The LMFDB lists the Jacobian of the genus-2 curve 1109.a.1109.1 (http://www.lmfdb.org/Genus2Curve/Q/1109/a/1109/1) as being isolated in its rational-isogeny class. However, the LMFDB does not purport to have complete data of the genus-2 curves over the rationals whose Jacobian has a specified conductor, even for small conductors.
Is this isogeny class as stated? How could we check one way or the other?
