Atkin-Lehner |
2+ 3+ 19+ 67- |
Signs for the Atkin-Lehner involutions |
Class |
7638b |
Isogeny class |
Conductor |
7638 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
72960 |
Modular degree for the optimal curve |
Δ |
8968055996547072 = 230 · 38 · 19 · 67 |
Discriminant |
Eigenvalues |
2+ 3+ 0 -2 -4 2 -6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-163080,24867648] |
[a1,a2,a3,a4,a6] |
j |
479656110558473439625/8968055996547072 |
j-invariant |
L |
0.41158987539233 |
L(r)(E,1)/r! |
Ω |
0.41158987539233 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
61104s1 22914k1 |
Quadratic twists by: -4 -3 |