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Genus 2 fields with degree 3 elliptic subfields

Tanush Shaska

I-AIMS paper 2001-1 · Published in Forum Math. 16 (2004), 263–280 · 2004

In this paper we study genus 2 function fields K with degree 3 elliptic subfields. We compute an equation for the locus of these fields K in the moduli space of genus 2 curves. From this we derive that the number of Aut(K)-classes of such subfields of fixed K is 0, 1, 2 or 4.

MSC classes: Primary 11G30; Secondary 14H05, 14H10, 14H45, 11G99

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