Atkin-Lehner |
2- 7- 71- |
Signs for the Atkin-Lehner involutions |
Class |
111328bi |
Isogeny class |
Conductor |
111328 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
331776 |
Modular degree for the optimal curve |
Δ |
-11735474573312 = -1 · 212 · 79 · 71 |
Discriminant |
Eigenvalues |
2- -3 2 7- -1 1 2 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-3724,186592] |
[a1,a2,a3,a4,a6] |
Generators |
[-24:512:1] [21:343:1] |
Generators of the group modulo torsion |
j |
-11852352/24353 |
j-invariant |
L |
8.3539532384438 |
L(r)(E,1)/r! |
Ω |
0.63634532011143 |
Real period |
R |
1.6410023331321 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999983235 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
111328k1 15904h1 |
Quadratic twists by: -4 -7 |