Talk about a fateful trade. In 1954, Jackson Pollock gave two of his paintings to New York art dealer Martha Jackson in exchange for her sporty green convertible. Two years later, on a hot August evening after a day of drinking gin, Pollock crashed that same Oldsmobile 88 less than a mile from his home on New York's Long Island, killing himself and a friend of his mistress. He was 44 years old.

The mistress, Ruth Kligman, was also in the car but survived. Years later she wrote in a memoir that Pollock had been "speeding wildly" and missed a curve, causing the crash.

On May 13, Christie's will offer up one of the canvases connected to that macabre trade, 1951's "Number 5 (Elegant Lady)," at its New York evening sale of postwar and contemporary art. When Pollock got the car, similar models were selling new for around $3,000. Christie's said its price tag for "Number 5" will be $15 million to $20 million.

At that price, the Pollock isn't expected to break the artist's auction record—earlier examples have been auctioned for as much as $58.3 million and sold privately for even more. But "Number 5" could still provide a fresh test for the artist's market, since Pollocks don't come up as often as his abstract expressionist peers like Mark Rothko.

Collectors also tend to pay a premium for pieces that represent a milestone moment in an artist's career, so dealers will be watching to see if bidders are drawn in by the painting's grisly back story. Better-than-expected prices have been paid lately for J.M.W. Turner's final landscape and for Andy Warhol's last, ghostly self-portrait.

Like Vincent van Gogh or Francis Bacon, Pollock is also one of those artists whose appeal hinges as much on his mythic lifestyle as his artwork. Christie's intends to play up his rough-and-tumble persona when it previews the painting to collectors in Hong Kong and London, said Christie's specialist Robert Manley.

The son of an Iowa land surveyor, Pollock moved to New York in 1930 and studied in the Depression with muralist master Thomas Hart Benton. By the mid-1940s, he had married abstract painter Lee Krasner and began startling New York's art circles by experimenting with a new way to paint: Instead of applying his paintbrush to a canvas propped up on an easel, Pollock laid his canvases flat on the wooden floor of his barn studio in Long Island. That way, he could walk over, and around, his compositions, allowing runny house paint to flick off his paintbrush in a frenetic style later called "action painting."

Pollock created dozens of these drippy hits between 1947 and 1951. Later, he shied away from his signature method and the fame it earned him, retreating into his studio and local bars like Jungle Pete's. His artist friends knew he was an alcoholic; to collectors, he became a recluse.

But "Number 5" represented his attempt to come up with another good idea. In 1951, he started a series of roughly 25 large-scale paintings using a single paint color, black. These swirling pieces were abstracts, but his compositions became increasingly biomorphic. At a glance, they evoke the sea-creature shapes of Pollock's earliest paintings or the surrealist works of Joan Miró.

Since Pollock created these "Black Enamel" paintings at the peak of his popularity, the artist easily found buyers for them, and today at least half belong to museums, said Mr. Manley.

The seller of "Number 5" is E.ON Corp.EOAN.XE +0.80% , an energy company based in Düsseldorf, Germany, that has owned the work since 1980. For the next few decades, the Pollock hung in conference rooms, and workers were never told about its history, said Dorothee Gräfin von Posadowsky-Wehner, the head of E.ON's arts and culture program. Even she only learned of the painting's sad back story after the company decided to sell it to keep funding a local museum. "I thought, 'My God, how tragic,'" she added. "But it's also strange because you don't see death in the actual painting. Only life."