scholarly journals Periodic continued fractions and elliptic curves over quadratic fields

2016 ◽  
Vol 76 ◽  
pp. 200-218
Author(s):  
Mohammad Sadek
Keyword(s):  
Elliptic Curves ◽  
Continued Fractions ◽  
Quadratic Fields ◽  
Periodic Continued Fractions

scholarly journals p-Torsion points on elliptic curves defined over quadratic fields

1984 ◽  
Vol 96 ◽  
pp. 139-165 ◽  
Author(s):  
Fumiyuki Momose
Keyword(s):  
Elliptic Curves ◽  
Prime Number ◽  
Number Field ◽  
Algebraic Number ◽  
Algebraic Number Field ◽  
Quadratic Fields ◽  
Finite Degree ◽  
Torsion Points

Let p be a prime number and k an algebraic number field of finite degree d. Manin [14] showed that there exists an integer n = n(k,p) (≧0) which satisfies the condition

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