Federal prosecutors have charged 13 alleged members of the hacking group Anonymous in connection with cyberattacks that the collective launched in 2010 against ­anti-piracy groups and financial institutions unwilling to process donations to WikiLeaks.

The indictment returned Thursday in U.S. District Court in Alexandria charges the 13 men with conspiring to intentionally cause damage to protected computers. Prosecutors accused the men of participating in a series of cyberattacks that briefly disrupted Mastercard’s and Visa’s Web sites and also targeted the Web sites of anti-piracy groups across the world.

Detailed in 28 pages, the charges are the latest in the Justice Department’s effort to root out cybercrime by prosecuting hackers across the country — especially those affiliated with Anonymous. Last year, federal prosecutors charged five alleged Anonymous members who they say stole confidential information from U.S. companies and temporarily shut down government Web sites. This year, prosecutors charged a journalist who they say worked with the group to modify a story on the Los Angeles Times’ Web site.

Anonymous is a loosely knit group with no clear leaders that is generally interested in promoting a more freewheeling Internet. Those indicted Thursday range in age from 21 to 65 and are spread across the country, including one man from the D.C. area.

The allegations in this case stem from a series of cyberattacks that began in September 2010, when members of Anonymous decided to retaliate for the shuttering of Pirate Bay, a popular Sweden-based file-sharing site, according to the indictment. Dubbed “Operation Payback” by those who participated in it, the attacks drew national and international attention as the hackers briefly disrupted the Web sites for Mastercard and Visa because they had stopped processing payments to WikiLeaks.

The effort was not overly sophisticated, but it was effective. The group posted messages on online bulletin boards urging supporters to install a program called a Low Orbit Ion Cannon and then, at a specified time, unleash the program on a particular Web site’s IP address, according to the indictment. That sends an overwhelming amount of Internet traffic to the targeted site and possibly disrupts or shuts it down, according to the indictment. The technique is referred to as a Distributed Denial of Service, or DDoS, attack.

For months, according to the indictment, the hackers, who see some copyright laws as unjust, targeted the Web sites of companies and people they thought were opposed to file sharing. They attacked the sites of those that have been the faces of anti-piracy in the United States — the Recording Industry Association of America and the Motion Picture Association of America — and the sites of their equivalents worldwide. They attacked the sites of law firms helping in anti-piracy cases. They attacked the site of the U.S. Copyright Office. They even attacked the site of rocker Gene Simmons, who has spoken out against music piracy.

Gregg Housh, an Internet activist and former Anonymous member who still watches the group’s activity, said the attacks started as a protest of anti-piracy efforts but evolved as those involved learned of major companies’ refusal to process WikiLeaks donations. He said the recent indictment was unlikely to deter Anonymous hackers, but instead would “fire up the base, a lot.”

“I think it’s just going to turn into a rally of support, not people being scared,” Housh said, “and that’s exactly what they don’t want.”

Housh defended Operation Payback — of which he said he had no part — as an effort to re-create a traditional protest online. He noted that customers’ abilities to use their credit cards were not affected; only the credit card companies’ Web sites were shut down.

“Something has to be done to come up with a way to protest online that everyone doesn’t end up getting thrown in jail,” he said.

Prosecutors identified those charged as Dennis Owen Collins, 52, of Toledo; Jeremy Leroy Heller, 23, of Takoma Park; Zhiwei Chen, 21, of Atlanta; Joshua S. Phy, 27, of Gloucester, N.J.; Ryan Russell Gubele, 27, of Seattle; Robert Audubon Whitfield, 27, of Georgetown, Tex.; Anthony Tadros, 22, of Storrs Mansfield, Conn.; Geoffrey Kenneth Commander, 65, of Hancock, N.H.; Phillip Garrett Simpson, 28, of Tucson; Austen L. Stamm, 26, of Beloit, Kan.; Timothy Robert McClain, 26, of Clemson, S.C.; Wade Carl Williams, 27, of Missoula, Mont.; and Thomas J. Bell, 28, of Rockland, Mass.