Parity of ranks in curve families

Problem 2.5 (Dujella, 2026). Propose a heuristic to predict the distribution of parities of ranks within known families of elliptic curves over $\mathbb{Q}$ with the torsion group $\mathbb{Z}/2\mathbb{Z}\times\mathbb{Z}/6\mathbb{Z}$ (respectively $\mathbb{Z}/8\mathbb{Z}$) and rank $\geqslant 3$.

Remark. Certain experimental data concerning the parity of ranks in some of these families can be found in Dujella, A., Kazalicki, M., Peral, J.C.: Elliptic curves with torsion groups $\mathbb{Z}/8\mathbb{Z}$ and $\mathbb{Z}/2\mathbb{Z}\times\mathbb{Z}/6\mathbb{Z}$. Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 115, Article 169 (2021).