Atkin-Lehner |
2+ 3- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368bt |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
Δ |
399667986432 = 215 · 38 · 11 · 132 |
Discriminant |
Eigenvalues |
2+ 3- -2 0 11- 13+ 0 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-3756,-83216] |
[a1,a2,a3,a4,a6] |
Generators |
[-34:72:1] |
Generators of the group modulo torsion |
j |
245314376/16731 |
j-invariant |
L |
4.8736688332244 |
L(r)(E,1)/r! |
Ω |
0.61245963956389 |
Real period |
R |
0.99469183787351 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999994286 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368v2 41184ba2 27456w2 |
Quadratic twists by: -4 8 -3 |