A family of cyclic quartic fields arising from modular curves
Author:
Lawrence C. Washington
Journal:
Math. Comp. 57 (1991), 763-775
MSC:
Primary 11R16; Secondary 11G05
DOI:
https://doi.org/10.1090/S0025-5718-1991-1094964-6
MathSciNet review:
1094964
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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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© Copyright 1991
American Mathematical Society