The abelian -commutative- group defined on elliptic curves [Le groupe abélien -commutatif- défini sur les courbes elliptiques].




The continuous white line displays the following elliptic curve:
                     2    3
                    y  = x  - x + 1


An elliptic curve is an abelian -i.e. commutative- group:


The 3 points 'P', 'Q' and 'R' have rational coordinates:

                            1       1
                    P = {- --- , + ---}
                            1       1
                            1       7
                    Q = {+ --- , + ---}
                            4       8
                            19       103
                    R = {+ ---- , + -----}
                            25       125



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