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L-Functions and Algebraic Varieties. A conference in memory of Alexey Zykin
February 5, 2018 15:00–16:00, Moscow, Moscow Independent University, 11 Bolshoi Vlassievsky per.
 


Integral points on a family of elliptic curves

M. Hindry
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M. Hindry



Abstract: We consider the family of elliptic curves with equation [ $y^{2}+y=x^{3}-a^{2x}$ ] Using various Diophantine tools (reduction mod p, Néron-Tate heights, linear forms in elliptic logarithms) we will show many properties of the set of integral points and especially related the set to the rank of the elliptic curve.
 
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