Atkin-Lehner |
2+ 3+ 13- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
117312k |
Isogeny class |
Conductor |
117312 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
122880 |
Modular degree for the optimal curve |
Δ |
-622740897792 = -1 · 222 · 35 · 13 · 47 |
Discriminant |
Eigenvalues |
2+ 3+ 0 -3 1 13- -4 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-3073,76801] |
[a1,a2,a3,a4,a6] |
Generators |
[-63:128:1] [3:260:1] |
Generators of the group modulo torsion |
j |
-12246522625/2375568 |
j-invariant |
L |
9.5540000583446 |
L(r)(E,1)/r! |
Ω |
0.87630881419344 |
Real period |
R |
2.7256373282732 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999998014 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117312cy1 3666m1 |
Quadratic twists by: -4 8 |