Atkin-Lehner |
2+ 3- 5- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
32160j |
Isogeny class |
Conductor |
32160 |
Conductor |
∏ cp |
96 |
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 |
[121:-1500:1] |
Generators of the group modulo torsion |
j |
8620168984064/19079296875 |
j-invariant |
L |
6.4977200371852 |
L(r)(E,1)/r! |
Ω |
0.31693108411129 |
Real period |
R |
0.21356246551352 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999998 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
32160d1 64320bx1 96480y1 |
Quadratic twists by: -4 8 -3 |