Atkin-Lehner |
2- 3- 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368dr |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
442368 |
Modular degree for the optimal curve |
Δ |
-15713223579795456 = -1 · 222 · 39 · 114 · 13 |
Discriminant |
Eigenvalues |
2- 3- -2 0 11+ 13+ -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-88716,11824400] |
[a1,a2,a3,a4,a6] |
Generators |
[13:3267:1] |
Generators of the group modulo torsion |
j |
-404075127457/82223856 |
j-invariant |
L |
4.3473026055335 |
L(r)(E,1)/r! |
Ω |
0.37604865771277 |
Real period |
R |
1.4450598731266 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001617 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368bv1 20592bt1 27456bs1 |
Quadratic twists by: -4 8 -3 |