Atkin-Lehner |
2+ 3- 7- 41+ |
Signs for the Atkin-Lehner involutions |
Class |
82656u |
Isogeny class |
Conductor |
82656 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
86016 |
Modular degree for the optimal curve |
Δ |
34587072576 = 26 · 38 · 72 · 412 |
Discriminant |
Eigenvalues |
2+ 3- 2 7- 4 -2 6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-5169,-142760] |
[a1,a2,a3,a4,a6] |
Generators |
[158810:1744029:1000] |
Generators of the group modulo torsion |
j |
327367684288/741321 |
j-invariant |
L |
8.8224480595658 |
L(r)(E,1)/r! |
Ω |
0.56312785965165 |
Real period |
R |
7.8334324131995 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002748 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
82656i1 27552bc1 |
Quadratic twists by: -4 -3 |