Atkin-Lehner |
2+ 5+ 59+ |
Signs for the Atkin-Lehner involutions |
Class |
47200f |
Isogeny class |
Conductor |
47200 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
107520 |
Modular degree for the optimal curve |
Δ |
-205379000000 = -1 · 26 · 56 · 593 |
Discriminant |
Eigenvalues |
2+ -3 5+ -3 0 0 -2 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-12925,-566000] |
[a1,a2,a3,a4,a6] |
Generators |
[384:7148:1] |
Generators of the group modulo torsion |
j |
-238789577664/205379 |
j-invariant |
L |
2.7349631897181 |
L(r)(E,1)/r! |
Ω |
0.22386671241192 |
Real period |
R |
6.1084632909889 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000012 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
47200m1 94400da1 1888b1 |
Quadratic twists by: -4 8 5 |