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It's hard to say if this core will work.
Normaly HF-cores will be 10 Mhz and more.
If the core can't handle the ocsilator frequentie, the ocsilator will shut-off.
But the price isn't to high to test this core.
BTW, if the freq isn't enough to charge the C to the right Voltage it can be also the transistor.......low HEF-type !
Some built the ocsilator with a FET, I don't try it yet, but maybe this can help to raise the freq and the Voltage.