Atkin-Lehner |
2- 3+ 7+ 11+ |
Signs for the Atkin-Lehner involutions |
Class |
51744bs |
Isogeny class |
Conductor |
51744 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
23808 |
Modular degree for the optimal curve |
Δ |
-3569922048 = -1 · 212 · 3 · 74 · 112 |
Discriminant |
Eigenvalues |
2- 3+ -2 7+ 11+ -1 -4 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,131,2773] |
[a1,a2,a3,a4,a6] |
Generators |
[-9:28:1] [12:77:1] |
Generators of the group modulo torsion |
j |
25088/363 |
j-invariant |
L |
7.4567772433311 |
L(r)(E,1)/r! |
Ω |
1.0417389216226 |
Real period |
R |
0.59650080333287 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999992 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
51744bd1 103488cp1 51744ch1 |
Quadratic twists by: -4 8 -7 |