A flight I had says on the E Ticket under class - H(Y).
On Air New Zealand's points claim (Star Alliance partner), it has both H and Y.
Which one is it?
If it helps, it was with All Nippon Airways, from Tokyo Haneda to Hachijoji-jima island.
Y is the universal designator for economy, the other fare classes tend to be discounted fares within economy. Without seeing the full copy it could be that you booked a ticket in H class which is in the economy cabin (Y).
Somewhere within your booking record there should be a "fare basis" listed, usually starting with a letter followed by 4 to 7 more numbers and letters. The first letter is normally the fare class.
Another possibility is that you are booked in H class going one direction and Y class coming back (assuming it is round trip) or if the flight is 2 legs it could be two fare classes one for each leg.
But the fare basis is the best way to determine.