Atkin-Lehner |
3+ 7- 11+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
129591c |
Isogeny class |
Conductor |
129591 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
12029952 |
Modular degree for the optimal curve |
Δ |
44176157064728073 = 33 · 74 · 119 · 172 |
Discriminant |
Eigenvalues |
1 3+ 4 7- 11+ 0 17+ -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-57721560,-168778869957] |
[a1,a2,a3,a4,a6] |
j |
334071914262529617/693889 |
j-invariant |
L |
3.9436423650352 |
L(r)(E,1)/r! |
Ω |
0.054772812189012 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
9 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
129591d1 129591b1 |
Quadratic twists by: -3 -11 |