Atkin-Lehner |
2- 3+ 11+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
120384cd |
Isogeny class |
Conductor |
120384 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
33792 |
Modular degree for the optimal curve |
Δ |
-92454912 = -1 · 214 · 33 · 11 · 19 |
Discriminant |
Eigenvalues |
2- 3+ 2 4 11+ -1 3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,96,-288] |
[a1,a2,a3,a4,a6] |
Generators |
[201:2853:1] |
Generators of the group modulo torsion |
j |
221184/209 |
j-invariant |
L |
9.9445622729668 |
L(r)(E,1)/r! |
Ω |
1.0408137436598 |
Real period |
R |
4.7773015569561 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000036997 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
120384f1 30096o1 120384ck1 |
Quadratic twists by: -4 8 -3 |