PRINCIPAL QUARTIC EXTENSIONS AND ELLIPTIC CURVES

Abstract : We associate to an S 4 extension, M/K, a Brauer-Severi variety, whose K-rational points correspond to quartic polynomials of the form u 4 + Au + B with splitting field M. The condition that M/K is generated by such a polynomial is a necessary and sufficient condition for M ⊆ K(E[4]) for some elliptic curve E/K. We point out a flaw in the related work of Holden, provide numerical examples, and describe a family of elliptic curves with the same mod 4 representation.
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Submitted on : Monday, October 17, 2016 - 5:56:24 PM
Last modification on : Thursday, October 20, 2016 - 1:01:15 AM

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Kevin Mugo. PRINCIPAL QUARTIC EXTENSIONS AND ELLIPTIC CURVES. 2016. 〈hal-01382899〉

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