Atkin-Lehner |
2- 3- 13+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
51714p |
Isogeny class |
Conductor |
51714 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
294912 |
Modular degree for the optimal curve |
Δ |
1240399400677632 = 28 · 310 · 136 · 17 |
Discriminant |
Eigenvalues |
2- 3- -2 0 -4 13+ 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-51746,-4188895] |
[a1,a2,a3,a4,a6] |
Generators |
[-107:391:1] |
Generators of the group modulo torsion |
j |
4354703137/352512 |
j-invariant |
L |
7.0197055445733 |
L(r)(E,1)/r! |
Ω |
0.31816883168283 |
Real period |
R |
1.3789270124588 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000135 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
17238f1 306c1 |
Quadratic twists by: -3 13 |