Atkin-Lehner |
2+ 3+ 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
82368m |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
442368 |
Modular degree for the optimal curve |
Δ |
-33244506086178816 = -1 · 230 · 39 · 112 · 13 |
Discriminant |
Eigenvalues |
2+ 3+ -2 -2 11- 13- -4 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,19764,-8706960] |
[a1,a2,a3,a4,a6] |
Generators |
[1394:1331:8] |
Generators of the group modulo torsion |
j |
165469149/6443008 |
j-invariant |
L |
4.2493741203381 |
L(r)(E,1)/r! |
Ω |
0.17721031139882 |
Real period |
R |
5.9948178037334 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002878 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368cv1 2574a1 82368c1 |
Quadratic twists by: -4 8 -3 |