Atkin-Lehner |
2- 17+ 59+ |
Signs for the Atkin-Lehner involutions |
Class |
68204a |
Isogeny class |
Conductor |
68204 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
64512 |
Modular degree for the optimal curve |
Δ |
-22785865136 = -1 · 24 · 176 · 59 |
Discriminant |
Eigenvalues |
2- -1 -3 1 -6 -4 17+ 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-2697,55306] |
[a1,a2,a3,a4,a6] |
Generators |
[-45:289:1] [-11:289:1] |
Generators of the group modulo torsion |
j |
-5619712/59 |
j-invariant |
L |
6.551375527389 |
L(r)(E,1)/r! |
Ω |
1.2087984257415 |
Real period |
R |
0.45164516182777 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000084 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
236b1 |
Quadratic twists by: 17 |