Atkin-Lehner |
2- 3- 11- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
120384dk |
Isogeny class |
Conductor |
120384 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1179648 |
Modular degree for the optimal curve |
Δ |
13251306621763584 = 230 · 310 · 11 · 19 |
Discriminant |
Eigenvalues |
2- 3- -2 4 11- 2 6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-215436,38087440] |
[a1,a2,a3,a4,a6] |
j |
5786435182177/69341184 |
j-invariant |
L |
3.1971012788709 |
L(r)(E,1)/r! |
Ω |
0.3996376663602 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
120384bc1 30096bb1 40128br1 |
Quadratic twists by: -4 8 -3 |