Atkin-Lehner |
3- 11- 17- 19- |
Signs for the Atkin-Lehner involutions |
Class |
117249x |
Isogeny class |
Conductor |
117249 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
9984 |
Modular degree for the optimal curve |
Δ |
-117249 = -1 · 3 · 112 · 17 · 19 |
Discriminant |
Eigenvalues |
1 3- 3 0 11- -2 17- 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,8,-13] |
[a1,a2,a3,a4,a6] |
Generators |
[21435:46778:3375] |
Generators of the group modulo torsion |
j |
557183/969 |
j-invariant |
L |
13.124766771512 |
L(r)(E,1)/r! |
Ω |
1.7433846709731 |
Real period |
R |
7.5283251868253 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000032533 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117249o1 |
Quadratic twists by: -11 |