Atkin-Lehner |
2+ 3- 13+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
72384v |
Isogeny class |
Conductor |
72384 |
Conductor |
∏ cp |
104 |
Product of Tamagawa factors cp |
deg |
359424 |
Modular degree for the optimal curve |
Δ |
-4096669527834624 = -1 · 219 · 313 · 132 · 29 |
Discriminant |
Eigenvalues |
2+ 3- -1 -3 -2 13+ -1 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-53121,5611743] |
[a1,a2,a3,a4,a6] |
Generators |
[171:1248:1] [-102:3159:1] |
Generators of the group modulo torsion |
j |
-63239829700321/15627554046 |
j-invariant |
L |
10.857150656054 |
L(r)(E,1)/r! |
Ω |
0.41827264471898 |
Real period |
R |
0.24958763309867 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999814 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
72384bo1 2262j1 |
Quadratic twists by: -4 8 |