  For a knot in the 3-sphere, the Upsilon invariant is a piecewise linear
function defined on the interval [0,2]. For an L-space knot, the Upsilon
invariant is determined only by the Alexander polynomial of the knot. We
exhibit infinitely many pairs of hyperbolic L-space knots such that two knots
of each pair have distinct Alexander polynomials, so they are not concordant,
but share the same Upsilon invariant. Conversely, we examine the restorability
of the Alexander polynomial of an L-space knot from the Upsilon invariant
through the Legendre-Fenchel transformation.
