Atkin-Lehner |
2+ 3- 7+ 13- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
111384s |
Isogeny class |
Conductor |
111384 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
1179648 |
Modular degree for the optimal curve |
Δ |
3236781868040448 = 28 · 312 · 72 · 134 · 17 |
Discriminant |
Eigenvalues |
2+ 3- 2 7+ 0 13- 17+ 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1823799,-948007478] |
[a1,a2,a3,a4,a6] |
Generators |
[90498:9553271:8] |
Generators of the group modulo torsion |
j |
3594902683578163792/17343867177 |
j-invariant |
L |
8.2000813857085 |
L(r)(E,1)/r! |
Ω |
0.12991384515232 |
Real period |
R |
7.8899224899955 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000044726 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
37128be1 |
Quadratic twists by: -3 |