Atkin-Lehner |
13- 71+ |
Signs for the Atkin-Lehner involutions |
Class |
11999b |
Isogeny class |
Conductor |
11999 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
48984 |
Modular degree for the optimal curve |
Δ |
-3795466975089803 = -1 · 139 · 713 |
Discriminant |
Eigenvalues |
0 -1 0 0 0 13- 0 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-248993,-47830989] |
[a1,a2,a3,a4,a6] |
j |
-160989184000/357911 |
j-invariant |
L |
0.21369520376021 |
L(r)(E,1)/r! |
Ω |
0.1068476018801 |
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 |
107991e1 11999c1 |
Quadratic twists by: -3 13 |