Atkin-Lehner |
2+ 3- 13+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
69966p |
Isogeny class |
Conductor |
69966 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
50688 |
Modular degree for the optimal curve |
Δ |
-17987838804 = -1 · 22 · 37 · 132 · 233 |
Discriminant |
Eigenvalues |
2+ 3- -1 -4 -4 13+ -2 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,495,-4991] |
[a1,a2,a3,a4,a6] |
Generators |
[32:-223:1] |
Generators of the group modulo torsion |
j |
108750551/146004 |
j-invariant |
L |
2.3561838923046 |
L(r)(E,1)/r! |
Ω |
0.65406118006907 |
Real period |
R |
0.30019922243149 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000646 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
23322k1 69966be1 |
Quadratic twists by: -3 13 |