Atkin-Lehner |
3- 13+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
15717b |
Isogeny class |
Conductor |
15717 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
10752 |
Modular degree for the optimal curve |
Δ |
-157561526187 = -1 · 34 · 137 · 31 |
Discriminant |
Eigenvalues |
0 3- 0 2 -1 13+ -4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-2253,44633] |
[a1,a2,a3,a4,a6] |
Generators |
[-9:253:1] |
Generators of the group modulo torsion |
j |
-262144000/32643 |
j-invariant |
L |
5.0164582199368 |
L(r)(E,1)/r! |
Ω |
0.99413214433448 |
Real period |
R |
0.6307584771961 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
47151b1 1209b1 |
Quadratic twists by: -3 13 |