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over F5, and thus ⟨1,2⟩ ⊥ 5⟨1,2⟩ is anisotropic over the 5-adic numbers Q5, but ⟨1,1,1,1⟩ is an unimodular form of dimension 4, hence isotropic over Q5 (in fact, it is even hyperbolic over Q5
as an isotropic [...] square class basis {−1,2,5}. The torsion subgroup WtF is given by
{H, ⟨1,−2⟩, ⟨1,−5⟩, ⟨1,−10⟩, ⟨2,−5⟩, ⟨2,−10⟩, ⟨5,−10⟩, ⟨1,−2,5,−10⟩}
and ⟨1,−2,5,−10⟩ is a supreme torsion form as can be readily verified [...] −t2t3⟨⟨x + 1⟩⟩ ⊥ −⟨⟨(x + 1)(x + 4)⟩⟩) (5.3)
= −⟨⟨t1 √ x,x + 1,−t2t3⟩⟩ + t3⟨⟨t1
√ x,x + 4, t3(x + 1)⟩⟩ (5.4)
= −⟨⟨2t1, x + 1,−t2t3⟩⟩ + t3⟨⟨t1, x + 4, t3(x + 1)⟩⟩. (5.5)
We shall now show that (ϕE)an is not …
