Senator Robert Menendez of New Jersey was convicted on Tuesday of taking part in a complicated bribery scheme in which he traded political favors for cash, gold bars and other gifts.

Federal prosecutors said the plot began in February 2018, less than a month after Mr. Menendez, a Democrat, was cleared of charges tied to an unrelated federal corruption case in New Jersey.

Here are the central elements of the case against the senator and his two co-defendants, Wael Hana and Fred Daibes, two New Jersey businessmen:

Aiding Egypt

Mr. Menendez was charged with using his influence and power as a senator in ways that benefited both the government of Egypt and Mr. Hana, an American citizen who emigrated from Egypt and was trying to get a halal meat certification company off the ground in New Jersey.

Mr. Menendez, a former leader of the Senate Foreign Relations Committee, was accused of steering weapons and aid to Egypt in exchange for bribes.

Prosecutors also described an effort by Mr. Hana to enlist Mr. Menendez’s help in smoothing over a U.S.-Egyptian dispute during this period. After an American tourist was seriously injured in a mistaken 2015 Egyptian military attack, some members of Congress balked at awarding certain military aid to Egypt, according to the indictment.

A year later, after a meeting with an Egyptian general, Mr. Menendez also urged the State Department to take a more active role in a dispute over a hydroelectric dam Ethiopia was building on the Nile River, prosecutors said. Egypt was opposed to the dam and feared it would cut into the country’s water supply.