WATKINS'S CONJECTURE FOR ELLIPTIC CURVES WITH NON-SPLIT MULTIPLICATIVE REDUCTION

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dc.contributor.authorCaro, Jerson
dc.contributor.authorPasten, Hector
dc.date.accessioned2025-01-20T21:01:31Z
dc.date.available2025-01-20T21:01:31Z
dc.date.issued2022
dc.description.abstractLet E be an elliptic curve over the rational numbers. Watkins [Experiment. Math. 11 (2002), pp. 487-502 (2003)] conjectured that the rank of E is bounded by the 2-adic valuation of the modular degree of E. We prove this conjecture for semistable elliptic curves having exactly one rational point of order 2, provided that they have an odd number of primes of non-split multiplicative reduction or no primes of split multiplicative reduction.
dc.fuente.origenWOS
dc.identifier.doi10.1090/proc/15942
dc.identifier.eissn1088-6826
dc.identifier.issn0002-9939
dc.identifier.urihttps://doi.org/10.1090/proc/15942
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/92903
dc.identifier.wosidWOS:000881424400005
dc.issue.numero8
dc.language.isoen
dc.pagina.final3251
dc.pagina.inicio3245
dc.revistaProceedings of the american mathematical society
dc.rightsacceso restringido
dc.subjectWatkins's conjecture
dc.subjectmodular degree
dc.subjectrank
dc.subjectparity conjecture
dc.titleWATKINS'S CONJECTURE FOR ELLIPTIC CURVES WITH NON-SPLIT MULTIPLICATIVE REDUCTION
dc.typeartículo
dc.volumen150
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
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