Bibliographic Details
| Title: |
A family of monogenic S4 quartic fields arising from elliptic curves. |
| Authors: |
Gassert, T. Alden1 gassert@hws.edu, Smith, Hanson1,2 hanson.smith@colorado.edu, Stange, Katherine E.2 kstange@math.colorado.edu |
| Source: |
Journal of Number Theory. Apr2019, Vol. 197, p361-382. 22p. |
| Subjects: |
Polynomials, Elliptic curves, Integers, Foundations of arithmetic, Algorithms |
| Abstract: |
Abstract We consider partial torsion fields (fields generated by a root of a division polynomial) for elliptic curves. By analysing the reduction properties of elliptic curves, and applying the Montes Algorithm, we obtain information about the ring of integers. In particular, for the partial 3-torsion fields for a certain one-parameter family of non-CM elliptic curves, we describe a power basis. As a result, we show that the one-parameter family of quartic S 4 fields given by T 4 − 6 T 2 − α T − 3 for α ∈ Z such that α ± 8 are squarefree, are monogenic. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
