Even points on an algebraic curve

Computing singular elements modulo squares

“…For the proof of the proposition see [3,Section 3]. Using a pair of compatible bases has an evident advantage over working with a single basis.…”

“…It is easy to get coordinates with respect to one basis from Legendre symbols computed against the other one. The following proposition is a special case of [3,Proposition 5]. (1) If λ ∈ K × is a singular element, then its coordinates ε 1 , .…”