38 citations · 186 across the 31 of their papers we have counts for
7 papers · 1 filter
Elliptic curves with large torsion and positive rank over number fields of small degree and ECM factorization
Andrej Dujella, Filip Najman
In this paper, we present several methods for construction of elliptic curves with large torsion group and positive rank over number fields of small degree. We also discuss potenti…
Ranks of elliptic curves with prescribed torsion over number fields
Johan Bosman, Peter Bruin, Andrej Dujella +1
We study the structure of the Mordell--Weil group of elliptic curves over number fields of degree 2, 3, and 4. We show that if is a group, then either the class of all elliptic…
On the number of elliptic curves with prescribed isogeny or torsion group over number fields of prime degree
Filip Najman
Let be a prime and a number field of degree . We count the number of elliptic curves, up to -isomorphism, having a prescribed property, where this property is e…
Exceptional elliptic curves over quartic fields
Filip Najman
We study the number of elliptic curves, up to isomorphism, over a fixed quartic field having a prescribed torsion group as a subgroup. Let , where $…
Large strings of consecutive smooth integers
Filip Najman
In this note we improve an algorithm from a recent paper by Bauer and Bennett for computing a function of Erdös that measures the minimal gap size in the sequence of integer…
Torsion of elliptic curves over cubic fields
Filip Najman
Although it is not known which groups can appear as torsion groups of elliptic curves over cubic number fields, it is known which groups can appear for infinitely many non-isomorph…
Torsion groups of elliptic curves over quadratic fields
Sheldon Kamienny, Filip Najman
We describe methods to determine all the possible torsion groups of an elliptic curve that actually appear over a fixed quadratic field. We use these methods to find, for each grou…