The ones pictured in the Amazon ad are most likely Sword beans Canavalia gladiata. Jack beans (Canavalia ensiformis) have smaller pods usually tho still quite large.

Here is a link that might be useful: Jack Bean

For purposes of this discussion, are we looking for an exceptionally tall vine or just a large pod and seed? In the story the vine, the "bean stalk", grew up to the sky as I recall. And it was study enough that Jack could climb it. And he needed an ax to chop it down.

Jim

I am looking something that can produce large pods and seeds. The vine doesn't have to reach the sky :) Although I am wondering what is the tallest bean plant out there too!

Thanks farmerdill for the info, very helpful!

There are several large-seeded beans I could recommend. Knowing your climate, Spicyseeds, would narrow the choices.

Zeedman, my zone is 6a (connecticut)

Spicyseeds, I have a few two year old Japanese sword bean seeds you can have. email me at hdodge86@sbcglobal.net if you are interested in them.
Harry