3 citations · 4 across the 6 of their papers we have counts for
6 papers · 1 filter
Quadratic Twists of Heronian Elliptic Curves with Arbitrarily Large 2-Selmer Rank
Vinodkumar Ghale, Md Imdadul Islam
This paper explicitly determines the 2-Selmer group of the family of elliptic curves arising from Heron triangles of area 2mn. By analyzing the quadratic twists induced by powers o…
Heronian elliptic curves and the size of the -Selmer group
Debopam Chakraborty, Vinodkumar Ghale
A generalization of the congruent number problem is to find positive integers that appear as the areas of Heron triangles. Selmer group of a congruent number elliptic curve has…
A Diophantine Criterion for the Shafarevich-Tate Groups of Elliptic Curves from Heron Triangles
Vinodkumar Ghale
The solvability of Diophantine quartic equations is a contemporary area of interest due to its connection with generalized Fermat's equation. In this work, we are interested in the…
Class number divisibility of constructed from elliptic curves of -Selmer rank exactly
Debopam Chakraborty, Vinodkumar Ghale, MD Imdadul Islam
The class number divisibility problem for number fields is one of the classical problems in algebraic number theory, which originated from Gauss' class number conjectures. The rela…
Construction of an infinite family of elliptic curves of 2-selmer rank 1 from heron triangles
Debopam Chakraborty, Vinodkumar Ghale, Anupam Saikia
Given any positive integer n, it is well known that there always exist triangles with rational sides a, b and c such that the area of the triangle is n. Assuming finiteness of the…
Heron triangles and a family of elliptic curves with rank zero
Vinodkumar Ghale, Shamik Das, Debopam Chakraborty
Given any positive integer , it is well-known that there always exists a triangle with rational sides and such that the area of the triangle is . For a given prime…