Abstract Let E: y 2= x 3+ A x 2+ B x+ C be a nonconstant elliptic curve over Q (t) with at least
one nontrivial Q (t)-rational 2-torsion point. We describe a method for finding t 0∈ Q for …

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 find a parametrization of rank≥ 3 over the function field Q (a, i, s, n, k, l) where s2= i3+
a2. From this we get families of rank≥ 3 and≥ 4 over fields of rational functions in four …

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 …

This thesis deals with several theoretical and computational problems in the theory of p-adic
heights on elliptic curves. In Chapter 3 we provide a new algorithm for the computation of the …

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 …

We study the Legendre family of elliptic curves E t: y 2= x (x− 1)(x− Δ t), parametrized by
triangular numbers Δ t= t (t+ 1)/2. We prove that the rank of E t over the function field Q‒(t) is …

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) …

Sažetak Kroz ovaj rad su uvedeni osnovni pojmovi o eliptičkim krivuljama nad poljem
racionalnih brojeva\(\mathbb {Q}\) i nad konačnim poljima\(\mathbb {F} _p\). Definiran je …