New q -Analogues of Van Hamme's (E.2) Supercongruence and of a Supercongruence by Swisher.

In this paper, a couple of q -supercongruences for truncated basic hypergeometric series are proved, most of them modulo the cube of a cyclotomic polynomial. One of these results is a new q -analogue of the (E.2) supercongruence by Van Hamme, another one is a new q -analogue of a supercongruence by Swisher, while the other results are closely related q -supercongruences. The proofs make use of special cases of a very-well-poised 6 ϕ 5 summation. In addition, the proofs utilize the method of creative microscoping (which is a method recently introduced by the first author in collaboration with Wadim Zudilin), and the Chinese remainder theorem for coprime polynomials.