Atkin-Lehner |
2- 3- 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
82368ew |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
98304 |
Modular degree for the optimal curve |
Δ |
-1245119496192 = -1 · 214 · 312 · 11 · 13 |
Discriminant |
Eigenvalues |
2- 3- 0 -4 11- 13- -8 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,420,-53584] |
[a1,a2,a3,a4,a6] |
Generators |
[50:304:1] |
Generators of the group modulo torsion |
j |
686000/104247 |
j-invariant |
L |
4.8229998633484 |
L(r)(E,1)/r! |
Ω |
0.40739970491347 |
Real period |
R |
2.9596240515923 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000004674 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368bc1 20592c1 27456bl1 |
Quadratic twists by: -4 8 -3 |