Atkin-Lehner |
2- 3+ 7+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
85176bh |
Isogeny class |
Conductor |
85176 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
184320 |
Modular degree for the optimal curve |
Δ |
10640681133264 = 24 · 39 · 7 · 136 |
Discriminant |
Eigenvalues |
2- 3+ -2 7+ -6 13+ -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-9126,-296595] |
[a1,a2,a3,a4,a6] |
Generators |
[-66:135:1] [322:5491:1] |
Generators of the group modulo torsion |
j |
55296/7 |
j-invariant |
L |
8.8914702834196 |
L(r)(E,1)/r! |
Ω |
0.49252660628386 |
Real period |
R |
9.0263857528163 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999996992 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
85176b1 504b1 |
Quadratic twists by: -3 13 |