Fornea, MicheleGuitart Morales, XavierMasdeu, Marc2023-02-132024-09-172022-09-170001-8708https://hdl.handle.net/2445/193534For modular elliptic curves over number fields of narrow class number one, and with multiplicative reduction at a collection of $p$-adic primes, we define new $p$-adic invariants. Inspired by Nekováŕ and Scholl's plectic conjectures, we believe these invariants control the Mordell-Weil group of higher rank elliptic curves and we support our expectations with numerical experiments.application/pdfengcc-by-nc-nd (c) Elsevier B.V., 2022https://creativecommons.org/licenses/by-nc-nd/4.0/Teoria algebraica de nombresFuncions LGrups discontinusCorbes el·líptiquesAlgebraic number theoryL-functionsDiscontinuous groupsElliptic curvesinfo:eu-repo/semantics/article7281122023-02-13info:eu-repo/semantics/openAccess