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math.NT2023
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…
math.NT2023
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…
math.NT2023
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…