Atkin-Lehner |
2- 3- 5- 71+ |
Signs for the Atkin-Lehner involutions |
Class |
68160di |
Isogeny class |
Conductor |
68160 |
Conductor |
∏ cp |
128 |
Product of Tamagawa factors cp |
deg |
114688 |
Modular degree for the optimal curve |
Δ |
-1192527360000 = -1 · 212 · 38 · 54 · 71 |
Discriminant |
Eigenvalues |
2- 3- 5- -4 -2 -4 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-5305,155975] |
[a1,a2,a3,a4,a6] |
Generators |
[23:-216:1] [-65:480:1] |
Generators of the group modulo torsion |
j |
-4031826095296/291144375 |
j-invariant |
L |
11.411276258509 |
L(r)(E,1)/r! |
Ω |
0.85003690319037 |
Real period |
R |
0.41951400197051 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999551 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
68160cw1 34080d1 |
Quadratic twists by: -4 8 |