Atkin-Lehner |
2+ 3+ 13- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
117312m |
Isogeny class |
Conductor |
117312 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
1013760 |
Modular degree for the optimal curve |
Δ |
-68210939314372608 = -1 · 216 · 33 · 135 · 473 |
Discriminant |
Eigenvalues |
2+ 3+ -2 -1 5 13- 6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-184449,-32916735] |
[a1,a2,a3,a4,a6] |
j |
-10589490159355012/1040816334753 |
j-invariant |
L |
2.2909472927969 |
L(r)(E,1)/r! |
Ω |
0.11454735245647 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117312da1 14664f1 |
Quadratic twists by: -4 8 |