Atkin-Lehner |
13+ 71+ |
Signs for the Atkin-Lehner involutions |
Class |
11999a |
Isogeny class |
Conductor |
11999 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
15120 |
Modular degree for the optimal curve |
Δ |
-752919455483 = -1 · 139 · 71 |
Discriminant |
Eigenvalues |
0 3 -2 0 0 13+ 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-676,42292] |
[a1,a2,a3,a4,a6] |
Generators |
[1092:7676:27] |
Generators of the group modulo torsion |
j |
-7077888/155987 |
j-invariant |
L |
5.7725169280522 |
L(r)(E,1)/r! |
Ω |
0.75499095512721 |
Real period |
R |
1.9114523455051 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
107991b1 923a1 |
Quadratic twists by: -3 13 |