Is it a Jalapeño?

Summer was about its tail end when B started to sow pepper seeds in a smaller pot.  The weather started to get cooler just as the little plants started to grow that I had to place the pot indoors -- where it stagnated all fall/winter.

Then as it got some sun during the unseasonably warm winter, it began to bloom, and the last few weeks it started to bear flowers and fruit (yes, peppers are fruits!).  Two weekends ago, the peppers got repotted in a bigger pot, and thankfully survived the disturbance.  There's close to a dozen little buds, and one close mature pepper!

One question remain: what type of pepper is this exactly?