Atkin-Lehner |
2- 3- 7+ 13- 17- |
Signs for the Atkin-Lehner involutions |
Class |
111384bw |
Isogeny class |
Conductor |
111384 |
Conductor |
∏ cp |
128 |
Product of Tamagawa factors cp |
deg |
1277952 |
Modular degree for the optimal curve |
Δ |
2598886964485650384 = 24 · 39 · 7 · 132 · 178 |
Discriminant |
Eigenvalues |
2- 3- -2 7+ 0 13- 17- 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-346386,-11881595] |
[a1,a2,a3,a4,a6] |
Generators |
[-478:6669:1] |
Generators of the group modulo torsion |
j |
394055318218528768/222812668422981 |
j-invariant |
L |
5.2303858789646 |
L(r)(E,1)/r! |
Ω |
0.21215827461237 |
Real period |
R |
3.0816532576998 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999504953 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
37128h1 |
Quadratic twists by: -3 |