Atkin-Lehner |
2+ 3- 11- 53+ |
Signs for the Atkin-Lehner involutions |
Class |
111936f |
Isogeny class |
Conductor |
111936 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
172032 |
Modular degree for the optimal curve |
Δ |
-207593819136 = -1 · 210 · 38 · 11 · 532 |
Discriminant |
Eigenvalues |
2+ 3- -2 -4 11- 2 6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-5709,-169389] |
[a1,a2,a3,a4,a6] |
Generators |
[195:2484:1] |
Generators of the group modulo torsion |
j |
-20099254724608/202728339 |
j-invariant |
L |
5.9798193984419 |
L(r)(E,1)/r! |
Ω |
0.27444924741101 |
Real period |
R |
2.7235542812783 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000027096 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
111936g1 13992a1 |
Quadratic twists by: -4 8 |