Atkin-Lehner |
2+ 3- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368bu |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
196608 |
Modular degree for the optimal curve |
Δ |
10568143872 = 210 · 38 · 112 · 13 |
Discriminant |
Eigenvalues |
2+ 3- -2 0 11- 13+ -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-169896,-26953976] |
[a1,a2,a3,a4,a6] |
Generators |
[2066:91872:1] |
Generators of the group modulo torsion |
j |
726516846671872/14157 |
j-invariant |
L |
4.4695243395371 |
L(r)(E,1)/r! |
Ω |
0.23515475595027 |
Real period |
R |
4.7516839733526 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999980109 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368dq1 10296d1 27456x1 |
Quadratic twists by: -4 8 -3 |