Atkin-Lehner |
2- 3+ 7+ 13+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
111384bj |
Isogeny class |
Conductor |
111384 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
344064 |
Modular degree for the optimal curve |
Δ |
57317841728784 = 24 · 39 · 77 · 13 · 17 |
Discriminant |
Eigenvalues |
2- 3+ -3 7+ 2 13+ 17+ 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-16119,-698409] |
[a1,a2,a3,a4,a6] |
j |
1470708907776/182003003 |
j-invariant |
L |
1.7085867181886 |
L(r)(E,1)/r! |
Ω |
0.42714663148985 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
111384a1 |
Quadratic twists by: -3 |