Your card works. I just Tweeted your link and a card shows up. There's no image, because you've not included any information about the image you want in the card markup on the page. The documentation on the summary large image card is here.
There is a lot more information in the troubleshooting post so I'll leave you to follow the steps there.
There is no need to apply for whitelisting and you will not receive any email from Twitter related to your card.