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As described in Section 3.4 of [MR:3540958 , arXiv:1602.03715 ], the completeness of the genus 2 curve database for curves of absolute discriminant $|\Delta|\le 10^6$ has been tested against other tables of genus 2 curves, including those of [Stoll ], and Merriman and Smart [10.1017/S030500410007153X ]. However, as explained on the completeness page, it is only complete within the boxes that were searched, and it is likely that there are at least a few genus 2 curves of minimal discriminant $|D|\le 10^6$ that are not included (even though no such curves are currently known).

The reliability of specific data associated to genus 2 curves is discussed below.

All invariants not specifically mentioned above were computed using rigorous algorithms that do not depend on any unproved hypotheses.