Mordell’s theorem,which says that the group of rational points on an elliptic curve is finitelygenerated;
Mordell's theorem indicates that the group of rational points on an elliptic curve is finitely generated.
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- Jan 2024
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a special case of Hasse’s theorem, due to Gauss, which de-scribes the number of points on an elliptic curve defined over a finite field.
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Nagell–Lutz theorem, which gives a precise procedure for finding all of therational points of finite order on an elliptic curve;
The Nagell-Lutz theorem provides a constructive algorithm on elliptic curves for finding all of the ration points of finite order.
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the emphasis of this book is on number theoretic aspects ofelliptic curves, so we feel that an informal approach to the underlying geom-etry is permissible, since it allows us more rapid access to the number theory.
The approach of the book is underpinned more by number theory rather than geometry, though the geometry is used for some basic motivations.
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Silverman, Joseph H., and John T. Tate. Rational Points on Elliptic Curves. 2nd ed. Undergraduate Texts in Mathematics. 1992. Reprint, New York: Springer, 2015.
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