= Negative unit obstruction for the fourteen-coefficient isogeny cover
{title2=$N^2=-U^4+14U^2V^2-V^4$}
This <quartic covering in a two-isogeny descent> has no solution with coprime integers $U,V$ not both zero. If precisely one is odd, the right side is $3$ modulo four. If both are odd, their fourth powers are one modulo sixteen and $14U^2V^2=14$ modulo sixteen, so the right side is twelve modulo sixteen. Neither residue is a square. Coprimality excludes the remaining parity case. Consequently the negative unit <square class> is absent from the <two-torsion square-class homomorphism> for $Y^2=X^3+14X^2+X$.
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