On representing coordinates of points on elliptic curves by quadratic forms

Author name not available (Why is that?)

Abstract: Given an elliptic quartic of type

Y^{2} = f (X)

representing an elliptic curve of positive rank over

Q

, we investigate the question of when the

Y

-coordinate can be represented by a quadratic form of type

a p^{2} + b q^{2}

. In particular, we give examples of equations of surfaces of type

c_{0} + c_{1} x + c_{2} x^{2} + c_{3} x^{3} + c_{4} x^{4} = (a p^{2} + b q^{2})^{2}

,

a, b, c i n Q

where we can deduce the existence of infinitely many rational points. We also investigate surfaces of type

Y^{2} = f (a p^{2} + b q^{2})

where the polynomial

f

is of degree

3

.

No records found.

No records found.

This page was built for publication: On representing coordinates of points on elliptic curves by quadratic forms