SANTA CRUZ, Calif.  — Rescuers have stopped searching the cold Pacific Ocean for a couple, two young children and a sinking sailboat as questions of a hoax arise amid no reports of the missing family or any registration of the vessel in question.

The Coast Guard on Tuesday called off the search for a boat that reportedly sank in rough seas far off the Central California coast, saying nothing more could be done and that the family’s distress calls might have been a hoax.

“We’ve exhausted the possibilities,” Coast Guard Chief Petty Officer Mike Lutz said. The Coast Guard is treating the incident as a rescue, with the possibility the calls came from a trickster.

Coast Guard Executive Officer Noah Hudson in Monterey said it was tough to call off a search, but that if it was a hoax, “it’s unfortunate that we were forced to use so many resources for so much time.”

Making a false federal distress call is a federal felony, and perpetrators face up to six years in prison and a $250,000 fine. The 42-hour search involved hundreds of rescuers from the Coast Guard and the California Air National Guard. A Hercules C-130 four-engine turboprop aircraft buzzed above the seas, while helicopters, cutters and lifeboats plied the waters, as costs soared into the hundreds of thousands of dollars.

The Coast Guard handles several hundred hoax calls a year, some involving major rescue efforts. A massive search was launched last year in the Atlantic Ocean east of Sandy Hook, N.J., after a caller falsely radioed for help, claiming, “We have 21 souls on board, 20 in the water.”

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Kurtis Thorsted, 55, of Salinas, Calif., was released from federal prison last summer after being convicted, for the second time, of making false calls to the Coast Guard. Court records show he made 51 distress calls over a five-month period, claiming in one case to be in trouble in a kayak off the coast of Santa Cruz.

Crews off Monterey started looking for the family by sea and air after receiving the first distress call Sunday afternoon. In one call, a man’s calm voice is heard saying, “Coast Guard, Coast Guard, we are abandoning ship. This is the (Charmblow). We are abandoning ship.”

The caller said they had to abandon the boat and were trying to tie together a makeshift life raft out of a cooler and life-preserver ring, a method taught in survival classes. The Coast Guard then lost radio contact with the boat.

The Monterey Bay at this time of year is about 50 degrees; a person could survive between 30 minutes and an hour without a survival suit or wetsuit.

Investigators said they believed, from the distress calls, that the family included a husband and wife, their 4-year-old son and his cousin, Coast Guard Lt. Heather Lampert has said.

Sailors along this renowned stretch of coastline are a close-knit group who were gripped by the news of the missing family, but also baffled by important omitted details.

Harbor masters at the string of ports that dot the coastline from Monterey to Half Moon Bay told The Associated Press the same thing: No boats launched from their docks were missing, and no family had disappeared from their community.

“It’s all kind of strange,” said Brad Miller, who operates a fishing charter out of Santa Cruz. “But why would somebody want to make something like that up? What’s the point of that?”