I'm assuming you were approved for a "left downwind departure" by ATC. Most likely this was given because the downwind leg is closest aligned to your direction of flight. When departing the pattern there is no need to stop climbing, so climb away.
The AIM covers traffic pattern departures, but as you probably noticed there is no mention of a downwind departure. The AIM is non-regulatory, but is considered best practices. The pattern entry/exits in the AIM are applicable to towered patterns as well, but in the interest of best, safest practices, only the entry/exits discussed in the AIM should be used at uncontrolled airports. A downwind departure is not recommended because it could conflict with traffic entering the pattern with a 45* to the downwind or traffic entering the pattern from a midfield entry. Page 7-5 in the Airplane Flying Handbook
https://www.faa.gov/regulations_policie ... fh_ch7.pdf illustrates what I'm trying to explain.
