On the equation x4 + m x2y2 + y4 = z2

Research output: Contribution to journalArticle

3 Scopus citations

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

ASJC Scopus subject areas

  • Algebra and Number Theory

Fingerprint Dive into the research topics of 'On the equation x<sup>4</sup> + m x<sup>2</sup>y<sup>2</sup> + y<sup>4</sup> = z<sup>2</sup>'. Together they form a unique fingerprint.

  • Cite this