Three elliptic curves with rank at least seven

Abstract

Three rational elliptic curves whose ranks are at least 7 are exhibited. The arithmetical details are given for one of the curves, namely <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="y squared equals x cubed plus 1692602 x squared minus 530052723915 x"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>y</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> <mml:mo>=</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>x</mml:mi> <mml:mn>3</mml:mn> </mml:msup> </mml:mrow> <mml:mo>+</mml:mo> <mml:mn>1692602</mml:mn> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>x</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> <mml:mo>−<!-- − --></mml:mo> <mml:mn>530052723915</mml:mn> <mml:mi>x</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">{y^2} = {x^3} + 1692602{x^2} - 530052723915x</mml:annotation> </mml:semantics> </mml:math> </inline-formula> .

Locations

• Mathematics of Computation - View - PDF