On the Equation x4 + mx2y2 + y4 = z2

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

By relating the title equation to an elliptic curve E and performing calculations with the L-series of E, we are able (subject to the standard conjectures) to determine solvability in rationals of the title equation for all m in the range |m| ≤ 3000. A wild assertion of Euler is corrected, a table of solutions given for |m| ≤ 200, and statistical information tabulated concerning the distribution of Mordell-Weil ranks and conjectural orders of Shafarevich-Tate groups.

Original languageEnglish (US)
Pages (from-to)268-298
Number of pages31
JournalJournal of Number Theory
Volume50
Issue number2
DOIs
StatePublished - Feb 1995

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Assertion
Elliptic Curves
Solvability
Euler
Table
Series
Range of data
Standards

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

On the Equation x4 + mx2y2 + y4 = z2 . / Bremner, Andrew; Jones, John.

In: Journal of Number Theory, Vol. 50, No. 2, 02.1995, p. 268-298.

Research output: Contribution to journalArticle

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