Atkin-Lehner |
2+ 3- 5- 13+ 59- |
Signs for the Atkin-Lehner involutions |
Class |
69030w |
Isogeny class |
Conductor |
69030 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
921600 |
Modular degree for the optimal curve |
Δ |
-867057413938560000 = -1 · 210 · 311 · 54 · 133 · 592 |
Discriminant |
Eigenvalues |
2+ 3- 5- -2 0 13+ -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-41499,44928805] |
[a1,a2,a3,a4,a6] |
Generators |
[-319:5222:1] [86:-6523:1] |
Generators of the group modulo torsion |
j |
-10842138866394289/1189379168640000 |
j-invariant |
L |
8.0018803726376 |
L(r)(E,1)/r! |
Ω |
0.23071897427375 |
Real period |
R |
2.1676480006258 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999978 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
23010k1 |
Quadratic twists by: -3 |