The torsion subgroup of a family of elliptic curves over the maximal abelian extension of ℚ

Jerome Tomagan Dimabayao

Czechoslovak Mathematical Journal (2020)

  • Volume: 70, Issue: 4, page 979-995
  • ISSN: 0011-4642

Abstract

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We determine explicitly the structure of the torsion group over the maximal abelian extension of ℚ and over the maximal p -cyclotomic extensions of ℚ for the family of rational elliptic curves given by y 2 = x 3 + B , where B is an integer.

How to cite

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Dimabayao, Jerome Tomagan. "The torsion subgroup of a family of elliptic curves over the maximal abelian extension of $\mathbb {Q}$." Czechoslovak Mathematical Journal 70.4 (2020): 979-995. <http://eudml.org/doc/297410>.

@article{Dimabayao2020,
abstract = {We determine explicitly the structure of the torsion group over the maximal abelian extension of $\mathbb \{Q\}$ and over the maximal $p$-cyclotomic extensions of $\mathbb \{Q\}$ for the family of rational elliptic curves given by $y^2 = x^3 + B$, where $B$ is an integer.},
author = {Dimabayao, Jerome Tomagan},
journal = {Czechoslovak Mathematical Journal},
keywords = {torsion group; elliptic curve; cyclotomic field},
language = {eng},
number = {4},
pages = {979-995},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The torsion subgroup of a family of elliptic curves over the maximal abelian extension of $\mathbb \{Q\}$},
url = {http://eudml.org/doc/297410},
volume = {70},
year = {2020},
}

TY - JOUR
AU - Dimabayao, Jerome Tomagan
TI - The torsion subgroup of a family of elliptic curves over the maximal abelian extension of $\mathbb {Q}$
JO - Czechoslovak Mathematical Journal
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 70
IS - 4
SP - 979
EP - 995
AB - We determine explicitly the structure of the torsion group over the maximal abelian extension of $\mathbb {Q}$ and over the maximal $p$-cyclotomic extensions of $\mathbb {Q}$ for the family of rational elliptic curves given by $y^2 = x^3 + B$, where $B$ is an integer.
LA - eng
KW - torsion group; elliptic curve; cyclotomic field
UR - http://eudml.org/doc/297410
ER -

References

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