Atkin-Lehner |
2- 3- 5- 7+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
11970cc |
Isogeny class |
Conductor |
11970 |
Conductor |
∏ cp |
192 |
Product of Tamagawa factors cp |
deg |
18432 |
Modular degree for the optimal curve |
Δ |
81443880000 = 26 · 37 · 54 · 72 · 19 |
Discriminant |
Eigenvalues |
2- 3- 5- 7+ 2 -2 -4 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-6512,203411] |
[a1,a2,a3,a4,a6] |
Generators |
[-39:649:1] |
Generators of the group modulo torsion |
j |
41886766402489/111720000 |
j-invariant |
L |
7.2613744221365 |
L(r)(E,1)/r! |
Ω |
1.0856181316453 |
Real period |
R |
0.13934792482256 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
95760fe1 3990k1 59850cj1 83790dr1 |
Quadratic twists by: -4 -3 5 -7 |