Atkin-Lehner |
2+ 3+ 5+ 11- 17- |
Signs for the Atkin-Lehner involutions |
Class |
84150t |
Isogeny class |
Conductor |
84150 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
4147200 |
Modular degree for the optimal curve |
Δ |
-56498713920000000 = -1 · 212 · 33 · 57 · 113 · 173 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 1 11- -5 17- -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-30029817,63347375341] |
[a1,a2,a3,a4,a6] |
Generators |
[2978:-19441:1] |
Generators of the group modulo torsion |
j |
-7099013253976488644787/133922877440 |
j-invariant |
L |
4.5847360849156 |
L(r)(E,1)/r! |
Ω |
0.25346494708798 |
Real period |
R |
0.25122562625902 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000218 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
84150du2 16830bl1 |
Quadratic twists by: -3 5 |