Atkin-Lehner |
3+ 7+ 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
117117c |
Isogeny class |
Conductor |
117117 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
33408 |
Modular degree for the optimal curve |
Δ |
-4567563 = -1 · 33 · 7 · 11 · 133 |
Discriminant |
Eigenvalues |
-2 3+ -2 7+ 11+ 13- 2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,39,42] |
[a1,a2,a3,a4,a6] |
Generators |
[-1:1:1] [0:6:1] |
Generators of the group modulo torsion |
j |
110592/77 |
j-invariant |
L |
5.0213210101388 |
L(r)(E,1)/r! |
Ω |
1.5473566207519 |
Real period |
R |
0.81127403658551 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000006213 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117117f1 117117j1 |
Quadratic twists by: -3 13 |