Atkin-Lehner |
2+ 3- 5+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
22320k |
Isogeny class |
Conductor |
22320 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
18432 |
Modular degree for the optimal curve |
Δ |
-11861763120 = -1 · 24 · 314 · 5 · 31 |
Discriminant |
Eigenvalues |
2+ 3- 5+ -4 -4 -6 2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,222,5083] |
[a1,a2,a3,a4,a6] |
Generators |
[3:76:1] |
Generators of the group modulo torsion |
j |
103737344/1016955 |
j-invariant |
L |
3.1134382699853 |
L(r)(E,1)/r! |
Ω |
0.9332390715024 |
Real period |
R |
3.3361636530852 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
11160m1 89280gc1 7440h1 111600bs1 |
Quadratic twists by: -4 8 -3 5 |