Atkin-Lehner |
2- 13+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
12688d |
Isogeny class |
Conductor |
12688 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
53760 |
Modular degree for the optimal curve |
Δ |
82253821478608 = 24 · 135 · 614 |
Discriminant |
Eigenvalues |
2- 0 2 -2 6 13+ -2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-122524,-16501677] |
[a1,a2,a3,a4,a6] |
Generators |
[10170207230214:475922543520675:4524874264] |
Generators of the group modulo torsion |
j |
12713561533627711488/5140863842413 |
j-invariant |
L |
4.9869412748548 |
L(r)(E,1)/r! |
Ω |
0.2551848001201 |
Real period |
R |
19.542469898316 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
3172a1 50752j1 114192br1 |
Quadratic twists by: -4 8 -3 |