If you read this webpage, you see there are disagreements on definitions.

If your text material defines a trapezoid as aquadrilateral having exactly one pair of parallel sidesthen there are no equilaterals.

However, if it is defined as a quadrilateral with at least one pair of parallel sides, then being equilateral implies the figure is a rhombus which includes squares.

One the other hand, an isosceles trapezoid is one in which that is a pair of consecutive angles having the same measure.