Atkin-Lehner |
2- 3- 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368dp |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
344064 |
Modular degree for the optimal curve |
Δ |
624038327497728 = 210 · 318 · 112 · 13 |
Discriminant |
Eigenvalues |
2- 3- 2 -4 11+ 13+ 6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-27624,1295512] |
[a1,a2,a3,a4,a6] |
Generators |
[146:612:1] |
Generators of the group modulo torsion |
j |
3122884507648/835956693 |
j-invariant |
L |
6.4759874875103 |
L(r)(E,1)/r! |
Ω |
0.47972715466052 |
Real period |
R |
3.3748284959711 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000235 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368bs1 20592o1 27456cg1 |
Quadratic twists by: -4 8 -3 |