Atkin-Lehner |
2- 3+ 5+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
85440bb |
Isogeny class |
Conductor |
85440 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
159744 |
Modular degree for the optimal curve |
Δ |
74742912000 = 210 · 38 · 53 · 89 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 0 -4 -2 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-14941,-697859] |
[a1,a2,a3,a4,a6] |
Generators |
[34660:783189:64] |
Generators of the group modulo torsion |
j |
360239905232896/72991125 |
j-invariant |
L |
3.0192183079432 |
L(r)(E,1)/r! |
Ω |
0.43182471635427 |
Real period |
R |
6.9917681607655 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000016911 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
85440q1 21360e1 |
Quadratic twists by: -4 8 |