Atkin-Lehner |
2- 5+ 13- 83- |
Signs for the Atkin-Lehner involutions |
Class |
86320q |
Isogeny class |
Conductor |
86320 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
319488 |
Modular degree for the optimal curve |
Δ |
-1553572167680000 = -1 · 220 · 54 · 134 · 83 |
Discriminant |
Eigenvalues |
2- 1 5+ -1 -3 13- 1 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-59376,5863124] |
[a1,a2,a3,a4,a6] |
Generators |
[124:-650:1] [-110:3328:1] |
Generators of the group modulo torsion |
j |
-5652022596440689/379290080000 |
j-invariant |
L |
11.653158038633 |
L(r)(E,1)/r! |
Ω |
0.46825915697866 |
Real period |
R |
0.7776915481163 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999915 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
10790e1 |
Quadratic twists by: -4 |