= Confluent elliptic collinearity determinant
{title2=$\det(c(u),c'(u),c(w)),\quad c(z)=(1,\wp(z),\wp'(z))^t$}
For distinct finite point classes on a complex <elliptic curve>, ordinary column determinants test whether a line meets the curve at those three points. Repeated columns instead vanish for a purely linear-algebraic reason. To prescribe a tangent intersection at $u$, replace the second equal column by its derivative; to prescribe a triple intersection, use $c(u),c'(u),c''(u)$. These confluent determinants vanish exactly when the corresponding degree-three intersection divisor has point sum zero, away from the affine chart's pole. A local homogeneous lift supplies the version at the origin.
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