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The multiplicative loops of Jha-Johnson semifields are non-automorphic finiteloops whose left and right nuclei are the multiplicative groups of a fieldextension of their centers. They yield examples of finite loops withnon-trivial automorphism group and non-trivial inner mappings. Upper bounds aregiven for the number of non-isotopic multiplicative loops of order $q^{nm}-1$that are defined using the twisted polynomial ring $K[t;\sigma]$ and a twistedirreducible polynomial of degree $m$, when the automorphism $\sigma$ has order$n$.