Atkin-Lehner |
2+ 3- 13- 47- |
Signs for the Atkin-Lehner involutions |
Class |
117312bi |
Isogeny class |
Conductor |
117312 |
Conductor |
∏ cp |
180 |
Product of Tamagawa factors cp |
deg |
3317760 |
Modular degree for the optimal curve |
Δ |
-90042145333051392 = -1 · 218 · 39 · 135 · 47 |
Discriminant |
Eigenvalues |
2+ 3- 0 -1 -5 13- 4 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-12057793,16111712927] |
[a1,a2,a3,a4,a6] |
Generators |
[-1141:168480:1] [-439:146016:1] |
Generators of the group modulo torsion |
j |
-739583643739785288625/343483525593 |
j-invariant |
L |
13.797877176602 |
L(r)(E,1)/r! |
Ω |
0.27710442686523 |
Real period |
R |
0.276628107691 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999956712 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117312cc1 1833a1 |
Quadratic twists by: -4 8 |