Atkin-Lehner |
2+ 13- 79+ |
Signs for the Atkin-Lehner involutions |
Class |
8216b |
Isogeny class |
Conductor |
8216 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1024 |
Modular degree for the optimal curve |
Δ |
-262912 = -1 · 28 · 13 · 79 |
Discriminant |
Eigenvalues |
2+ -2 0 -3 -2 13- -8 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-33,67] |
[a1,a2,a3,a4,a6] |
Generators |
[-1:10:1] [1:6:1] |
Generators of the group modulo torsion |
j |
-16000000/1027 |
j-invariant |
L |
4.0380531181348 |
L(r)(E,1)/r! |
Ω |
3.055949122761 |
Real period |
R |
0.33034361469416 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999994 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
16432d1 65728c1 73944v1 106808h1 |
Quadratic twists by: -4 8 -3 13 |