Atkin-Lehner |
3+ 5- 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
117975w |
Isogeny class |
Conductor |
117975 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1267200 |
Modular degree for the optimal curve |
Δ |
1942654153922625 = 3 · 53 · 119 · 133 |
Discriminant |
Eigenvalues |
-1 3+ 5- 2 11+ 13+ -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-916033,-337829194] |
[a1,a2,a3,a4,a6] |
Generators |
[-551:283:1] [21085150:-475554771:15625] |
Generators of the group modulo torsion |
j |
288411730543/6591 |
j-invariant |
L |
7.0922525568059 |
L(r)(E,1)/r! |
Ω |
0.15432005444777 |
Real period |
R |
45.958074483372 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000306 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
117975cj1 117975x1 |
Quadratic twists by: 5 -11 |