Atkin-Lehner |
2+ 3+ 7+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
68544k |
Isogeny class |
Conductor |
68544 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
168960 |
Modular degree for the optimal curve |
Δ |
134292501504 = 210 · 33 · 75 · 172 |
Discriminant |
Eigenvalues |
2+ 3+ -2 7+ -2 6 17- 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-67296,6719400] |
[a1,a2,a3,a4,a6] |
j |
1219067475001344/4857223 |
j-invariant |
L |
1.8248566409102 |
L(r)(E,1)/r! |
Ω |
0.91242832140224 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
68544dh1 4284b1 68544d1 |
Quadratic twists by: -4 8 -3 |