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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Elliptic curves of bounded degree and height


Author: Joseph H. Silverman
Journal: Proc. Amer. Math. Soc. 105 (1989), 540-545
MSC: Primary 11G05; Secondary 14G25, 14K07
DOI: https://doi.org/10.1090/S0002-9939-1989-0953747-8
MathSciNet review: 953747
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Abstract: We show that there are only finitely many elliptic curves of bounded degree and height, provided that one takes a naive height defined in terms of minimal Weierstrass equations. We show that the corresponding statement is false if instead one uses the Faltings-Parshin modular height.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0953747-8
Article copyright: © Copyright 1989 American Mathematical Society