Atkin-Lehner |
2+ 5- 31- 41- |
Signs for the Atkin-Lehner involutions |
Class |
50840f |
Isogeny class |
Conductor |
50840 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
20480 |
Modular degree for the optimal curve |
Δ |
252166400 = 28 · 52 · 312 · 41 |
Discriminant |
Eigenvalues |
2+ -2 5- -4 -2 0 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-300,-1952] |
[a1,a2,a3,a4,a6] |
Generators |
[-12:8:1] [-9:10:1] |
Generators of the group modulo torsion |
j |
11702923216/985025 |
j-invariant |
L |
6.3864309576411 |
L(r)(E,1)/r! |
Ω |
1.1529729784588 |
Real period |
R |
2.7695492769396 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999997 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
101680j1 |
Quadratic twists by: -4 |