AN ANALOGUE OF CIRCULAR UNITS FOR PRODUCTS OF ELLIPTIC CURVES - Baba, Srinath; Sreekantan, Ramesh (Proceedings of the Edinburgh Mathematical Society, 2004)
We construct certain elements in the motivic cohomology group $H^3_{\mathcal{M}}(E× E',\mathbb{Q}(2))$, 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