  An \"{u}bercrossing diagram is a knot diagram with only one crossing that may
involve more than two strands of the knot. Such a diagram without any nested
loops is called a petal projection. Every knot has a petal projection from
which the knot can be recovered using a permutation that represents strand
heights. Using this permutation, we give an algorithm that determines the
$p$-colorability and the determinants of knots from their petal projections. In
particular, we compute the determinants of all prime knots with crossing number
less than $10$ from their petal permutations.
