Atkin-Lehner |
2- 3+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368cz |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
98304 |
Modular degree for the optimal curve |
Δ |
3368395210752 = 226 · 33 · 11 · 132 |
Discriminant |
Eigenvalues |
2- 3+ 0 2 11- 13+ 2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-8460,-286192] |
[a1,a2,a3,a4,a6] |
Generators |
[-59:87:1] |
Generators of the group modulo torsion |
j |
9460870875/475904 |
j-invariant |
L |
6.9043148037861 |
L(r)(E,1)/r! |
Ω |
0.49935750449158 |
Real period |
R |
3.456599099525 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000003359 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368a1 20592s1 82368cp1 |
Quadratic twists by: -4 8 -3 |