unless there is something you are not mentioning the tax basis to your sister is 50% of the Fair Market Value on the date your last parents died + any improvements she made.
since it seems your sister owned and occupied the property as her principal residence for 3 years before the sale to you, if there is any gain, she's entitled to use the home sale exclusion which means up to $250,000 of any gain would be tax-free. if she sold at a loss it would not be deductible because the sale was to a realted party.
on the other hand, while you owned the property for 3 years you did not occupy it for the minimum 2 years required. your basis is 50% of the date of death value + what you paid your sister for her 1/2. you are not entitled to use the home sale exclusion.
