Atkin-Lehner |
2- 3+ 5- 7- 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
90090cl |
Isogeny class |
Conductor |
90090 |
Conductor |
∏ cp |
1728 |
Product of Tamagawa factors cp |
deg |
663552 |
Modular degree for the optimal curve |
Δ |
-22508950464000000 = -1 · 212 · 33 · 56 · 72 · 112 · 133 |
Discriminant |
Eigenvalues |
2- 3+ 5- 7- 11+ 13- 0 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-81272,11493371] |
[a1,a2,a3,a4,a6] |
Generators |
[-251:4129:1] |
Generators of the group modulo torsion |
j |
-2198759759636881923/833664832000000 |
j-invariant |
L |
12.188764640866 |
L(r)(E,1)/r! |
Ω |
0.35816834962238 |
Real period |
R |
0.70897553328715 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000182 |
(Analytic) order of Ш |
t |
6 |
Number of elements in the torsion subgroup |
Twists |
90090d3 |
Quadratic twists by: -3 |