S. Kamienny
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View article: Torsion points on elliptic curves over number fields of small degree
Torsion points on elliptic curves over number fields of small degree Open
Dedicated to the memory of Bas EdixhovenWe determine the set S(d) of possible prime orders of K -rational points on elliptic curves over number fields K of degree d for d = 4, 5, 6, and 7.Definition 1.1.Let d ≥ 1 be an integer.Then we defi…
View article: Rational families of 17-torsion points of elliptic curves over number fields
Rational families of 17-torsion points of elliptic curves over number fields Open
Fumiyuki Momose is very much missed.He was a generous warm human being, with immense energy and generosity of spirit, and an extremely gifted mathematician.One of his abiding interests was rational torsion on elliptic curves over number fi…
View article: Points of order $13$ on elliptic curves
Points of order $13$ on elliptic curves Open
We pick up the study of 13-torsion in elliptic curves where Mazur and Tate left off 45 years ago. We consider various questions concerning elliptic curves defined over the maximal totally real subfield of the 13th cyclotomic field (where J…
View article: Torsion points on elliptic curves over number fields of small degree
Torsion points on elliptic curves over number fields of small degree Open
We determine the set $S(d)$ of possible prime orders of $K$-rational points on elliptic curves over number fields $K$ of degree $d$, for $d = 4$, $5$, $6$, and $7$.