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|a (DE-627)JST120815249
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|a (JST)26430478
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|a DE-627
|b ger
|c DE-627
|e rakwb
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|a eng
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|a AGASHE, Amod
|e verfasserin
|4 aut
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|a Rational torsion in elliptic curves and the cuspidal subgroup
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|c 2018
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|a Text
|b txt
|2 rdacontent
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|a Computermedien
|b c
|2 rdamedia
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|a Online-Ressource
|b cr
|2 rdacarrier
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|a SoitAune courbe elliptique sur Q de conducteurNsans facteurs carré, ayant un point rationnel d’ordre un nombre premierrne divisant pas 6N. On montre alors querdivise l’ordre du sous-groupe cuspidalCdeJ₀(N). SiAest une courbe de Weil, on peut la considérer comme une sous-variéte abélienne deJ₀(N). Notre preuve montre plus precisément querdivise l’ordre deA∩C. De plus, sous les hypothèses plus haut, mais sans supposer querne divise pasN, on montre qu’il existe un facteur premierpdeNtel que la valeur propre de l’involution d’Atkin–LehnerWp agissant sur la forme modulaire associée àAest égale à −1. LetAbe an elliptic curve over Q of square free conductorNthat has a rational torsion point of prime orderrsuch thatrdoes not divide 6N. We show that thenrdivides the order of the cuspidal subgroupCofJ₀(N). If A is optimal, then viewingAas an abelian subvariety ofJ₀(N), our proof shows more precisely thatrdivides the order ofA∩C. Also, under the hypotheses above minus the hypothesis thatrdoes not divideN, we show that for some primepthat dividesN, the eigenvalue of the Atkin–Lehner involutionWp acting on the newform associated toAis −1.
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|a © Société Arithmétique de Bordeaux, 2018
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|a Elliptic curves
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|a torsion subgroup
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|a cuspidal subgroup
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|a Mathematics
|x Pure mathematics
|x Algebra
|x Coefficients
|x Fourier coefficients
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|a Mathematics
|x Pure mathematics
|x Discrete mathematics
|x Number theory
|x Numbers
|x Real numbers
|x Rational numbers
|x Integers
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|a Mathematics
|x Pure mathematics
|x Linear algebra
|x Matrix theory
|x Eigenfunctions
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|a Mathematics
|x Pure mathematics
|x Geometry
|x Geometric shapes
|x Curves
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|a Mathematics
|x Pure mathematics
|x Linear algebra
|x Vector analysis
|x Mathematical vectors
|x Eigenvectors
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4 |
|a Mathematics
|x Pure mathematics
|x Linear algebra
|x Matrix theory
|x Eigenvalues
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|a Mathematics
|x Pure mathematics
|x Linear algebra
|x Determinants
|x Jacobians
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|a Mathematics
|x Pure mathematics
|x Geometry
|x Geometric shapes
|x Curves
|x Mathematical cusps
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|a Mathematics
|x Pure mathematics
|x Arithmetic
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|a research-article
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|i Enthalten in
|t Journal de Théorie des Nombres de Bordeaux
|d Société Arithmétique de Bordeaux, 1993
|g 30(2018), 1, Seite 81-91
|w (DE-627)320967603
|w (DE-600)2028468-8
|x 21188572
|7 nnns
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|g volume:30
|g year:2018
|g number:1
|g pages:81-91
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|u https://www.jstor.org/stable/26430478
|3 Volltext
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|a AR
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|d 30
|j 2018
|e 1
|h 81-91
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