Probably rather a cultivar.
There is a lively Hosta-forum with hoards of friendly geeks to ID your plant. The pic with flowers should help to narrow it down

there is a VERY ACTIVE hosta forum ... and to confirm my guess.. i suggest you try over there...

as noted.. its not a species ...

i suggest you google: Hosta Elegans ... and compare

as a start ...

with no history of the plant... its going to be hard.. choosing among the 4 or 5 thousand named plants.. to name a big blue ... but guessing can be fun ... [e.g. if we knew it had been there for 20 years.. or came from grandma.. we could narrow down the possibilities ....]

ken