Family: elliptic-quartic — Genus-one quartic

[roed-math]

One family: Genus-one quartic (elliptic-quartic) — P1, algorithmic.

• Standard form: y^2 = q(x), deg q = 4
• Parent: genus-one-curve
• Examples: y^2 = x^4 + 3*x + 1

Contents: the registry entry, its docs/FAMILIES.md section and its rows in the classification corpus.

References cited (the claim each one supports):

• Tzanakis2013 — solving quartic elliptic equations via elliptic logarithms
• CremonaStoll2002 — minimization and reduction of 2-covering quartic models

Independent of every other family PR: it needs only the registry backbone it is based on.

Part of the series that splits #1 into reviewable pieces:

1. 01-bibliography — packaging, docs, annotated bibliography
2. 02-parsing — equation strings to a term model
3. 03-registry — the YAML family registry (3 seed families)
4. 04-matchers — shape recognizers
5. 05-classify — the classification pipeline
6. 06-solvers — solver framework, two seed solvers, and the CLI
7. 07..09-backbone — the 23 parent families of the DAG, by depth
8. one PR per remaining family (38 of them, mutually independent)
9. 99-polish — restore the full doctests and tighten the invariants