Atkin-Lehner |
3+ 7- 17+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
77469g |
Isogeny class |
Conductor |
77469 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
152064 |
Modular degree for the optimal curve |
Δ |
-574191474003 = -1 · 33 · 79 · 17 · 31 |
Discriminant |
Eigenvalues |
2 3+ 0 7- 6 -5 17+ 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-3348,84125] |
[a1,a2,a3,a4,a6] |
Generators |
[2756:8543:64] |
Generators of the group modulo torsion |
j |
-35287552000/4880547 |
j-invariant |
L |
11.552326601846 |
L(r)(E,1)/r! |
Ω |
0.89024212897788 |
Real period |
R |
3.2441529732569 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002837 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
11067m1 |
Quadratic twists by: -7 |