Atkin-Lehner |
3- 5+ 13+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
86775r |
Isogeny class |
Conductor |
86775 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
658560 |
Modular degree for the optimal curve |
Δ |
-81453251953125 = -1 · 34 · 510 · 13 · 892 |
Discriminant |
Eigenvalues |
-1 3- 5+ 5 -5 13+ -3 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-223763,-40761858] |
[a1,a2,a3,a4,a6] |
Generators |
[613:6940:1] |
Generators of the group modulo torsion |
j |
-126878670165625/8340813 |
j-invariant |
L |
5.2356894329059 |
L(r)(E,1)/r! |
Ω |
0.10975410357823 |
Real period |
R |
5.9629768466309 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000009985 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
86775k1 |
Quadratic twists by: 5 |