Atkin-Lehner |
2+ 3- 19- |
Signs for the Atkin-Lehner involutions |
Class |
51984r |
Isogeny class |
Conductor |
51984 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
13824 |
Modular degree for the optimal curve |
Δ |
-113689008 = -1 · 24 · 39 · 192 |
Discriminant |
Eigenvalues |
2+ 3- 0 -3 2 -1 -4 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-570,5263] |
[a1,a2,a3,a4,a6] |
Generators |
[11:18:1] |
Generators of the group modulo torsion |
j |
-4864000/27 |
j-invariant |
L |
4.8483710994773 |
L(r)(E,1)/r! |
Ω |
1.8818931205888 |
Real period |
R |
1.2881632454047 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000067 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
25992g1 17328l1 51984i1 |
Quadratic twists by: -4 -3 -19 |