Yesterday morning, Jonathan Weisman, an editor at the Times, woke up and looked at Twitter, where he had a public message from a stranger. “Hostile foreign power?” it said. “Jews.”

The sender’s Twitter profile said, “The (((Chosen))) should not be so foolish to believe the current state of affairs shall last forever…Open Borders For Israel. TRUMP 2016~Alt-Right.”

Weisman was not surprised by the message. He has the unfortunate distinction of being one of the ten journalists receiving the most anti-Semitic harassment on Twitter, according to a report published today by the Anti-Defamation League. “I basically wake up to this every morning,” Weisman told me. “You actually do become inured to it. But it’s omnipresent.”

The A.D.L. report documents the frightening rise of anti-Semitic tweets targeting journalists, especially those who write anything critical about Donald Trump. From August, 2015, to July, 2016, the A.D.L. found 2.6 million tweets that included anti-Semitic language, with a spike in anti-Semitism this year, as news coverage of the Presidential campaign increased. Researchers looked more closely at attacks on the Twitter accounts of some fifty thousand journalists and found almost twenty thousand anti-Semitic tweets directed at them, with almost seventy per cent of the invective coming from sixteen hundred accounts. “These aggressors are disproportionately likely to self-identify as Donald Trump supporters, conservatives, or part of the ‘alt-right,’ a loosely connected group of extremists, some of whom are white supremacists,” the A.D.L. reported. “The words that appear most frequently in the 1,600 Twitter attackers’ bios are ‘Trump,’ ‘nationalist,’ ‘conservative,’ and ‘white.’ ”

Many of the anti-Semitic tweets include images of the journalists they are directed at, Photoshopped to show them inside gas chambers or among the corpses of Holocaust victims. Tweets about putting Jewish journalists and their family members in ovens or having them made into lampshades are not uncommon.

On Sunday evening, Hadas Gold, a media reporter at Politico who was born in Israel, received a private message on Twitter that included an image of her with a bullet hole in her forehead and a yellow Star of David on her shirt. “Don’t mess with our boy Trump or you will be first in line for the camp,” the message said.

Gold, whose grandmother fled Poland shortly before the Jews in the family’s neighborhood were deported to concentration camps, told me that she received far worse images via e-mail in the next few days. In her case, Twitter acted quickly, suspending the accounts of the sender and others who used the image within half an hour.

But Twitter’s speedy response was atypical. Despite the fact that the social-media company’s terms of service prevent any use of the platform for “hateful conduct,” Twitter is notoriously slow to respond to complaints, especially when they do not involve high-profile users.

Only a fifth of the anti-Semitic accounts studied by the A.D.L. were suspended. “It is notable that they did suspend twenty-one per cent of the accounts,” Jonathan A. Greenblatt, the A.D.L.’s C.E.O., told me. “But there are seventy-nine per cent that they didn’t. It validates what I have heard from journalist after journalist, and others who have found themselves victimized: oftentimes the companies, and in particular Twitter, have not done enough.”

Oren Segal, one of the A.D.L. report’s authors, noted that Twitter, unlike other social-media platforms, doesn’t actively monitor its own service for language that clearly violates its policies. “Twitter very much feels its users are responsible for flagging material,” he said. “Twitter’s approach of relying on its users is one of the more controversial parts of their terms of service and dealing with this.”

Twitter’s decision not to aggressively police its content has had a cost. The company’s reputation as the platform with the most laissez-faire attitude toward hate speech reportedly contributed to Disney’s recent decision not to buy the company. “Words have consequences,” Greenblatt noted. “They have not just moral consequences but economic consequences if they’re not dealt with.”

A spokesperson for Twitter, who refused to be named, said in a statement, “Hateful conduct has no place on Twitter and we address this issue every day with government, our partners in civil society and our peers in the technology sector.”

That’s not the way it looks to some of the journalists who receive the most venom on the platform. Jeffrey Goldberg, the new editor of the Atlantic, is on the list of journalists who are most attacked on the service. “I can’t say that I’m not pleased,” he joked. “I mean, I finally made a top-ten list.” But he has stopped using the service as much as he once did, partly because of the unrelenting attacks.

“It gets wearying, after a while, to open Twitter and have a hundred different messages from people who want to see my family gassed,” Goldberg said. “It makes me depressed about humanity, and I don’t want to start my day that way. After a while, my experience became something like, ‘Thank you Gestapobro88 for your suggestion that my family should be shoved into the ovens, but I’ve already gotten that message from many of your compatriots this morning.’ ”

Goldberg noted that anti-Semitism isn’t the only form of hate speech on Twitter. The platform is becoming “a cesspool for anti-Semites, homophobes, and racists,” he said. Jake Tapper, the chief Washington correspondent for CNN, who is also on the A.D.L.’s list, said, “It's probably what it's like to be a woman or person of color on social media on any given day.”

Ben Shapiro, a conservative writer and vehement opponent of Trump, is the victim of more anti-Semitic harassment than any other journalist on Twitter, according to the A.D.L. report. Shapiro told me that the vitriol has not affected his use of the service. “Jew-haters can go screw themselves,” he said. He doesn’t want Twitter to kick hateful users offline. “Twitter's a private company,” he said. “I'm not in favor of bans. I'm in favor of exposing this garbage to the light of day.”

Other journalists who have dealt with the incessant hostility are caught between wanting to expose it and not wanting to give more attention to a very small percentage of Twitter’s three hundred million users.

Weisman once spent a couple of days retweeting the worst anti-Semites who attacked him, but he was conflicted about whether it was the best approach. “That was like kicking the hornet’s nest,” he said. “That brought this whole phenomenon in high public relief. But it also gave them what they wanted. It’s a bit of an ethical quandary.”

Gold never actually posted the threatening image sent to her on Twitter. (She posted it to a smaller group of friends and family on Facebook, and one of her Facebook friends posted it to Twitter.) She was reluctant even to discuss the episode publicly because she felt it gave a noxious and abusive user too much attention. “It’s not like this is the first time we’ve had to deal with this,” she said, of Jews and anti-Semitism. She was even able to joke about it: “All of our holidays are, ‘They tried to kill us, we survived, let’s eat.’ ”

Twitter’s future may depend on whether it can prevent the platform from being defined by its most hateful users. The company’s response to the A.D.L. report was not encouraging. On one hand, a spokesman insisted that Twitter has a new “policy and products” to address online threats, “to be shared in the coming weeks.” But, speaking of the A.D.L. data, the company also said, “We don't believe these numbers are accurate.”

Asked about Twitter’s challenge to its methodology, Greenblatt said, “Prior to releasing our report, we opened the door to Twitter to respond to our findings. We never heard back from them.”