A family of cyclic quartic fields arising from modular curves

Washington, Lawrence C.

doi:10.1090/S0025-5718-1991-1094964-6

A family of cyclic quartic fields arising from modular curves
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Math. Comp. 57 (1991), 763-775 Request permission

Abstract:

We study a family of cyclic quartic fields arising from the covering of modular curves ${X_1}(16) \to {X_0}(16)$. An integral basis and a fundamental system of units are found. It is shown that a root of the quartic polynomial we construct is a translate of a cyclotomic period by an integer of the quadratic subfield of the quartic field.

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