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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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
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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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1991-1094964-6
PII: S 0025-5718(1991)1094964-6
Article copyright: © Copyright 1991 American Mathematical Society