Atkin-Lehner |
2+ 3+ 5+ 67- |
Signs for the Atkin-Lehner involutions |
Class |
80400f |
Isogeny class |
Conductor |
80400 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
-15436800 = -1 · 210 · 32 · 52 · 67 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 0 -2 -4 3 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-8,192] |
[a1,a2,a3,a4,a6] |
Generators |
[-4:12:1] [-2:14:1] |
Generators of the group modulo torsion |
j |
-2500/603 |
j-invariant |
L |
9.2285945634038 |
L(r)(E,1)/r! |
Ω |
1.8013918957642 |
Real period |
R |
0.64037943278 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000013 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
40200bd1 80400bj1 |
Quadratic twists by: -4 5 |