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What kind of reals do you want ?

One could do

sage: E = EllipticCurve_from_c4c6(AA(4),AA(5).sqrt()); E
Elliptic Curve defined by y^2 = x^3 - 1/12*x - 0.002588041640624757? over Algebraic Real Field
sage: E.point_set(AA)                                                           
Abelian group of points on Elliptic Curve defined by y^2 = x^3 - 1/12*x - 0.002588041640624757? over Algebraic Real Field