Estimated tax payment logistics

Hi all. Sorry if this is a stupid question. I'm a relatively fresh contractor still figuring out my back end business stuff. I'm not very tax savvy and last year got my first penalty for failure to pay estimated quarterly taxes (I'm a single-member LLC making about 60k-70k average annually). I had been under the (mistaken, I now realize) impression that since it's a disregarded entity I didn't need quarterly payments, just my annual return.

I've since been working to educate myself and figure this out this year, so I've done my calculations and made my estimated payments to the IRS, but I haven't found a definitive answer to what may be a very obvious question: is there any paperwork I need to file with my quarterly payments to justify the amount I'm paying?

The IRS site says "You may send estimated tax payments with Form 1040-ES by mail, or you can pay online" but I didn't see a place to file the 1040-ES online. Did I miss it, or is it not actually required?

Thanks in advance for your help.