To find the exact model of the Mac enter the serial number here:
Check Your Service and Support Coverage - Apple Support
The system serial number on an iMac is located on the bottom of the stand.
A1311 represents models from Late-2009 to 2011. Luckily all of these models support macOS 10.13 High Sierra. As long as you have access to another qualifying Mac, then you can create a bootable macOS 10.13 USB installer using the instructions in this Apple article:
How to create a bootable installer for macOS - Apple Support
A qualifying Mac is one which can run the OS you want to download which in this case is macOS 10.13. Most Macs from 2010 to 2018 will qualify, but you can use the information in this article which shows which versions of macOS are compatible with various Apple hardware:
https://eshop.macsales.com/guides/Mac_OS_X_Compatibility
If you only have access to another Mac from 2008 to 2009, then you can create a bootable macOS 10.11 USB installer.
Once you boot to the 10.13 installer you will need to launch Disk Utility and click "View" and select "Show All Devices" so that the physical drive appears on the left pane of Disk Utility. For either 10.11 or 10.13, select the physical drive and erase it as GUID partition and MacOS Extended (Journaled). The macOS installer will end up converting it to APFS during the OS installation of macOS 10.13.
Since this is not a macOS drive you will only have access to Internet Recovery Mode. You should use Command + Option + R. If you have trouble booting, then connect the Mac directly to the router using an Ethernet cable for a faster more reliable connection to bypass any hard to troubleshoot WiFi issues. Internet Recovery Mode is only an option if macOS 10.12.4+ has been installed at some point in the past.
