Atkin-Lehner |
2+ 3- 13- |
Signs for the Atkin-Lehner involutions |
Class |
624f |
Isogeny class |
Conductor |
624 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
64 |
Modular degree for the optimal curve |
Δ |
1872 = 24 · 32 · 13 |
Discriminant |
Eigenvalues |
2+ 3- -2 -4 0 13- 2 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-39,-108] |
[a1,a2,a3,a4,a6] |
Generators |
[12:36:1] |
Generators of the group modulo torsion |
j |
420616192/117 |
j-invariant |
L |
2.1165060726217 |
L(r)(E,1)/r! |
Ω |
1.9064113549902 |
Real period |
R |
2.2204085881902 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
312d1 2496s1 1872h1 15600e1 |
Quadratic twists by: -4 8 -3 5 |