Atkin-Lehner |
3+ 7+ 13+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
16653b |
Isogeny class |
Conductor |
16653 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
82944 |
Modular degree for the optimal curve |
Δ |
-8266673214891 = -1 · 38 · 7 · 13 · 614 |
Discriminant |
Eigenvalues |
-2 3+ -3 7+ 2 13+ 0 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-40082,3105170] |
[a1,a2,a3,a4,a6] |
Generators |
[-222:1006:1] [-100:2470:1] |
Generators of the group modulo torsion |
j |
-7121683981554577408/8266673214891 |
j-invariant |
L |
2.7648927352366 |
L(r)(E,1)/r! |
Ω |
0.73389424505989 |
Real period |
R |
0.47092833092898 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000004 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
49959e1 116571s1 |
Quadratic twists by: -3 -7 |