Group generated by the Weierstrass points of a plane quartic
Group generated by the Weierstrass points of a plane quartic
We describe the group generated by the Weierstrass points in the Jacobian of the curve $X^4+Y^4+Z^4+3 (X^2 Y^2+X^2 Z^2+Y^2 Z^2) =0.$ This curve is the only curve of genus 3, apart from the fourth Fermat curve, possessing exactly twelve Weierstrass points.