Geodesic
Fields of definition of elliptic curves with prescribed torsion
Peter Bruin 1   ; Filip Najman 2
1 Mathematisch Instituut Universiteit Leiden Postbus 9512 2300 RA Leiden, Netherlands
2 Department of Mathematics University of Zagreb Bijenička cesta 30 10000 Zagreb, Croatia
Acta Arithmetica, Tome 181 (2017) no. 1, pp. 85-95 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

We prove that all elliptic curves over quadratic fields with a subgroup isomorphic to $C_{16}$, as well as all elliptic curves over cubic fields with a subgroup isomorphic to $C_2\times C_{14}$, are base changes of elliptic curves defined over $\mathbb{Q}$. We obtain these results by studying geometric properties of modular curves and maps between modular curves, and then obtaining a modular description of these curves and maps.
DOI : 10.4064/aa170323-20-9
Keywords: prove elliptic curves quadratic fields subgroup isomorphic elliptic curves cubic fields subgroup isomorphic times base changes elliptic curves defined mathbb obtain these results studying geometric properties modular curves maps between modular curves obtaining modular description these curves maps

Peter Bruin  1   ; Filip Najman  2

1 Mathematisch Instituut Universiteit Leiden Postbus 9512 2300 RA Leiden, Netherlands
2 Department of Mathematics University of Zagreb Bijenička cesta 30 10000 Zagreb, Croatia 
@article{10_4064_aa170323_20_9,
     author = {Peter Bruin and Filip Najman},
     title = {Fields of definition of elliptic curves with prescribed torsion},
     journal = {Acta Arithmetica},
     pages = {85--95},
     year = {2017},
     volume = {181},
     number = {1},
     doi = {10.4064/aa170323-20-9},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/aa170323-20-9/}
}
TY  - JOUR
AU  - Peter Bruin
AU  - Filip Najman
TI  - Fields of definition of elliptic curves with prescribed torsion
JO  - Acta Arithmetica
PY  - 2017
SP  - 85
EP  - 95
VL  - 181
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4064/aa170323-20-9/
DO  - 10.4064/aa170323-20-9
LA  - en
ID  - 10_4064_aa170323_20_9
ER  - 
%0 Journal Article
%A Peter Bruin
%A Filip Najman
%T Fields of definition of elliptic curves with prescribed torsion
%J Acta Arithmetica
%D 2017
%P 85-95
%V 181
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/aa170323-20-9/
%R 10.4064/aa170323-20-9
%G en
%F 10_4064_aa170323_20_9
Peter Bruin; Filip Najman. Fields of definition of elliptic curves with prescribed torsion. Acta Arithmetica, Tome 181 (2017) no. 1, pp. 85-95. doi: 10.4064/aa170323-20-9

Cité par Sources :