174

There are 174 7-crossing semi-meanders, ways of arranging a semi-infinite curve in the plane so that it crosses a straight line seven times. There are 174 invertible 3 × 3 {\displaystyle 3\times 3} (0,1)-matrices. There are also 174 combinatorially distinct ways of subdividing a topological cuboid into a mesh of tetrahedra, without adding extra vertices, although not all can be represented geometrically by flat-sided polyhedra. The Mordell curve y 2 = x 3 − 174 {\displaystyle y^{2}=x^{3}-174} has rank three, and 174 is the smallest positive integer for which y 2 = x 3 − k {\displaystyle y^{2}=x^{3}-k} has this rank. The corresponding number for curves y 2 = x 3 + k {\displaystyle y^{2}=x^{3}+k} is 113