Atkin-Lehner |
5+ 37+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
82325a |
Isogeny class |
Conductor |
82325 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
26496 |
Modular degree for the optimal curve |
Δ |
1286328125 = 58 · 37 · 89 |
Discriminant |
Eigenvalues |
0 2 5+ 2 -3 1 0 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-283,-532] |
[a1,a2,a3,a4,a6] |
Generators |
[-12:31:1] |
Generators of the group modulo torsion |
j |
160989184/82325 |
j-invariant |
L |
7.3660292681783 |
L(r)(E,1)/r! |
Ω |
1.2291105202898 |
Real period |
R |
2.996487762187 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000004522 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
16465a1 |
Quadratic twists by: 5 |