Atkin-Lehner |
2+ 3- 11- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
128502o |
Isogeny class |
Conductor |
128502 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
491520 |
Modular degree for the optimal curve |
Δ |
32916935593872 = 24 · 39 · 116 · 59 |
Discriminant |
Eigenvalues |
2+ 3- -2 0 11- 6 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-37593,-2782499] |
[a1,a2,a3,a4,a6] |
Generators |
[-106:107:1] |
Generators of the group modulo torsion |
j |
4549540393/25488 |
j-invariant |
L |
4.2696145242654 |
L(r)(E,1)/r! |
Ω |
0.34297998021656 |
Real period |
R |
1.5560727553364 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000237818 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
42834y1 1062h1 |
Quadratic twists by: -3 -11 |