Two people who left the scene after the Audi S3 they were in overturned near The Meadows have been traced.
The crash happened at around 3.15am today at Hope Park Terrace, located on the east side of The Meadows.
Three women - aged 19, 20 and 25 - and one man aged 36, are receiving treatment in the city's Edinburgh Royal Infirmary following the incident.
Police said that another male and female exited the vehicle and left the scene before emergency services arrived, and police had asked them to come forward.
A statement released by police this afternoon said: "Police in Edinburgh can confirm that all individuals believed to have been within the Audi S3, which overturned in Hope Park Terrace on Monday morning, have been identified or traced.
"Three women and one man remain in hospital for treatment. However, no one else requires any medical attention.
"Inquiries into the full circumstances surrounding this incident are ongoing and anyone with information is asked to come forward and quote incident number 357 of the 17th December."
A number of roads in the east end of The Meadows were closed this morning as Road Policing Officers conducted enquiries following the incident.
Despite the crash taking place in the early hours of the morning, police have stressed that the area is often still frequented with joggers, dog walkers and other members of the public.
Motorists with any dash-cam footage, or with information relevant to the inquiry, have also been urged to get in touch.
Those with information should contact the Road Policing Unit in Edinburgh via 101 and quote incident number 357 of the 17th December.