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Hi,
So you are not far away from me, I'm living west of Stuttgart at the moment.
Sorry, your other picture does not show the abdomen tip; I add a picture where the peculiar cautum tergite is marked by an arrow. However, a clear picture of the antenna is absolutely necessary for identification.
If you remember the size correctly, arcuatum would be less possible than cautum and fasciolatum. Nevertheless I do not believe in cautum for the reasons already mentioned; my cautum specimens also had no dark wing parts. C. fasciolatum somehow looks different (https://www.dipte...d_id=63936)... I would call the pictures "Chrysotoxum cf. arcuatum" at best.
BTW, there are lots of misidentified pictures in the internet, some don't even show the right genus.
Well, unambiguous identifications from pictures are impossible in many, many cases - we must accept that. Console yourself with the fact that most people don't even know that your specimen is a hoverfly and not a wasp, let alone a Chrysotoxum.
Best wishes, Sundew