= Modulo-sixteen obstruction for the negative unit descent class
For $y^2=x^3+ax^2+bx$ with $a\equiv8$ and $b\equiv9\pmod{16}$, the <square class> $-1$ in a <two-isogeny descent> would require <coprime integers> $u,v$ and an <integer> $N$ with $N^2=-u^4+au^2v^2-bv^4$. If $u$ is odd and $v$ even, the right side is $15$ modulo $16$; if $u$ is even and $v$ odd, it is $7$; if both are odd, it is $14$. None is a square modulo $16$. Therefore $-1$ does not occur in the <two-torsion square-class homomorphism> image.
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