Atkin-Lehner |
2+ 3- 7- 17- |
Signs for the Atkin-Lehner involutions |
Class |
68544cj |
Isogeny class |
Conductor |
68544 |
Conductor |
∏ cp |
144 |
Product of Tamagawa factors cp |
deg |
165888 |
Modular degree for the optimal curve |
Δ |
-120764587474944 = -1 · 215 · 37 · 73 · 173 |
Discriminant |
Eigenvalues |
2+ 3- -1 7- -5 -1 17- -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-16428,967664] |
[a1,a2,a3,a4,a6] |
Generators |
[142:1224:1] [-130:952:1] |
Generators of the group modulo torsion |
j |
-20525811272/5055477 |
j-invariant |
L |
9.8856731338339 |
L(r)(E,1)/r! |
Ω |
0.56110334812927 |
Real period |
R |
0.12234913247752 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999996 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68544bk1 34272bk1 22848k1 |
Quadratic twists by: -4 8 -3 |