Atkin-Lehner |
2- 3- 7+ 11+ |
Signs for the Atkin-Lehner involutions |
Class |
121968dp |
Isogeny class |
Conductor |
121968 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
3244032 |
Modular degree for the optimal curve |
Δ |
4139986917959811072 = 214 · 37 · 72 · 119 |
Discriminant |
Eigenvalues |
2- 3- -4 7+ 11+ 2 6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-714747,210976810] |
[a1,a2,a3,a4,a6] |
Generators |
[-726:18634:1] |
Generators of the group modulo torsion |
j |
5735339/588 |
j-invariant |
L |
4.9916095748508 |
L(r)(E,1)/r! |
Ω |
0.23947486120165 |
Real period |
R |
2.6054976835787 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000011541 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
15246bp1 40656cd1 121968fi1 |
Quadratic twists by: -4 -3 -11 |