Atkin-Lehner |
13- 71- |
Signs for the Atkin-Lehner involutions |
Class |
11999c |
Isogeny class |
Conductor |
11999 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
3768 |
Modular degree for the optimal curve |
Δ |
-786330467 = -1 · 133 · 713 |
Discriminant |
Eigenvalues |
0 -1 0 0 0 13- 0 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-1473,-21318] |
[a1,a2,a3,a4,a6] |
Generators |
[178:2307:1] |
Generators of the group modulo torsion |
j |
-160989184000/357911 |
j-invariant |
L |
2.7118907761758 |
L(r)(E,1)/r! |
Ω |
0.38524450723908 |
Real period |
R |
1.1732335894118 |
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 |
107991c1 11999b1 |
Quadratic twists by: -3 13 |