Atkin-Lehner |
2+ 3+ 5- 67- |
Signs for the Atkin-Lehner involutions |
Class |
32160d |
Isogeny class |
Conductor |
32160 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
67584 |
Modular degree for the optimal curve |
Δ |
-78148800000000 = -1 · 212 · 36 · 58 · 67 |
Discriminant |
Eigenvalues |
2+ 3+ 5- 2 0 -4 -3 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,6835,363237] |
[a1,a2,a3,a4,a6] |
Generators |
[179:2700:1] |
Generators of the group modulo torsion |
j |
8620168984064/19079296875 |
j-invariant |
L |
5.2715814870756 |
L(r)(E,1)/r! |
Ω |
0.42412954702773 |
Real period |
R |
0.38841180159595 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
32160j1 64320ch1 96480z1 |
Quadratic twists by: -4 8 -3 |