Valentine Vinculum Part 2
Agnishom is in love and decided to talk to his crush on Valentine's Day.
Agnishom: What's your phone number, sweetheart?
Agnishom's Love: Well, if you take your phone number and replace it the leftmost digit with a 1, you get my phone number.
Agnishom: And the 4-digit area code that comes before it?
Agnishom's Love: You know, the product of the four digits in the code is actually the square root of my phone number.
Agnishom: Hey, that's still insufficient information.
Agnishom's Love: Ah, but if I tell you the sum of digits of the code, then you can figure it out exactly.
What is the 4-digit code?
Note: Even though you have fewer pieces of information (e.g. you don't know how many digits the phone number has or what it is), you can still figure out the 4-digit code from the conversation.