Atkin-Lehner |
2+ 3- 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
82368be |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
-2404839849984 = -1 · 221 · 36 · 112 · 13 |
Discriminant |
Eigenvalues |
2+ 3- -1 1 11+ 13- 1 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-19308,-1035344] |
[a1,a2,a3,a4,a6] |
Generators |
[36945:545963:125] |
Generators of the group modulo torsion |
j |
-4165509529/12584 |
j-invariant |
L |
6.4377227548789 |
L(r)(E,1)/r! |
Ω |
0.20246812751279 |
Real period |
R |
7.9490570170625 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999936789 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
82368ez1 2574w1 9152k1 |
Quadratic twists by: -4 8 -3 |