Atkin-Lehner |
2+ 7- 17- |
Signs for the Atkin-Lehner involutions |
Class |
53312u |
Isogeny class |
Conductor |
53312 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
9216 |
Modular degree for the optimal curve |
Δ |
-13647872 = -1 · 214 · 72 · 17 |
Discriminant |
Eigenvalues |
2+ -1 0 7- 5 -5 17- -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,47,113] |
[a1,a2,a3,a4,a6] |
Generators |
[-1:8:1] |
Generators of the group modulo torsion |
j |
14000/17 |
j-invariant |
L |
4.2353315522589 |
L(r)(E,1)/r! |
Ω |
1.4949409692068 |
Real period |
R |
1.4165547802418 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000096 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
53312by1 3332d1 53312a1 |
Quadratic twists by: -4 8 -7 |