5
votes
2answers
208 views

Find the rational points on $1 + 18 x + 81 x^2 + 44 x^3 = y^2$ with Sage

I'm trying to use Sage on-line,but I meet some trouble with the code of it. I want to find the rational points on an ellipse curve,such as $$1 + 18 x + 81 x^2 + 44 x^3 = y^2,\tag1$$ I know that ...
23
votes
1answer
1k views

How to compute rational or integer points on elliptic curves

This is an attempt to get someone to write a canonical answer, as discussed in this meta thread. We often have people come to us asking for solutions to a diophantine equation which, after some clever ...
0
votes
3answers
673 views

Finding positive integer solutions to functions with only positive integer input

For the equation $f(x,y) = x^2/y$ given that $x$ and $y$ are integers What is the easiest/fastest way to find at least one tuple $(x_0,y_0)$ solution to $f(x,y)=4$ or any other number really. I ...