Atkin-Lehner |
2+ 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
8712j |
Isogeny class |
Conductor |
8712 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
23040 |
Modular degree for the optimal curve |
Δ |
-18411167366064 = -1 · 24 · 310 · 117 |
Discriminant |
Eigenvalues |
2+ 3- 2 -4 11- -6 6 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,726,206305] |
[a1,a2,a3,a4,a6] |
Generators |
[-28:405:1] |
Generators of the group modulo torsion |
j |
2048/891 |
j-invariant |
L |
4.3040418595563 |
L(r)(E,1)/r! |
Ω |
0.53552271246521 |
Real period |
R |
2.0092713900701 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
17424u1 69696cx1 2904n1 792e1 |
Quadratic twists by: -4 8 -3 -11 |