Remove header image from Showcase in Twenty Eleven

I’d like the front page of my website, which is using the Showcase template in Twenty Eleven, to have neither a header image nor header text. I presume I’ll need to edit a CSS or PHP file somewhere in the theme directory but don’t know where. I’d also quite like to suppress the menu just on that page too, and if that’s possible I’d be grateful if someone could let me know. Thanks.