Root number in integer parameter families of elliptic curves

In a previous article [7], the author proves that value of root number varies in non-isotrivial family elliptic curves indexed by one parameter t running through $${\mathbb {Q}}$$ . However, well-known example Washington has $$-1$$ for every fiber when runs {Z}}$$ Such examples are rare since, as proven this paper, integer fibers large class families curves. This result depends on squarefree conjecture and Chowla’s conjecture, is unconditional many cases.