Atkin-Lehner |
2+ 3- 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
82368bk |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
161280 |
Modular degree for the optimal curve |
Δ |
-6350280228864 = -1 · 215 · 36 · 112 · 133 |
Discriminant |
Eigenvalues |
2+ 3- 3 1 11+ 13- 5 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-5196,188368] |
[a1,a2,a3,a4,a6] |
Generators |
[-48:572:1] |
Generators of the group modulo torsion |
j |
-649461896/265837 |
j-invariant |
L |
9.3718035648334 |
L(r)(E,1)/r! |
Ω |
0.70602858191633 |
Real period |
R |
1.1061643259299 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
82368cm1 41184bg1 9152m1 |
Quadratic twists by: -4 8 -3 |