How do I remove this Elder Scroll from my inventory?

In the quest Discerning the Transmundane I received an Elder Scroll.

This is great and all, and who doesn't want to own an Elder Scroll, but the problem is that it weighs 20 (pounds? kilos? I'm not sure) and is marked as a quest item, causing me to be unable to store it in a chest etc.

Is there a way to make it unmarked as a quest item, giving me the ability to keep it but store it away? If not, is there a way to get rid of it without using the console (I'll use the console if I have to, but I'd rather not).

According to the wiki you linked:

The Elder Scroll can be sold to Urag gro-Shub in the College of Winterhold's Arcanaeum for 2000 gold.

You don't get to keep it, but at least you don't have to carry it around everywhere.

Any item marked as Quest Items actually weighs nothing at all (even when it has a weight displayed), so there is no need for you to give it away.

You can sell it to the orc guy in the Winterhold College library like I did, but I don't know if you need it again. Selling it gets you 2000 gold.