Atkin-Lehner |
2+ 3- 5+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
68400ce |
Isogeny class |
Conductor |
68400 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
16621200 = 24 · 37 · 52 · 19 |
Discriminant |
Eigenvalues |
2+ 3- 5+ -3 4 -4 -4 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-75,-155] |
[a1,a2,a3,a4,a6] |
Generators |
[-4:9:1] |
Generators of the group modulo torsion |
j |
160000/57 |
j-invariant |
L |
4.980810723439 |
L(r)(E,1)/r! |
Ω |
1.6701316909273 |
Real period |
R |
0.74557155433464 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000896 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34200cj1 22800bg1 68400cy1 |
Quadratic twists by: -4 -3 5 |