Atkin-Lehner |
3+ 5+ 7+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
68355b |
Isogeny class |
Conductor |
68355 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
731136 |
Modular degree for the optimal curve |
Δ |
1884819701953125 = 33 · 58 · 78 · 31 |
Discriminant |
Eigenvalues |
-2 3+ 5+ 7+ 5 -2 3 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-110103,-13905992] |
[a1,a2,a3,a4,a6] |
j |
948359688192/12109375 |
j-invariant |
L |
1.0491684091639 |
L(r)(E,1)/r! |
Ω |
0.26229210170891 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68355f1 68355h1 |
Quadratic twists by: -3 -7 |