## Abstract

Let *A* be the coordinate ring of an affine elliptic curve (over an infinite field *k*) of the form *X* – {*p*}, where *X* is projective and *p* is a closed point on *X*. Denote by *F* the function field of *X*. We show that the image of *H*.(GL_{2} (*A*), ℤ) in *H*.(GL_{2} (*F*), ℤ) coincides with the image of *H*.(GL_{2} (*k*), ℤ). As a consequence, we obtain numerous results about the *K*-theory of *A* and *X*. For example, if *k* is a number field, we show that *r*
_{2} (*K*
_{2} (*A*) ⊗ ℚ) = 0, where *r _{m}* denotes the

*m*th level of the rank filtration.

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