Crystal quartz oscillator is it good for amplitude modulation?

This may be buildable if you use an appropriate transistor, as shown in the schematic. (A 2N3563 might be another such.) But construction is everything and I'm not going into details on that. I recommend that you follow AN47 - High Speed Amplifier Techniques for details. Regardless, I've used this particular structure in the past for frequencies in this area, with better success than some other approaches:

^{simulate this circuit – Schematic created using CircuitLab}

I've set it for a quiescent current of about \$5\:\text{mA}\$. \$C_1\$'s value will affect start-up time. So making it smaller will let it start up faster. But it will also cause much wider emitter variation and added distortion. I didn't build this yet. But the value for \$C_1\$ is an estimate for a good startup and run.

\$L_1\$ forms a tank with \$C_4\$ and \$C_5\$. Adjust \$L_1\$ to get the the output working and working right. The value I show is approximately right. There will be parasitics. Less, if you build things well. But some adjustment may be required to accommodate your construction.

The output isn't buffered and I've not even tried to consider doing anything practical with the output here, as you haven't specified anything you want to do. The next stage will also be critical to design and build, though, if you plan to do anything useful. An earlier project required two more transistors, beads over resistor leads, variable small-pF caps, etc. But that was to get a \$50\:\Omega\$ output working right. Just FYI.

If this is just about simulation then it should simulate, given a proper crystal model. I have two of them handy from ORCAD:

* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * 10Mhz frequency standard, AT cut, parallel resonant, Q=25000 .subckt QZP10MEG 1 2 lqz 1 11 2.54647909e-003 cs 11 12 9.96041181e-014 rqz 12 2 6.4 cp 1 2 2.49010295e-011 .ends * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * 10Mhz frequency standard, AT cut, series resonant, Q=25000 .subckt QZS10MEG 1 2 lqz 1 11 2.54647909e-003 cs 11 12 9.94718394e-014 rqz 12 2 6.4 cp 1 2 2.48679599e-011 .ends 

For transient simulation, use the UIC option on the .TRAN card.

However, the load capacitance in the above circuit is about twice the calibration load used to create those models. Again, just FYI.

EDIT: Just took a moment to stick this into LTspice and play around with various ways of using the .TRAN card and adding a reasonable load to remove the DC bias at the output. I decided on \$220\:\text{k}\Omega\$ as the output load for this last purpose. I also added a little "kicker", \$V_2\$ and \$C_6\$, to start the oscillator faster. The "kicker" isn't required so long as STARTUP isn't used in the .TRAN card. It just takes longer to start up, then.

Here's the output at about the \$10\:\text{ms}\$ point:

There's a reason why I mentioned the above circuit as opposed to the commonly found capacitor-only Colpitts version, which takes its output at the emitter. The reason is that the start-up and output then looks more like this:

And if you are working towards a sinusoidal output, that's not so good.

Getting back to the original oscillator above, here's the output from the start, including the kicker event and the removal of the kicker's capacitance at \$1.5\:\text{ms}\$:

(Note the difference also in how this starts up, compared to the distorted capacitor-only version.)

I got the circuit working (not at 10 MHz but it's the same thing I just need to change values of C,L)

Opening with Falstad:

$ 1 0.000005 10.20027730826997 50 5 50 5e-11 r 96 -48 96 48 0 1000 r 96 48 96 160 0 100 t 192 48 288 48 0 1 -4.545372149454615 0.4545832894619002 100 default w 288 64 352 64 0 w 288 160 352 160 0 g 288 160 288 192 0 0 w 96 160 288 160 0 w 192 48 96 48 0 w 96 -48 288 -48 0 w 288 32 400 32 0 c 400 32 448 32 4 0.00001 3.6212040083128896 0.001 0.1 w 448 32 448 272 0 w 448 272 272 272 0 c 144 224 224 224 4 0.01 1.3825306146411112 0.001 0 c 224 224 320 224 4 0.01 -1.3787514143569637 0.001 0 g 224 224 224 192 0 0 w 144 272 144 224 0 w 272 272 320 224 0 c 96 48 0 48 4 0.00001 -0.927947325179211 0.001 0 w 144 272 0 272 0 w 0 272 0 48 0 R 288 -48 288 -96 0 0 40 5 0 0 0.5 w 144 272 160 272 0 w 240 272 272 272 0 l 160 272 240 272 0 0.01 -0.00012397455663575458 0 r 288 32 288 -48 0 10 w 352 160 352 64 0 o 24 64 0 4099 0.0048828125 0.003125 0 2 24 3