Refined Kodaira classes and conductors of twisted elliptic curves

Jerzy Browkin, and Daniel Davies. Refined Kodaira classes and conductors of twisted elliptic curves. 2009. <http://eudml.org/doc/286062>.

@book{JerzyBrowkin2009,
abstract = {We consider elliptic curves defined over ℚ. It is known that for a prime p > 3 quadratic twists permute the Kodaira classes, and curves belonging to a given class have the same conductor exponent. It is not the case for p = 2 and 3. We establish a refinement of the Kodaira classification, ensuring that the permutation property is recovered by \{refined\} classes in the cases p = 2 and 3. We also investigate the nonquadratic twists. In the last part of the paper we discuss the number of isogeny classes of curves for given conductors of some special forms. Representative numerical data are given in the tables.},
author = {Jerzy Browkin, Daniel Davies},
keywords = {elliptic curves; Kodaira symbols; Conductor},
language = {eng},
title = {Refined Kodaira classes and conductors of twisted elliptic curves},
url = {http://eudml.org/doc/286062},
year = {2009},
}

TY - BOOK
AU - Jerzy Browkin
AU - Daniel Davies
TI - Refined Kodaira classes and conductors of twisted elliptic curves
PY - 2009
AB - We consider elliptic curves defined over ℚ. It is known that for a prime p > 3 quadratic twists permute the Kodaira classes, and curves belonging to a given class have the same conductor exponent. It is not the case for p = 2 and 3. We establish a refinement of the Kodaira classification, ensuring that the permutation property is recovered by {refined} classes in the cases p = 2 and 3. We also investigate the nonquadratic twists. In the last part of the paper we discuss the number of isogeny classes of curves for given conductors of some special forms. Representative numerical data are given in the tables.
LA - eng
KW - elliptic curves; Kodaira symbols; Conductor
UR - http://eudml.org/doc/286062
ER -