Hannah Cox was also registered at her baptism as base born (illegitimate):
FreeReg Baptism entry
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Field Value
County Somerset
Place (link for place information) Long Sutton
Church name Holy Trinity
Register type Parish Register
Baptism date 28 May 1804
Person forename Hannah
Person sex F
Mother forename Eleanor
Mother surname GAYLARD
Witness
Witness
Register note Base born