| 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 |
| 1369.1-a1 |
1369.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1369.1 |
\( 37^{2} \) |
\( 37^{6} \) |
$1.21541$ |
$(37)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$0.948950578$ |
$4.739517032$ |
1.340915534 |
\( \frac{1404928000}{50653} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -23\) , \( -50\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-23{x}-50$ |
| 1369.1-a2 |
1369.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1369.1 |
\( 37^{2} \) |
\( 37^{2} \) |
$1.21541$ |
$(37)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$0.316316859$ |
$42.65565329$ |
1.340915534 |
\( \frac{4096000}{37} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -3\) , \( 1\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-3{x}+1$ |
| 1369.1-a3 |
1369.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1369.1 |
\( 37^{2} \) |
\( 37^{2} \) |
$1.21541$ |
$(37)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$2.846851736$ |
$0.526613003$ |
1.340915534 |
\( \frac{727057727488000}{37} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -1873\) , \( -31833\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-1873{x}-31833$ |
| 1369.1-b1 |
1369.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1369.1 |
\( 37^{2} \) |
\( 37^{2} \) |
$1.21541$ |
$(37)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$15.61533633$ |
1.745847676 |
\( -\frac{128513880}{37} a + \frac{208280465}{37} \) |
\( \bigl[\phi\) , \( -\phi + 1\) , \( \phi + 1\) , \( -5 \phi - 4\) , \( 5 \phi + 1\bigr] \) |
${y}^2+\phi{x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(-5\phi-4\right){x}+5\phi+1$ |
| 1369.1-b2 |
1369.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1369.1 |
\( 37^{2} \) |
\( - 37^{4} \) |
$1.21541$ |
$(37)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$7.807668166$ |
1.745847676 |
\( \frac{43601381210}{1369} a + \frac{26944243845}{1369} \) |
\( \bigl[1\) , \( \phi\) , \( 0\) , \( -4 \phi - 15\) , \( 22 \phi - 8\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\phi{x}^{2}+\left(-4\phi-15\right){x}+22\phi-8$ |
| 1369.1-c1 |
1369.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1369.1 |
\( 37^{2} \) |
\( - 37^{4} \) |
$1.21541$ |
$(37)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$7.807668166$ |
1.745847676 |
\( -\frac{43601381210}{1369} a + \frac{1906638515}{37} \) |
\( \bigl[1\) , \( -\phi + 1\) , \( 0\) , \( 4 \phi - 19\) , \( -22 \phi + 14\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(4\phi-19\right){x}-22\phi+14$ |
| 1369.1-c2 |
1369.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1369.1 |
\( 37^{2} \) |
\( 37^{2} \) |
$1.21541$ |
$(37)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$15.61533633$ |
1.745847676 |
\( \frac{128513880}{37} a + \frac{79766585}{37} \) |
\( \bigl[\phi + 1\) , \( 0\) , \( \phi\) , \( 3 \phi - 8\) , \( -6 \phi + 7\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\left(3\phi-8\right){x}-6\phi+7$ |
| 1369.1-d1 |
1369.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
1369.1 |
\( 37^{2} \) |
\( 37^{2} \) |
$1.21541$ |
$(37)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.051111408$ |
$35.84317866$ |
1.638586443 |
\( \frac{110592}{37} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}-{x}$ |
*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.
