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Exponents of Class Groups and Elliptic Curves

✍ Scribed by Siman Wong

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 102 KB
Volume: 89
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.2000.2623

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✦ Synopsis

We show that the number of elliptic curves over Q with conductor N is < < = N 1Â4+= , and for almost all positive integers N, this can be improved to < < = N = . The second estimate follows from a theorem of Davenpart and Heilbronn on the average size of the 3-class groups of quadratic fields. The first estimate follows from the fact that the 3-class group of a quadratic field Q(-D) has size < < = |D| 1Â4+= , a non-trivial improvement over the Brauer Siegel estimate.

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