Atkin-Lehner |
2+ 3+ 5+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
68400n |
Isogeny class |
Conductor |
68400 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
161280 |
Modular degree for the optimal curve |
Δ |
58433906250000 = 24 · 39 · 510 · 19 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ -3 -2 0 -6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-16875,-759375] |
[a1,a2,a3,a4,a6] |
j |
172800/19 |
j-invariant |
L |
0.84373686918957 |
L(r)(E,1)/r! |
Ω |
0.42186843202258 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34200f1 68400m1 68400bb1 |
Quadratic twists by: -4 -3 5 |