Atkin-Lehner |
2- 3- 23+ 59+ |
Signs for the Atkin-Lehner involutions |
Class |
8142f |
Isogeny class |
Conductor |
8142 |
Conductor |
∏ cp |
216 |
Product of Tamagawa factors cp |
deg |
24192 |
Modular degree for the optimal curve |
Δ |
2516279758848 = 212 · 39 · 232 · 59 |
Discriminant |
Eigenvalues |
2- 3- 0 -4 0 2 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-23703,1400553] |
[a1,a2,a3,a4,a6] |
Generators |
[-114:1677:1] |
Generators of the group modulo torsion |
j |
1472769585318768625/2516279758848 |
j-invariant |
L |
6.8185479240228 |
L(r)(E,1)/r! |
Ω |
0.81323424471631 |
Real period |
R |
1.3974136743347 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
6 |
Number of elements in the torsion subgroup |
Twists |
65136m1 24426f1 |
Quadratic twists by: -4 -3 |