Just answer the question, preferably without consulting any external source.
I thought it was the first reprogrammable one. I'm pretty sure there were some before it.
No it certainly wasn't. Most historians would probably count the ABC* machine as the first general purpose digital computer and I wouldn't argue strongly. The question, however, is which was the first electronic computer, not general purpose. The answer to that particular question, as far as I know, is the Colossus machine(s) built in England during the 2nd world war to break the German Lorenz cyphers.
Colossus was not general purpose - in that sense it was not a true Turing Machine - but it was a computer and it was digital, so it meets the criteria of the question.
Being an alumnus of Iowa State University, I would say that the Atanasoff-Berry Computer (ABC) designed in 1937 was the first electronic computer. You can find more information about the legal disputes involving John Mauchly (designer of ENIAC) and Atanasoff (designer of ABC) at this location:
The rest is for you to decide
It could be argued that pianolas, weaving machines and fairground organs were in there long before Eniac or Colossus.
Although these all used a form of punched card or roll for their 'programs' they were dedicated to a specific problem and could not store any program.
With all the secrecy of the time etc I'm not sure which was the first to fit into that particular definition, but no matter what definition is used ENIAC was beaten by various other machines (ABC, Colossus, Z1 etc.) and therefore cannot claim to be the first of anything in my opinion.