Atkin-Lehner |
3- 5+ 13+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
86775o |
Isogeny class |
Conductor |
86775 |
Conductor |
∏ cp |
50 |
Product of Tamagawa factors cp |
deg |
666000 |
Modular degree for the optimal curve |
Δ |
-5733014234802075 = -1 · 35 · 52 · 132 · 895 |
Discriminant |
Eigenvalues |
0 3- 5+ 4 4 13+ -6 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-73503,8466869] |
[a1,a2,a3,a4,a6] |
Generators |
[-303:1735:1] |
Generators of the group modulo torsion |
j |
-1756729147170979840/229320569392083 |
j-invariant |
L |
8.2459382015394 |
L(r)(E,1)/r! |
Ω |
0.41386720458237 |
Real period |
R |
0.39848232048428 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999985729 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
86775j1 |
Quadratic twists by: 5 |