Atkin-Lehner |
2- 3- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368ep |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
1204224 |
Modular degree for the optimal curve |
Δ |
-2406332879774613504 = -1 · 216 · 313 · 116 · 13 |
Discriminant |
Eigenvalues |
2- 3- 2 0 11- 13+ -8 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,213396,64269520] |
[a1,a2,a3,a4,a6] |
j |
22494434350748/50367250791 |
j-invariant |
L |
2.1522930823347 |
L(r)(E,1)/r! |
Ω |
0.17935776218437 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368u1 20592f1 27456ca1 |
Quadratic twists by: -4 8 -3 |