Atkin-Lehner |
2- 3- 17- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
50592g |
Isogeny class |
Conductor |
50592 |
Conductor |
∏ cp |
180 |
Product of Tamagawa factors cp |
deg |
587520 |
Modular degree for the optimal curve |
Δ |
-110006724866420736 = -1 · 212 · 39 · 175 · 312 |
Discriminant |
Eigenvalues |
2- 3- -3 -4 -3 1 17- -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-93517,19354619] |
[a1,a2,a3,a4,a6] |
Generators |
[-379:708:1] [4709:322524:1] |
Generators of the group modulo torsion |
j |
-22082086519556608/26857110563091 |
j-invariant |
L |
8.5283851804925 |
L(r)(E,1)/r! |
Ω |
0.30198646723885 |
Real period |
R |
0.15689417510202 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999998 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
50592d1 101184v1 |
Quadratic twists by: -4 8 |