Atkin-Lehner |
2- 3- 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
82368fd |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
47104 |
Modular degree for the optimal curve |
Δ |
6671808 = 26 · 36 · 11 · 13 |
Discriminant |
Eigenvalues |
2- 3- 2 -4 11- 13- 6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1719,-27432] |
[a1,a2,a3,a4,a6] |
Generators |
[76:530:1] |
Generators of the group modulo torsion |
j |
12040481088/143 |
j-invariant |
L |
6.8280624859418 |
L(r)(E,1)/r! |
Ω |
0.74144833623191 |
Real period |
R |
4.6045436663913 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
4.0000000028329 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368ef1 41184z4 9152t1 |
Quadratic twists by: -4 8 -3 |