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Explicit estimates on a theorem of Shioda concerning the ranksof curves given by y2=x3-a2x+m2
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On the family of elliptic curves y2=x3-m2x+p2\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\varvec{y^2=x^3-m^2x+p^2}$$\end{document}
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ON QUADRATIC TWISTS OF ELLIPTIC CURVES y(2) = x(x - 1)(x - lambda)
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