Atkin-Lehner |
2+ 3+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
32856a |
Isogeny class |
Conductor |
32856 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
131328 |
Modular degree for the optimal curve |
Δ |
-1517391124093872 = -1 · 24 · 33 · 378 |
Discriminant |
Eigenvalues |
2+ 3+ 0 0 0 6 4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-4563,-1876392] |
[a1,a2,a3,a4,a6] |
Generators |
[6955790016:217212676597:7077888] |
Generators of the group modulo torsion |
j |
-256000/36963 |
j-invariant |
L |
5.116391555614 |
L(r)(E,1)/r! |
Ω |
0.21198830613663 |
Real period |
R |
12.067626863145 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999996 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
65712g1 98568p1 888c1 |
Quadratic twists by: -4 -3 37 |