Cubic fields with class groups of 2-rank at least 26 and 27

Five elliptic curves over Q whose 2-division cubic fields have class groups of 2-rank at least 27 (two complex fields) and at least 26 (three totally real fields) by the Brumer-Kramer bound [1, 2, Prop. 3.1]. The previous records, 26 and 25, are due to Elkies and Klagsbrun [3]. The curves themselves are listed in curves.md, their data is given in curves.gp, and verify.gp confirms that they give rise to the desired cubic fields. Each curve is a fibre of a rank-17 elliptic fibration on X1152 or X1008.