Atkin-Lehner |
3+ 7+ 19+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
86583b |
Isogeny class |
Conductor |
86583 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
702240 |
Modular degree for the optimal curve |
Δ |
-32647930749539343 = -1 · 311 · 74 · 195 · 31 |
Discriminant |
Eigenvalues |
1 3+ -2 7+ 3 -5 -7 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-72741,-11545344] |
[a1,a2,a3,a4,a6] |
j |
-17728773124168057/13597638796143 |
j-invariant |
L |
0.14068691005063 |
L(r)(E,1)/r! |
Ω |
0.14068696023463 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
86583w1 |
Quadratic twists by: -7 |