No - those are meant to like like that. Personally I prefer a trumpet to look like a trumpet but breeders have produced lots of doubles and split coronas. Yours may be a very old one called Van Sion.

Here is a link that might be useful: Van Sion

Wow! Thank you so much for that info. I found this page: http://oldhousegardens.com/VanSion.aspx and I'm pretty sure you're right on the type. I have about 7 in my yard right now.

Honestly I do like the more orderly trumpet daffodils but it's super cool to have these guys in our yard.

Thank you!

Here's another view:

Oh, those are lovely! I like the green in the flowers. I have quite a few of the traditional ones, but a little variety doesn't hurt!