Tekcan, Ahmet2024-10-112024-10-112011-01-010129-2021https://eds.p.ebscohost.com/eds/pdfviewer/pdfviewerhttps://hdl.handle.net/11452/46258Let p equivalent to 1(mod 4) be a prime number and let F p be a finite field. In this work, we derive some algebraic properties of principal indefinite binary quadratic forms F = (1, 1,- p - 1/4) of discriminant Delta = p. Later we consider the number of rational points on singular curves E F associated to F.eninfo:eu-repo/semantics/closedAccessIndefinite binary quadratic formPrincipal formElliptic curveSingular curveScience & technologyPhysical sciencesMathematicsArticle0002172502000128598673550219-175X