Atkin-Lehner |
3- 17- 83- |
Signs for the Atkin-Lehner involutions |
Class |
12699c |
Isogeny class |
Conductor |
12699 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
13824 |
Modular degree for the optimal curve |
Δ |
-344187232209 = -1 · 315 · 172 · 83 |
Discriminant |
Eigenvalues |
1 3- 3 -2 5 -4 17- -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-1998,-43983] |
[a1,a2,a3,a4,a6] |
j |
-1210333063393/472136121 |
j-invariant |
L |
2.8021566023518 |
L(r)(E,1)/r! |
Ω |
0.35026957529398 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
4233a1 |
Quadratic twists by: -3 |