| 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-a4 |
55.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( - 5^{3} \cdot 11^{12} \) |
$0.54414$ |
$(-2a+1), (-3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$2.207452860$ |
0.493601465 |
\( \frac{114278307303626907}{78460709418025} a + \frac{89325070732461329}{78460709418025} \) |
\( \bigl[1\) , \( \phi\) , \( 1\) , \( -54 \phi + 54\) , \( 374 \phi - 572\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\phi{x}^{2}+\left(-54\phi+54\right){x}+374\phi-572$ |
| 275.1-a4 |
275.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
275.1 |
\( 5^{2} \cdot 11 \) |
\( - 5^{9} \cdot 11^{12} \) |
$0.81369$ |
$(-2a+1), (-3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.109734269$ |
0.992576504 |
\( \frac{114278307303626907}{78460709418025} a + \frac{89325070732461329}{78460709418025} \) |
\( \bigl[\phi + 1\) , \( -\phi + 1\) , \( \phi + 1\) , \( -276 \phi - 2\) , \( -2201 \phi + 823\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(-276\phi-2\right){x}-2201\phi+823$ |
| 605.2-b4 |
605.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
605.2 |
\( 5 \cdot 11^{2} \) |
\( - 5^{3} \cdot 11^{18} \) |
$0.99097$ |
$(-2a+1), (-3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.939696922$ |
1.260735718 |
\( \frac{114278307303626907}{78460709418025} a + \frac{89325070732461329}{78460709418025} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -935 \phi - 387\) , \( 8620 \phi + 7934\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-935\phi-387\right){x}+8620\phi+7934$ |
| 3025.2-e4 |
3025.2-e |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
3025.2 |
\( 5^{2} \cdot 11^{2} \) |
\( - 5^{9} \cdot 11^{18} \) |
$1.48185$ |
$(-2a+1), (-3a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$5.108063728$ |
$0.236989958$ |
2.165515227 |
\( \frac{114278307303626907}{78460709418025} a + \frac{89325070732461329}{78460709418025} \) |
\( \bigl[\phi\) , \( \phi - 1\) , \( \phi\) , \( -2738 \phi + 800\) , \( 26641 \phi - 104488\bigr] \) |
${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-2738\phi+800\right){x}+26641\phi-104488$ |
| 4455.2-a4 |
4455.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
4455.2 |
\( 3^{4} \cdot 5 \cdot 11 \) |
\( - 3^{12} \cdot 5^{3} \cdot 11^{12} \) |
$1.63243$ |
$(-2a+1), (-3a+2), (3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.827147087$ |
1.479645692 |
\( \frac{114278307303626907}{78460709418025} a + \frac{89325070732461329}{78460709418025} \) |
\( \bigl[1\) , \( -1\) , \( \phi + 1\) , \( -491 \phi + 487\) , \( -10099 \phi + 14948\bigr] \) |
${y}^2+{x}{y}+\left(\phi+1\right){y}={x}^{3}-{x}^{2}+\left(-491\phi+487\right){x}-10099\phi+14948$ |
*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.
