Atkin-Lehner |
2+ 3- 7- 13+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
76986q |
Isogeny class |
Conductor |
76986 |
Conductor |
∏ cp |
128 |
Product of Tamagawa factors cp |
deg |
507904 |
Modular degree for the optimal curve |
Δ |
-4806831550470768 = -1 · 24 · 38 · 78 · 132 · 47 |
Discriminant |
Eigenvalues |
2+ 3- -2 7- 0 13+ -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-15408,3419824] |
[a1,a2,a3,a4,a6] |
Generators |
[-2420:-239576:125] [-136:1796:1] |
Generators of the group modulo torsion |
j |
-554946156479233/6593733265392 |
j-invariant |
L |
7.4150616219878 |
L(r)(E,1)/r! |
Ω |
0.36815707872213 |
Real period |
R |
0.62940709029997 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999997967 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
25662s1 |
Quadratic twists by: -3 |