Add to ORKGWe examine the ranks of a subfamily of curves in a previous article, which are derived from the existence of solutions to certain Pell equations. We exhibit an abundance of curves of moderately large rank, and prove under mild conditions that these curves have rank at least three.Comment: 4 page
We extend a result of Spearman which provides a sufficient condition for elliptic curves of the form...
Given the family of elliptic curves y2= x3-(1+u4) x, uQ, or equivalently y2=x3-(m4+n4)x for m,n inte...
In 2007, Bogomolov and Tschinkel proved that given two complex elliptic curves $E_1$ and $E_2$ along...
In this short note, we examine the ranks of a subfamily of curves from a previous paper derived from...
We determine average sizes/bounds for the $2$- and $3$-Selmer groups in various families of elliptic...
Fix an elliptic curve $E$ over a number field $F$ and an integer $n$ which is a power of $3$. We stu...
The study of elliptic curves grows out of the study of elliptic functions which dates back to work d...
AbstractWe give several new constructions for moderate rank elliptic curves over Q(T). In particular...
If an integer n is written as a sum of two biquadrates in two different ways, then the elliptic curv...
Given the family of elliptic curves y2= x3-(1+u4) x, uQ, or equivalently y2=x3-(m4+n4)x for m,n inte...
In 1987, Zagier and Kramarz published a paper in which they presented evidence that a positive propo...
In 1987, Zagier and Kramarz published a paper in which they presented evidence that a positive propo...
A class of prime numbers p is given for which the elliptic curve y² =x³-px has rank two. This extend...
A class of prime numbers p is given for which the elliptic curve y² =x³-px has rank two. This extend...
We count by height the number of elliptic curves over the rationals, both up to isomorphism over the...
We extend a result of Spearman which provides a sufficient condition for elliptic curves of the form...
Given the family of elliptic curves y2= x3-(1+u4) x, uQ, or equivalently y2=x3-(m4+n4)x for m,n inte...
In 2007, Bogomolov and Tschinkel proved that given two complex elliptic curves $E_1$ and $E_2$ along...
In this short note, we examine the ranks of a subfamily of curves from a previous paper derived from...
We determine average sizes/bounds for the $2$- and $3$-Selmer groups in various families of elliptic...
Fix an elliptic curve $E$ over a number field $F$ and an integer $n$ which is a power of $3$. We stu...
The study of elliptic curves grows out of the study of elliptic functions which dates back to work d...
AbstractWe give several new constructions for moderate rank elliptic curves over Q(T). In particular...
If an integer n is written as a sum of two biquadrates in two different ways, then the elliptic curv...
Given the family of elliptic curves y2= x3-(1+u4) x, uQ, or equivalently y2=x3-(m4+n4)x for m,n inte...
In 1987, Zagier and Kramarz published a paper in which they presented evidence that a positive propo...
In 1987, Zagier and Kramarz published a paper in which they presented evidence that a positive propo...
A class of prime numbers p is given for which the elliptic curve y² =x³-px has rank two. This extend...
A class of prime numbers p is given for which the elliptic curve y² =x³-px has rank two. This extend...
We count by height the number of elliptic curves over the rationals, both up to isomorphism over the...
We extend a result of Spearman which provides a sufficient condition for elliptic curves of the form...
Given the family of elliptic curves y2= x3-(1+u4) x, uQ, or equivalently y2=x3-(m4+n4)x for m,n inte...
In 2007, Bogomolov and Tschinkel proved that given two complex elliptic curves $E_1$ and $E_2$ along...