Elliptic curves of bounded degree and height

Silverman, Joseph H.

doi:10.1090/S0002-9939-1989-0953747-8

Elliptic curves of bounded degree and height
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by Joseph H. Silverman

Proc. Amer. Math. Soc. 105 (1989), 540-545

DOI: https://doi.org/10.1090/S0002-9939-1989-0953747-8

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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.

References

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Heights on families of abelian varieties

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