Atkin-Lehner |
2+ 3- 7- 43+ |
Signs for the Atkin-Lehner involutions |
Class |
86688p |
Isogeny class |
Conductor |
86688 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
414720 |
Modular degree for the optimal curve |
Δ |
108355599023616 = 29 · 315 · 73 · 43 |
Discriminant |
Eigenvalues |
2+ 3- -1 7- -2 7 7 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-81003,-8859454] |
[a1,a2,a3,a4,a6] |
Generators |
[-1342:729:8] |
Generators of the group modulo torsion |
j |
157481496648008/290304567 |
j-invariant |
L |
7.1498308388142 |
L(r)(E,1)/r! |
Ω |
0.283023417119 |
Real period |
R |
2.1051941302985 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001878 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
86688bl1 28896i1 |
Quadratic twists by: -4 -3 |