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A New Family Of Elliptic Curves With Positive Rank arising from Pythagorean Triples
elliptic curves rank pythagorean triples
2011/2/28
The aim of this paper is to introduce a new family of elliptic curves in the form of y2 = x(x−a2)(x−b2) that have positive ranks. We first generate a list of pythagorean triples (a, b, c) ...
A new family of elliptic curves with positive ranks arising from the Heron triangles
Elliptic curves Ranks Torsion group Heron’s Triangle
2011/2/28
The aim of this paper is to introduce a new family of elliptic curves with positive ranks.
We examine the moduli space E = T of complex tori T( ) =C/L( ) where L( ) = const · 2( )L . We find that the Dedekind eta function furnishes a bridge between the euclidean and hyperbolic structur...