Atkin-Lehner |
2- 3+ 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368cs |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
20480 |
Modular degree for the optimal curve |
Δ |
-173961216 = -1 · 212 · 33 · 112 · 13 |
Discriminant |
Eigenvalues |
2- 3+ -2 -2 11+ 13+ 6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-36,-640] |
[a1,a2,a3,a4,a6] |
Generators |
[13:33:1] [14:40:1] |
Generators of the group modulo torsion |
j |
-46656/1573 |
j-invariant |
L |
9.429839249458 |
L(r)(E,1)/r! |
Ω |
0.78702884412265 |
Real period |
R |
2.9953918842326 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000096 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368dc1 41184f1 82368db1 |
Quadratic twists by: -4 8 -3 |