In this paper, we present several methods for the construction of elliptic curves with large torsion group and positive rank
over number fields of small degree. We also discuss potential applications of such curves in the elliptic curve factorization
Authors:Andrej Dujella, Clemens Fuchs and Robert Tichy
In this paper, we prove that there does not exist a set with more than 26 polynomials with integer coefficients, such that
the product of any two of them plus a linear polynomial is a square of a polynomial with integer coefficients.