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4$\begingroup$ If you explained how those $E_n$ arise, it might be easier to identify if any integer points come up there. $\endgroup$Wojowu– Wojowu2026-03-29 11:52:41 +00:00Commented 2 days ago
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$\begingroup$ @Wojowu $E_n$ arose from this equation: $y^2 = x^3 + m^2 \cdot x^2 + \dfrac{1}{3} m^3 \cdot x + \dfrac{m^4 - 19m}{36} \quad \text{where $m \neq 0$}$ and if we were to let $t = \dfrac{m^4 - 19m}{36}$, a valid family of solutions would be $m(n) = 36n + 27$ and $t(n) = 46656n^4 + 139968n^3 + 157464n^2 + 78713n + 14748$ and making the necessary substitutions yield the initial problem I posed earlier. $\endgroup$Agbanwa Jamal– Agbanwa Jamal2026-03-29 18:12:20 +00:00Commented 2 days ago
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