Serpenticone

All or most were pelagic, ranging from planktic serpenticones and spherocones to mobile discocones and oxycones.

[...] disturbance to such a form might produce rapid acceleration in two ways — in shape, from serpenticone to criocone, in ornament, from tuberculate to costate, that is, costate post-tuberculate.

Coiling is serpenticone or heteromorph, sculpture is of ribbing (almost invariably simple), with external tuberculation in Choristoceratidae. Generally criocone although much of the phragmocone may be serpenticone.