There is no "Basic" edition when using the TurboTax online editions. If you are referring the Free online edition, then no it will not handle investment sales with a gain or loss. You will need to upgrade to the Premier online editions for what you need to report on a federal tax return - https://turbotax.intuit.com/personal-taxes/online/
There is a Basic edition in the TurboTax desktop CD/Download editions which can handle your needs. But it does not include a state tax return program. That would be an additional charge of $40 to download a state program. Or you could use the Deluxe desktop editions which will handle your needs and does include one state program download in the purchase price - https://turbotax.intuit.com/personal-taxes/cd-download/
