Atkin-Lehner |
2+ 13+ 103- |
Signs for the Atkin-Lehner involutions |
Class |
85696s |
Isogeny class |
Conductor |
85696 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
465484218368 = 215 · 13 · 1033 |
Discriminant |
Eigenvalues |
2+ -2 2 -3 5 13+ -3 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-3297,63967] |
[a1,a2,a3,a4,a6] |
Generators |
[69:412:1] [-46:347:1] |
Generators of the group modulo torsion |
j |
120993582536/14205451 |
j-invariant |
L |
8.5212376806274 |
L(r)(E,1)/r! |
Ω |
0.90483114109598 |
Real period |
R |
1.5695815667506 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.000000000013 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
85696g1 42848l1 |
Quadratic twists by: -4 8 |