Atkin-Lehner |
2- 7+ 11- 19- |
Signs for the Atkin-Lehner involutions |
Class |
128744f |
Isogeny class |
Conductor |
128744 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
768000 |
Modular degree for the optimal curve |
Δ |
-4324024274721536 = -1 · 28 · 74 · 117 · 192 |
Discriminant |
Eigenvalues |
2- -1 -3 7+ 11- 6 0 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,36623,-1665211] |
[a1,a2,a3,a4,a6] |
Generators |
[499:11858:1] [107:1862:1] |
Generators of the group modulo torsion |
j |
11977812992/9534371 |
j-invariant |
L |
8.4309364663923 |
L(r)(E,1)/r! |
Ω |
0.24285120498118 |
Real period |
R |
1.0848896733533 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000004907 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
11704b1 |
Quadratic twists by: -11 |