Atkin-Lehner |
2+ 7+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
129472b |
Isogeny class |
Conductor |
129472 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
884736 |
Modular degree for the optimal curve |
Δ |
84333171738411008 = 222 · 72 · 177 |
Discriminant |
Eigenvalues |
2+ 0 2 7+ 0 2 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-345644,76957232] |
[a1,a2,a3,a4,a6] |
Generators |
[-476:11560:1] |
Generators of the group modulo torsion |
j |
721734273/13328 |
j-invariant |
L |
6.9718327493936 |
L(r)(E,1)/r! |
Ω |
0.34150996938888 |
Real period |
R |
2.5518408189335 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000157375 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
129472cv1 4046i1 7616e1 |
Quadratic twists by: -4 8 17 |