I often capture a Sylesti that has blue stars, and find out that it has no genes even hidden. In what way is that Sylesti Rare?

it has two carries.
Carries and Hiddens (Carry = trait genetics in a slot without a vis, Hidden = genetics of a second more recessive trait in a slot with a vis) can only be seen in a pet's genetics once it has been genetically tested (the traits are still there, and interact normally when breeding. They just can't be seen in the genetics info.)

(the only exception to this is that carries can automatically be seen on pets made via the generator)

There are people who offer free testing services in the Groups, Guilds, Clubs, and Services Forum.

Yes, but usually the image address tells if the sylesti has hidden traits. In these there is only NN in every slot.

It will only tell you that if the pet has been genetically tested, otherwise, a pet with only carries will show up exactly like a pet with no traits at all.

If it has been tested and still shows up as no carries, then there is probably a problem.

OK, I get it now. Thank you!

Thanks for the link!

You're welcome. It can be confusing sometimes what the url shows and what it doesn't and when it shows.

One of the best investments I made on site was the Genetic Scanner, which tests all pets I fight in battle. I know what I am capturing before I do so, and the nice thing is they remain genetically tested even after I capture them. (I still have the infinite test kit as well and I love it). So I know whether a pet has all carries etc..

As far as I know, Common pets will have no traits at all (and they are often the prettiest pets I have seen), Uncommon will have one carried, Rares will have one Visible or two carried and so on.

So, if you see uncommon and above with no visible traits, it means they have a carried trait somewhere.