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Description
When you search for curves with at least 1 rational point, X(1) does not show up for example:
https://beta.lmfdb.org/ModularCurve/Q/?genus=0&points=1-
(we claim that X(1) has no rational points).
In general searching by points on modular curves does not lead to the expected results.
For example in this search
https://beta.lmfdb.org/ModularCurve/Q/?level=163%2C27&points_type=all&family=X0
we are missing the levels 163, 27 (even though clicking on the individual curves seems to show we know about the CM points)
and in this search:
https://beta.lmfdb.org/ModularCurve/Q/?level=163%2C27&points_type=all&points=1-&family=X0
it finds 27, but both curves have 2 cusps defined over Q.
In this search:
https://beta.lmfdb.org/ModularCurve/Q/?level=163%2C27&points_type=all&points=2-&family=X0
neither curve is found despite the 2 Q-cusps.
Is this how we want it to behave with respect to CM and cusps?