I want to find the integral points of the following equation $$y^{2}=x^{3}-219x+1652$$
But, I don't have any computational program.
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Related but not really helpful to this question. Basically trying to pre-empt unschooled critics from yelling "no effort shown" (and that was the first google hit), – Jyrki Lahtonen May 04 '18 at 05:28
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2OTOH this question from MO may have something that actually helps. – Jyrki Lahtonen May 04 '18 at 05:31
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In the range $[-10^6,10^8]$, the polynomial $x^3-219x+1652$ does not give a perfect square or $0$ or $1$. So, there might be no integer solution. – Peter May 04 '18 at 12:28
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Still no solution upto $x=10^9$ – Peter May 04 '18 at 12:39
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Thanks for your answer Peter. – Claudia Reyes May 04 '18 at 18:24
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According to MAGMA-calculator, there are no integral solutions. – Peter May 04 '18 at 20:25
1 Answers
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There are NO rational points never mind integer ones.
Using Pari/GP's elltors(), the curve has no finite torsion points and Denis Simon's ellrank() code states that the rank = 0.
This gives the result.
Allan MacLeod
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