Atkin-Lehner |
3+ 7+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
117117d |
Isogeny class |
Conductor |
117117 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
338688 |
Modular degree for the optimal curve |
Δ |
-22046754196467 = -1 · 33 · 7 · 11 · 139 |
Discriminant |
Eigenvalues |
0 3+ 0 7+ 11- 13+ 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-86190,9742047] |
[a1,a2,a3,a4,a6] |
Generators |
[-13:3295:1] [185:358:1] |
Generators of the group modulo torsion |
j |
-543338496000/169169 |
j-invariant |
L |
9.9049878714668 |
L(r)(E,1)/r! |
Ω |
0.66440647621609 |
Real period |
R |
1.8635030336027 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999996719 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117117a2 9009a1 |
Quadratic twists by: -3 13 |