Heron Quadrilaterals via Elliptic Curves
نویسندگان
چکیده
A Heron quadrilateral is a cyclic quadri lateral whose area and side lengths are rational. In this work, we establish a correspondence between Heron quadri laterals and a family of elliptic curves of the form y2 = 3 2 x + αx2 − n x. This correspondence generalizes the no tions of Goins and Maddox who established a similar connec tion between Heron triangles and elliptic curves. We further study this family of elliptic curves, looking at their torsion groups and ranks. We also explore their connection with congruent numbers, which are the α = 0 case. Congruent numbers are positive integers which are the area of a right triangle with rational side lengths.
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