Atkin-Lehner |
3+ 5+ 11- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
47685b |
Isogeny class |
Conductor |
47685 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
21504 |
Modular degree for the optimal curve |
Δ |
-13241886075 = -1 · 34 · 52 · 113 · 173 |
Discriminant |
Eigenvalues |
0 3+ 5+ -1 11- 2 17+ -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-11,-5533] |
[a1,a2,a3,a4,a6] |
Generators |
[41:-248:1] [23:76:1] |
Generators of the group modulo torsion |
j |
-32768/2695275 |
j-invariant |
L |
6.4530843044575 |
L(r)(E,1)/r! |
Ω |
0.57527797330804 |
Real period |
R |
0.46738885401707 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
47685o1 |
Quadratic twists by: 17 |