The Division Equation

Abstract

Let A be an elliptic curve defined over a number field K. Let (x, y) be a generic point on A, and let

EquationSource% MathType!Translator!2!1!AMS LaTeX.tdl!AMSLaTeX! % MathType!MTEF!2!1!+- % feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOBamaabm % aabaGaamiEaiaacYcacaWG5baacaGLOaGaayzkaaGaeyypa0ZaaeWa % aeaacaWG4bGaeSigI8MaamOBaiaacYcacaWG5bGaeSigI8MaamOBaa % GaayjkaiaawMcaaiaac6caaaa!4562!]]</EquationSource><EquationSource Format="TEX"><![CDATA[$$n\left( {x,y} \right) = \left( {x \circ n,y \circ n} \right).$$