For the families L(ℓ²,ℓ-1) and L(ℓ²,2ℓ-1) with ℓ odd ≥5, the residual-circle equivariant η germ has vanishing first derivative but nonzero second derivative; the normalized value is -6080 for L(25,4) versus L(25,9).
Whitehead torsion,
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Second-Jet Equivariant $\eta$ Separations on Lens Spaces
For the families L(ℓ²,ℓ-1) and L(ℓ²,2ℓ-1) with ℓ odd ≥5, the residual-circle equivariant η germ has vanishing first derivative but nonzero second derivative; the normalized value is -6080 for L(25,4) versus L(25,9).