.002805844 |
\( \frac{35937}{17} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -13 a - 29\) , \( -38 a - 94\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-13a-29\right){x}-38a-94$ |
| 289.1-d3 |
289.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
289.1 |
\( 17^{2} \) |
\( 17^{4} \) |
$1.80496$ |
$(17)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$2.601067387$ |
$30.15633321$ |
4.002805844 |
\( \frac{20346417}{289} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 114 a - 277\) , \( -1131 a + 2772\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(114a-277\right){x}-1131a+2772$ |
| 289.1-d4 |
289.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
289.1 |
\( 17^{2} \) |
\( 17^{2} \) |
$1.80496$ |
$(17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.300533693$ |
$30.15633321$ |
4.002805844 |
\( \frac{82483294977}{17} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -1813 a - 4439\) , \( 63142 a + 154666\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-1813a-4439\right){x}+63142a+154666$ |
*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.
