Atkin-Lehner |
2+ 3+ 7- 17- |
Signs for the Atkin-Lehner involutions |
Class |
5712g |
Isogeny class |
Conductor |
5712 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
69120 |
Modular degree for the optimal curve |
Δ |
-421592736568502016 = -1 · 28 · 324 · 73 · 17 |
Discriminant |
Eigenvalues |
2+ 3+ -2 7- 0 2 17- 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-706644,-230527296] |
[a1,a2,a3,a4,a6] |
Generators |
[35631028:749995680:29791] |
Generators of the group modulo torsion |
j |
-152435594466395827792/1646846627220711 |
j-invariant |
L |
3.037406583568 |
L(r)(E,1)/r! |
Ω |
0.082279137209828 |
Real period |
R |
12.305292635815 |
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 |
2856h1 22848cw1 17136j1 39984o1 |
Quadratic twists by: -4 8 -3 -7 |