NFC spectrum analysis, weird frequencies showing
Firstly, info for non proffesionals:
ISO14443-A: https://www.msoos.org/largefiles/rfid_soos_pres.pdf
The subcarrier is at fc/16, so your subcarrier is at 13.56 * 15 / 16 = 12.7125
Glossary: https://www.nfc-research.at/index.php@id=40.html

PCD
Proximity coupling device: a transmitter that can read tags based on ISO14443 (PICC). The reader emits an electromagnetic field that powers a tag/transmitter by inductivity. Communicates with PICC using load modulation scheme.
PICC
Proximity inductive coupling card: a transponder that can be read or written by a proximity reader. Theses tags are based on the ISO14443 standard. Such tags do not have a power supply like a battery, but are powered by the electromagnetic field of the reader (PCD)

The info you provide

This is the response of an ISO14443-A Tag

So, this is how the card communicates with the base. Using the pdf previously provided,

PICC→PCD:
Load modulation
Subcarrier: fc/16 → fc/128
Coding: OOK, Manchester
Bandwidth: 106kbit/s→847kbit/s

The communication the card transfers to you is using OOK, on-off-key: https://en.wikipedia.org/wiki/On-off_keying.
One of the most visual caracteristic OOK using an oscilloscope is there is a lot of noise around the frequency of transmission. That's why you see lot's of, apparently, noise.
On-off-keying sends pulses (deformed pulses), so... where are the harmonics?
The peaks
The peaks your oscilloscope snitches are, indeed, the harmonics of the on-off-keying.
Did you perceive that the frequency between the center of transmission, 13.56, and one of the peak, is exactly the frequency between the center of transmission and your subcarrier?
That's exactly what happens in your image.