Atkin-Lehner |
2+ 3- 13+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
5304d |
Isogeny class |
Conductor |
5304 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
18432 |
Modular degree for the optimal curve |
Δ |
137822155630848 = 28 · 38 · 136 · 17 |
Discriminant |
Eigenvalues |
2+ 3- 0 2 -2 13+ 17- -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-40108,-3053056] |
[a1,a2,a3,a4,a6] |
Generators |
[-112:216:1] |
Generators of the group modulo torsion |
j |
27873248949250000/538367795433 |
j-invariant |
L |
4.7680721520147 |
L(r)(E,1)/r! |
Ω |
0.33775397586881 |
Real period |
R |
1.764624731563 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
10608a1 42432j1 15912l1 68952ba1 |
Quadratic twists by: -4 8 -3 13 |