Atkin-Lehner |
2+ 3- 11- 19- |
Signs for the Atkin-Lehner involutions |
Class |
120384bu |
Isogeny class |
Conductor |
120384 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1179648 |
Modular degree for the optimal curve |
Δ |
6113942208 = 26 · 37 · 112 · 192 |
Discriminant |
Eigenvalues |
2+ 3- 2 4 11- 2 6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1572519,759000332] |
[a1,a2,a3,a4,a6] |
j |
9217304063844205888/131043 |
j-invariant |
L |
5.473157854611 |
L(r)(E,1)/r! |
Ω |
0.68414483672352 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
120384r1 60192q4 40128h1 |
Quadratic twists by: -4 8 -3 |