High Cholesterol and Migraines – Is There a Connection?

I was recently diagnosed with high cholesterol, and I've been wondering if it could be connected to my migraines. Has anyone else experienced both conditions? If so, did lowering your cholesterol through diet, exercise, or medication have any effect on your migraine frequency or severity?
I'd also like to know if anyone can recommend a medication or treatment that has helped manage high cholesterol without making migraines worse. I'd really appreciate hearing about your experiences, any advice, and what has worked best for you. Thanks in advance!