| 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 |
| 3136.1-a1 |
3136.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
3136.1 |
\( 2^{6} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{6} \) |
$1.49526$ |
$(2), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$2.547029008$ |
2.278132001 |
\( \frac{1024}{343} \) |
\( \bigl[0\) , \( -\phi + 1\) , \( 0\) , \( \phi + 2\) , \( -26 \phi - 19\bigr] \) |
${y}^2={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(\phi+2\right){x}-26\phi-19$ |
| 3136.1-b1 |
3136.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
3136.1 |
\( 2^{6} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{2} \) |
$1.49526$ |
$(2), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.050649626$ |
$12.61848370$ |
2.286590550 |
\( -\frac{10240}{7} a + \frac{5120}{7} \) |
\( \bigl[0\) , \( -\phi - 1\) , \( 0\) , \( -3 \phi + 6\) , \( 1\bigr] \) |
${y}^2={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-3\phi+6\right){x}+1$ |
| 3136.1-c1 |
3136.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
3136.1 |
\( 2^{6} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{2} \) |
$1.49526$ |
$(2), (7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.050649626$ |
$12.61848370$ |
2.286590550 |
\( \frac{10240}{7} a - \frac{5120}{7} \) |
\( \bigl[0\) , \( \phi + 1\) , \( 0\) , \( 5 \phi + 2\) , \( 4 \phi + 3\bigr] \) |
${y}^2={x}^{3}+\left(\phi+1\right){x}^{2}+\left(5\phi+2\right){x}+4\phi+3$ |
| 3136.1-d1 |
3136.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
3136.1 |
\( 2^{6} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{2} \) |
$1.49526$ |
$(2), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.594960974$ |
0.803857711 |
\( -\frac{4}{7} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -4\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-4$ |
| 3136.1-d2 |
3136.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
3136.1 |
\( 2^{6} \cdot 7^{2} \) |
\( 2^{22} \cdot 7^{4} \) |
$1.49526$ |
$(2), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.594960974$ |
0.803857711 |
\( \frac{3543122}{49} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -40\) , \( -84\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-40{x}-84$ |
| 3136.1-e1 |
3136.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
3136.1 |
\( 2^{6} \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{2} \) |
$1.49526$ |
$(2), (7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$12.23735606$ |
1.368178000 |
\( \frac{432}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 2\bigr] \) |
${y}^2={x}^{3}+{x}+2$ |
| 3136.1-e2 |
3136.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
3136.1 |
\( 2^{6} \cdot 7^{2} \) |
\( 2^{22} \cdot 7^{8} \) |
$1.49526$ |
$(2), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.059339015$ |
1.368178000 |
\( \frac{11090466}{2401} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -59\) , \( -138\bigr] \) |
${y}^2={x}^{3}-59{x}-138$ |
| 3136.1-e3 |
3136.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
3136.1 |
\( 2^{6} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{4} \) |
$1.49526$ |
$(2), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$12.23735606$ |
1.368178000 |
\( \frac{740772}{49} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -19\) , \( 30\bigr] \) |
${y}^2={x}^{3}-19{x}+30$ |
| 3136.1-e4 |
3136.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
3136.1 |
\( 2^{6} \cdot 7^{2} \) |
\( 2^{22} \cdot 7^{2} \) |
$1.49526$ |
$(2), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$12.23735606$ |
1.368178000 |
\( \frac{1443468546}{7} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -299\) , \( 1990\bigr] \) |
${y}^2={x}^{3}-299{x}+1990$ |
*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.
