Atkin-Lehner |
3+ 7+ 11+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
27489c |
Isogeny class |
Conductor |
27489 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
6912 |
Modular degree for the optimal curve |
Δ |
-4040883 = -1 · 32 · 74 · 11 · 17 |
Discriminant |
Eigenvalues |
-1 3+ -4 7+ 11+ -2 17- 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-50,146] |
[a1,a2,a3,a4,a6] |
Generators |
[-8:14:1] [6:-14:1] |
Generators of the group modulo torsion |
j |
-5764801/1683 |
j-invariant |
L |
3.4654467020793 |
L(r)(E,1)/r! |
Ω |
2.3430524620168 |
Real period |
R |
0.24650512940251 |
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 |
82467k1 27489s1 |
Quadratic twists by: -3 -7 |