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AN ANALOGUE OF CIRCULAR UNITS FOR PRODUCTS OF ELLIPTIC CURVES

Published online by Cambridge University Press:  27 May 2004

Srinath Baba
Affiliation:
Department of Mathematics, McGill University, Montreal, Quebec H3A 2K6, Canada (sbaba@math.mcgill.ca)
Ramesh Sreekantan
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Colaba, Mumbai 400 005, India (ramesh@math.tifr.res.in)
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Abstract

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We construct certain elements in the motivic cohomology group $H^3_{\mathcal{M}}(E\times E',\mathbb{Q}(2))$, where $E$ and $E'$ are elliptic curves over $\mathbb{Q}$. When $E$ is not isogenous to $E'$ these elements are analogous to circular units in real quadratic fields, as they come from modular parametrizations of the elliptic curves. We then find an analogue of the class-number formula for real quadratic fields, which specializes to the usual quadratic class-number formula when $E$ and $E'$ are quadratic twists.

AMS 2000 Mathematics subject classification: Primary 11F67; 14G35. Secondary 11F11; 11E45; 14G10

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2004