On elliptic curves assigned to a pair of right triangles with an equal hypotenuse
AS Zargar, S Tomita - Quaestiones Mathematicae, 2024 - Taylor & Francis
Consider a pair of right triangles with an equal hypotenuse. This turns out to solve the
diophantine system of equations a 2+ b 2= c 2+ d 2= e 2 in integers. To this system we …
diophantine system of equations a 2+ b 2= c 2+ d 2= e 2 in integers. To this system we …
Families of Mordell Curves with Non-trivial Torsion and Rank of at Least Three
In this study, we consider a particular type of elliptic curves called Mordell curves, and
construct two infinite families of such curves with rank of at least three. We do this by using …
construct two infinite families of such curves with rank of at least three. We do this by using …
Elliptic curve involving subfamilies of rank at least 5 over Q (t) or Q (t, k)
Motivated by the work of Zargar and Zamani, we introduce a family of elliptic curves
containing several one-(respectively two-) parameter subfamilies of high rank over the …
containing several one-(respectively two-) parameter subfamilies of high rank over the …
Elliptic curve involving subfamilies of rank at least 5 over or
Motivated by the work of Zargar and Zamani, we introduce a family of elliptic curves
containing several one-(respectively two-) parameter subfamilies of high rank over the …
containing several one-(respectively two-) parameter subfamilies of high rank over the …
On the rank of elliptic curves arising from Pythagorean quadruplets, II
By a Pythagorean quadruplet $(a, b, c, d) $, we mean an integer solution to the quadratic
equation $ a^ 2+ b^ 2= c^ 2+ d^ 2$. We use Pythagorean quadruplets to construct infinite …
equation $ a^ 2+ b^ 2= c^ 2+ d^ 2$. We use Pythagorean quadruplets to construct infinite …