The HTTP interface (https://neo4j.com/docs/http-api/current) is currently disabled for the databases on Aura. 

Aura supports the Neo4j Query API and has an Aura API for Instance management.

 

For Query API:

• Neo4j Docs - Query API
• Neo4j Developer Blog - Querying Your Neo4j Aura Database Via HTTPS
• Neo4j Query API for Aura - configuration and Testing in Postman

 

For Aura API:

• Neoj Aura API - Overview
• Aura API Endpoints configuration and Testing in Postman