= Five-adic obstruction to square class two on the curve with coefficient one hundred
{title2=$W^2=2U^4+50V^4$}
This quartic has no primitive integral solution. If $5\nmid U$, reduction modulo five makes $W^2\equiv2$, impossible. If $5\mid U$, coprimality gives $5\nmid V$ and $5\mid W$; dividing by twenty-five then gives $(W/5)^2\equiv2V^4\equiv2\pmod5$, again impossible. It excludes the square class two in <two-isogeny descent> on $Y^2=X^3+100X$. The point $(5,25)$ supplies class five, so the subgroup property excludes class ten as well.
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