20191205 12:04:34 +0200  received badge  ● Student (source) 
20191203 18:07:18 +0200  asked a question  Mistake in SageMathCell code, finding integral points on elliptic curves I've the following number: $$12\left(n2\right)^2x^3+36\left(n2\right)x^212\left(n5\right)\left(n2\right)x+9\left(n4\right)^2\tag1$$ Now I know that $n\in\mathbb{N}^+$ and $n\ge3$ (and $n$ has a given value) besides that $x\in\mathbb{N}^+$ and $x\ge2$. I want to check if the number is a perfect square, so I can rewrite $(1)$ as follows: $$y^2=12\left(n2\right)^2x^3+36\left(n2\right)x^212\left(n5\right)\left(n2\right)x+9\left(n4\right)^2\tag2$$ Where $y\in\mathbb{Z}$. In this problem I've: $n=71$, the number is equal to; $$y^2=57132x^3+2484x^254648x+40401\tag3$$ So, I used SageMathCell to look for the integral points on the elliptic curve and the code that was used is the following: I found the coeficients I need to use using equation $(2)$ and $(3)$ (but I do not know if they are corect):
So the final code looks like: But I found no solutions and it should give at least one solution at $x=1585$.
