Before revision:  We also derive expressions for some entries in "Eighty New Invariants of N-Periodics in the Elliptic Billiard" (2020), arXiv:2004.12497  .
After revision:  We also derive expressions for some entries in "Eighty New Invariants of N-Periodics in the Elliptic Billiard" (2020), arXiv:2004.12497 , remain invariant in the self-intersected case. Toward that end, we derive explicit expressions for many low-N simple and self-intersected cases. We identify two special cases (one simple, one self-intersected) where a quantity prescribed to be invariant is actually variable .