Atkin-Lehner |
3+ 7+ 19+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
12369a |
Isogeny class |
Conductor |
12369 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
86400 |
Modular degree for the optimal curve |
Δ |
-13991970321231147 = -1 · 312 · 73 · 195 · 31 |
Discriminant |
Eigenvalues |
0 3+ 2 7+ -2 -2 3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-288947,-59956747] |
[a1,a2,a3,a4,a6] |
j |
-2667962889590455042048/13991970321231147 |
j-invariant |
L |
0.82341479649442 |
L(r)(E,1)/r! |
Ω |
0.1029268495618 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
37107d1 86583v1 |
Quadratic twists by: -3 -7 |