Atkin-Lehner |
2+ 3- 11+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
128832r |
Isogeny class |
Conductor |
128832 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
61440 |
Modular degree for the optimal curve |
Δ |
-5342920704 = -1 · 215 · 35 · 11 · 61 |
Discriminant |
Eigenvalues |
2+ 3- 3 -2 11+ -1 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-129,3519] |
[a1,a2,a3,a4,a6] |
Generators |
[15:72:1] |
Generators of the group modulo torsion |
j |
-7301384/163053 |
j-invariant |
L |
10.048630548755 |
L(r)(E,1)/r! |
Ω |
1.1400434948789 |
Real period |
R |
0.44071259311297 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000050715 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
128832j1 64416a1 |
Quadratic twists by: -4 8 |