scholarly journals On the number of large integer points on elliptic curves

2009 ◽  
Vol 138 (4) ◽  
pp. 317-327 ◽  
Author(s):  
P. G. Walsh
Keyword(s):  
Elliptic Curves ◽  
Large Integer ◽  
Integer Points

Integer points and the rank of Thue elliptic curves

1982 ◽  
Vol 66 (3) ◽  
pp. 395-404 ◽  
Author(s):  
Joseph H. Silverman
Keyword(s):  
Elliptic Curves ◽  
Integer Points

scholarly journals On the magnitude of integer points on elliptic curves

1995 ◽  
Vol 52 (2) ◽  
pp. 195-199 ◽  
Author(s):  
Ákos Pintér
Keyword(s):  
Elliptic Curves ◽  
Integer Points

The known effective bounds for the magnitude of integer points on elliptic curves are exponential in the “height” of curve. The bound given in this note is polynomial in the height and depends slightly on the discriminant.

ON THE NUMBER OF INTEGER POINTS ON THE ELLIPTIC CURVE y2 = x3 + Ax

2011 ◽  
Vol 07 (03) ◽  
pp. 611-621 ◽  
Author(s):  
KONSTANTINOS A. DRAZIOTIS
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Upper Bound ◽  
Integer Points

It is given an upper bound for the number of the integer points of the elliptic curve y2 = x3 + Ax (A ∈ ℤ) and a conjecture of Schmidt is proven for this family of elliptic curves.

scholarly journals Integer points on elliptic curves

2005 ◽  
Vol 222 (2) ◽  
pp. 237-252 ◽  
Author(s):  
Wen-Chen Chi ◽  
King Fai Lai ◽  
Ki-Seng Tan
Keyword(s):  
Elliptic Curves ◽  
Integer Points
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