Which hormone do not regulate the menstrual cycle?

Thyroxine is a hormone produced by the thyroid gland that regulates the metabolism of the body. It has no effect on menstrual cycle regulation.
A complex interplay of hormones produced by the hypothalamus, pituitary gland, and ovaries regulates the menstrual cycle. 

The two main hormones involved in regulating the menstrual cycle are oestrogen and progesterone. During the follicular phase, oestrogen levels rise and stimulate the growth of the uterine lining. During the luteal phase, progesterone levels rise and help to maintain the thickened uterine lining.
Luteinizing hormone (LH) is another important hormone that regulates the menstrual cycle. LH levels increase in the middle of the menstrual cycle, causing the follicle to rupture and release the egg.