Atkin-Lehner |
2- 3- 5+ 11- 17- |
Signs for the Atkin-Lehner involutions |
Class |
84150ge |
Isogeny class |
Conductor |
84150 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
3932160 |
Modular degree for the optimal curve |
Δ |
759148706250000 = 24 · 310 · 58 · 112 · 17 |
Discriminant |
Eigenvalues |
2- 3- 5+ -4 11- -6 17- -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-19525730,-33204365103] |
[a1,a2,a3,a4,a6] |
Generators |
[90433040:13098759081:4096] |
Generators of the group modulo torsion |
j |
72276643492008825169/66646800 |
j-invariant |
L |
7.6757666695626 |
L(r)(E,1)/r! |
Ω |
0.071820386266534 |
Real period |
R |
13.359310406024 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000835 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
28050f1 16830bd1 |
Quadratic twists by: -3 5 |