| 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 |
| 55.2-a7 |
55.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5^{12} \cdot 11^{3} \) |
$0.54414$ |
$(-2a+1), (-3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$2.207452860$ |
0.493601465 |
\( \frac{4560282420936767}{20796875} a + \frac{563715628160969}{4159375} \) |
\( \bigl[1\) , \( \phi\) , \( 1\) , \( 16 \phi - 226\) , \( -1110 \phi + 576\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\phi{x}^{2}+\left(16\phi-226\right){x}-1110\phi+576$ |
| 275.1-a7 |
275.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
275.1 |
\( 5^{2} \cdot 11 \) |
\( 5^{18} \cdot 11^{3} \) |
$0.81369$ |
$(-2a+1), (-3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.219468538$ |
0.992576504 |
\( \frac{4560282420936767}{20796875} a + \frac{563715628160969}{4159375} \) |
\( \bigl[\phi + 1\) , \( -\phi + 1\) , \( \phi + 1\) , \( -976 \phi - 1052\) , \( 24329 \phi + 11533\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(-976\phi-1052\right){x}+24329\phi+11533$ |
| 605.2-b7 |
605.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
605.2 |
\( 5 \cdot 11^{2} \) |
\( 5^{12} \cdot 11^{9} \) |
$0.99097$ |
$(-2a+1), (-3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.469848461$ |
1.260735718 |
\( \frac{4560282420936767}{20796875} a + \frac{563715628160969}{4159375} \) |
\( \bigl[\phi + 1\) , \( \phi - 1\) , \( \phi\) , \( 832 \phi - 2982\) , \( 18800 \phi - 57148\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(832\phi-2982\right){x}+18800\phi-57148$ |
| 3025.2-e7 |
3025.2-e |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
3025.2 |
\( 5^{2} \cdot 11^{2} \) |
\( 5^{18} \cdot 11^{9} \) |
$1.48185$ |
$(-2a+1), (-3a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1.277015932$ |
$0.947959835$ |
2.165515227 |
\( \frac{4560282420936767}{20796875} a + \frac{563715628160969}{4159375} \) |
\( \bigl[\phi\) , \( \phi - 1\) , \( \phi\) , \( -6588 \phi - 10750\) , \( 450281 \phi + 468042\bigr] \) |
${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-6588\phi-10750\right){x}+450281\phi+468042$ |
| 4455.2-a7 |
4455.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4455.2 |
\( 3^{4} \cdot 5 \cdot 11 \) |
\( 3^{12} \cdot 5^{12} \cdot 11^{3} \) |
$1.63243$ |
$(-2a+1), (-3a+2), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$1.654294174$ |
1.479645692 |
\( \frac{4560282420936767}{20796875} a + \frac{563715628160969}{4159375} \) |
\( \bigl[1\) , \( -1\) , \( \phi + 1\) , \( 139 \phi - 2033\) , \( 28079 \phi - 15418\bigr] \) |
${y}^2+{x}{y}+\left(\phi+1\right){y}={x}^{3}-{x}^{2}+\left(139\phi-2033\right){x}+28079\phi-15418$ |
*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.
