ON THE FAMILY OF ELLIPTIC CURVES X + 1/ X + Y + 1/ Y + t = 0 [0.03%]
关于椭圆曲线X + 1/X + Y + 1/Y + t = 0的家族
Abhishek Juyal,Dustin Moody
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 ...
Abhishek Juyal,Shiv Datt Kumar,Dustin Moody
Abhishek Juyal
We study the Legendre family of elliptic curves Et : y 2 = x(x - 1)(x - Δ t ), parametrized by triangular numbers Δ t = t(t + 1)/2. We prove that the rank of Et over the function field Q ‒ ( t ) is 1, while the rank is 0 over Q ( ...
Foad Khoshnam,Dustin Moody
Foad Khoshnam
Working over the field ℚ(t), Kihara constructed an elliptic curve with torsion group ℤ/4ℤ and five independent rational points, showing the rank is at least five. Following his approach, we give a new infinite family of elliptic curves w...