Genus 2 curves over ℚ


This page provides a download link for the list of 66,158 genus 2 curves over ℚ of discriminant |D| ≤ 1,000,000 whose computation is described in the paper A database of genus 2 curves over the rational numbers. This dataset is now incorporated as part of the LMFDB. There is also a download link to a list of 487,493 genus 2 curves over ℚ whose discriminants are 5-smooth that was computed using the same methods. Both download links provide colon-delimited text files with the format

D:N:[f(x),h(x)]

where f(x) and h(x) are integer polynomials defining the hyperelliptic curve

y2 + h(x)y = f(x),

which has absolute descriminant D and conductor N (the conductor of its Jacobian). Each curve is a global minimal model for its isomorphism class.

If you use this data in your research, please cite the paper using these bibliographic details, which you can also find on my home page.