Atkin-Lehner |
2- 3- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368eq |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
128 |
Product of Tamagawa factors cp |
Δ |
719207337600221184 = 218 · 38 · 114 · 134 |
Discriminant |
Eigenvalues |
2- 3- -2 0 11- 13+ 6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-273036,36751120] |
[a1,a2,a3,a4,a6] |
Generators |
[-448:8316:1] [-430:8640:1] |
Generators of the group modulo torsion |
j |
11779205551777/3763454409 |
j-invariant |
L |
10.144591023334 |
L(r)(E,1)/r! |
Ω |
0.26374228716606 |
Real period |
R |
4.8080036446455 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999998046 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
82368w3 20592bg3 27456bz3 |
Quadratic twists by: -4 8 -3 |