Atkin-Lehner |
2+ 3- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368bs |
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 |
[-3676:20405:64] |
Generators of the group modulo torsion |
j |
3122884507648/835956693 |
j-invariant |
L |
9.8572505434252 |
L(r)(E,1)/r! |
Ω |
0.37772384795774 |
Real period |
R |
6.524111855184 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000572 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368dp1 10296n1 27456d1 |
Quadratic twists by: -4 8 -3 |