Atkin-Lehner |
2- 3+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368dc |
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 |
[2:24:1] |
Generators of the group modulo torsion |
j |
-46656/1573 |
j-invariant |
L |
6.1093746715083 |
L(r)(E,1)/r! |
Ω |
1.506270055912 |
Real period |
R |
1.0139905936885 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999997562 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368cs1 41184d1 82368cq1 |
Quadratic twists by: -4 8 -3 |