{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T16:43:40Z","timestamp":1776789820723,"version":"3.51.2"},"reference-count":23,"publisher":"American Mathematical Society (AMS)","issue":"266","license":[{"start":{"date-parts":[[2009,7,1]],"date-time":"2009-07-01T00:00:00Z","timestamp":1246406400000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    Stroeker and Tzanakis gave convincing numerical and heuristic evidence for the fact that in their\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"script upper E l l o g\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">E<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mi>l<\/mml:mi>\n                            <mml:mi>l<\/mml:mi>\n                            <mml:mi>o<\/mml:mi>\n                            <mml:mi>g<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathcal {E}llog<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    method a certain parameter\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"lamda\">\n                        <mml:semantics>\n                          <mml:mi>\n                            \u03bb\n                            \n                          <\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">\\lambda<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    plays a decisive role in the size of the final bound for the integral points on elliptic curves. Furthermore, they provided an algorithm to determine the Mordell-Weil basis of the curve which corresponds to the optimal choice of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"lamda\">\n                        <mml:semantics>\n                          <mml:mi>\n                            \u03bb\n                            \n                          <\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">\\lambda<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . In this paper we show that working with more Mordell-Weil bases simultaneously, the final bound for the integral points can be further decreased.\n                  <\/p>","DOI":"10.1090\/s0025-5718-08-02160-1","type":"journal-article","created":{"date-parts":[[2009,12,1]],"date-time":"2009-12-01T13:09:23Z","timestamp":1259672963000},"page":"1201-1210","source":"Crossref","is-referenced-by-count":1,"title":["Parallel LLL-reduction for bounding the integral solutions of elliptic Diophantine equations"],"prefix":"10.1090","volume":"78","author":[{"given":"L.","family":"Hajdu","sequence":"first","affiliation":[]},{"given":"T.","family":"Kov\u00e1cs","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2008,7,1]]},"reference":[{"key":"1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1112\/jlms\/s1-43.1.1","article-title":"The Diophantine equation \ud835\udc66\u00b2=\ud835\udc4e\ud835\udc65\u00b3+\ud835\udc4f\ud835\udc65\u00b2+\ud835\udc50\ud835\udc65+\ud835\udc51","volume":"43","author":"Baker, A.","year":"1968","journal-title":"J. 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