On families of 9-congruent elliptic curves

Tom Fisher. "On families of 9-congruent elliptic curves." Acta Arithmetica 171.4 (2015): 371-387. <http://eudml.org/doc/279340>.

@article{TomFisher2015,
abstract = {We compute equations for the families of elliptic curves 9-congruent to a given elliptic curve. We use these to find infinitely many non-trivial pairs of 9-congruent elliptic curves over ℚ, i.e. pairs of non-isogenous elliptic curves over ℚ whose 9-torsion subgroups are isomorphic as Galois modules.},
author = {Tom Fisher},
journal = {Acta Arithmetica},
keywords = {elliptic curves; Galois representations},
language = {eng},
number = {4},
pages = {371-387},
title = {On families of 9-congruent elliptic curves},
url = {http://eudml.org/doc/279340},
volume = {171},
year = {2015},
}

TY - JOUR
AU - Tom Fisher
TI - On families of 9-congruent elliptic curves
JO - Acta Arithmetica
PY - 2015
VL - 171
IS - 4
SP - 371
EP - 387
AB - We compute equations for the families of elliptic curves 9-congruent to a given elliptic curve. We use these to find infinitely many non-trivial pairs of 9-congruent elliptic curves over ℚ, i.e. pairs of non-isogenous elliptic curves over ℚ whose 9-torsion subgroups are isomorphic as Galois modules.
LA - eng
KW - elliptic curves; Galois representations
UR - http://eudml.org/doc/279340
ER -