Atkin-Lehner |
2+ 3+ 7- 71+ |
Signs for the Atkin-Lehner involutions |
Class |
83496b |
Isogeny class |
Conductor |
83496 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
78336 |
Modular degree for the optimal curve |
Δ |
-25259710896 = -1 · 24 · 33 · 77 · 71 |
Discriminant |
Eigenvalues |
2+ 3+ -3 7- -3 -1 0 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-947,13896] |
[a1,a2,a3,a4,a6] |
Generators |
[40:-196:1] [-29:127:1] |
Generators of the group modulo torsion |
j |
-49948672/13419 |
j-invariant |
L |
7.6566952937346 |
L(r)(E,1)/r! |
Ω |
1.133823626344 |
Real period |
R |
0.84412327407065 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000299 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
11928d1 |
Quadratic twists by: -7 |