Let $ E_ {m, n} $ be an elliptic curve over $\mathbb {Q} $ of the form $ y^ 2= x^ 3-m^ 2x+ n^
2$, where $ m $ and $ n $ are positive integers. Brown and Myers showed that the curve …

In this paper, we study the torsion subgroup and rank of elliptic curves for the subfamilies of
E_ m, p: y^ 2= x^ 3-m^ 2x+ p^ 2 E m, p: y 2= x 3-m 2 x+ p 2, where m is a positive integer and …

We prove, using elementary methods, that each member of the infinite families of elliptic
curves given by $ E_m\colon y^ 2= x^ 3-x+ m^ 6$ and $ E_m'\colon y^ 2= x^ 3+ xm^ 6$ have …

In this article, we consider a family of elliptic curves defined by $ E_ {m}: y^ 2= x^ 3-m^ 2
x+(pqr)^ 2$ where $ m $ is a positive integer and $ p, q,~\text {and}~ r $ are distinct odd …

A family of elliptic curves of rank ≥ 5 over Q(m) Page 1 Notes on Number Theory and Discrete
Mathematics Print ISSN 1310–5132, Online ISSN 2367–8275 Vol. 25, 2019, No. 4, 24–29 DOI …

Let C m: y 2= x 3− m 2 x+ p 2 q 2 be a family of elliptic curves over ℚ, where m is a positive
integer and p, q are distinct odd primes. We study the torsion part and the rank of C m (ℚ) …

THE MORDELL-WEIL BASES FOR THE ELLIPTIC CURVE y2 = x3 − m2x + m 1. Introduction
The family Em,n : y2 = x3 − m2x + n 2 of ell Page 1 Czechoslovak Mathematical Journal, 71 …

In this short note, we extend results in several papers by proving effectively that for m
sufficiently large, an elliptic curve given by y2= f (x)+ m2, with f (x) a cubic polynomial that …

We construct a subfamily of elliptic curves E (r, s):(ys)(y+s)= x (xr)(x+r) with r= 2 (m^ 4-2m^
3+2m^ 2+2m+1), s= 2 (m^ 2-2m-1)(m^ 2+1)^ 2, and show that its rank is at least five …