### ON THE FAMILY OF ELLIPTIC CURVES X + 1/X + Y + 1/Y + t = 0

March 23, 2021

Author(s)

, Abhishek Juyal

We study various properties of the family of elliptic curves x+ 1/x+y+ 1/y+t = 0, which is isomorphic to the Weierstrass curve E_t: Y^2=X(X^2+(t^2/4-2)X+1). This equation arises from the study of the Mahler measure of polynomials. We show that the rank of