There are 2 resonant modes in crystals. The manufacturer tunes the frequency for one mode only as it impossible to tune for both modes.
1st f is the series mode frequency then slightly higher f (e.g. 0.1%) is the anti-resonant high impedance mode. In Series mode ESR is critical for gain margin, and in parallel mode, load capacitance is critical for frequency accuracy.
For more Crystal Theory
https://www.ecsxtal.com/store/pdf/oscir_des.pdf
If you already undertand, try the quiz.
https://www.learnabout-electronics.org/Oscillators/osc26.php
When buying crystals they are usually specified as S or P type where Parallel type also needs a load capacitance, so they have in part number instead S or pF load to denote series or parallel tuned.
Good luck on the tricky quiz.
If you understand , let me know.
- other quality factors besides Q are usually stated by Series Resistance where lower is better, but in Series Mode, consistency is best, when multiple vendors and SMT sizes are considered, thus 150 +/-50 Ohms is best in smallest SMT package from one vendor vs than 25~250 from different vendors with different SMT case sizes.
- other test metrics include, >5x Gain margin due to Negative Resistance/Xtal R ratio and temperature stability and temperature range of cut.
The "S" tempco. curve of "AT cut" crystals can be made symmetric or asymmetric around 25'C so custom ordered for a ppm stability limit over a required T range, such as 25, 500, 100, or 200 ppm over a various ranges of T, e.g. --40~+85 or 0~70 etc.
if the OP is still with me... The tuning core of L is used to optimize gain in the given schematic to ensure adequate gain margin at Xtal series mode frequency. This is fairly wide bandwidth compare to Xtal frequency and C value does not change for offset f of < 10% , just value of L and use tuning.