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Mar 20, 2019 at 16:38 comment added Michael Griffin @L.Miller Great!
Mar 20, 2019 at 8:34 comment added L. Milla Thank you for this great answer! Looking into the details of Baker's Theorem, one can see that $AC\wp$ is also an algebraic integer (without the square). Thus with Masser's Appendix it follows that $(AC)^2\cdot\sqrt{D}E_2^*(\tau)/\omega(\tau)^2$ is an algebraic integer which is enough for my means - and so I don't need the Gross-Zagier-Formula.
Mar 6, 2019 at 7:36 vote accept L. Milla
Feb 14, 2019 at 14:44 history bounty ended L. Milla
Feb 11, 2019 at 17:16 history edited Michael Griffin CC BY-SA 4.0
Addressed a mistake in the original answer about ramified primes.
Feb 11, 2019 at 5:49 history answered Michael Griffin CC BY-SA 4.0