The Ultramarines are the ancestors of two thirds of the Imperial Space Marines. Out of roughly one million extant Space Marines, six hundred and sixty thousand are direct descendants of the Ultramarines Legion and its heroes. All of those, to one extent or another, venerate the Codex Astartes as their guiding light. Even Chapters formed from other Legion stock do so, with some notable exceptions.

If you're talking about "influence", the Ultramarines can't be beat. Their close ties with a great many of those descendant chapters make them a terrifying proposition if they start calling in favours, too.