No, this is not correct.

Levellers didn't call themselves levellers initially, that was a pejorative term assigned to them by their political opponents which they eventually adopted because more people knew them by that name than their original name "Agitators."

Levellers were populists who opposed common ownership of property and originally called for freedom of religion and equality for all under the law. Later they called for excluding anyone that didn't own land from the electorate.

The communistic faction during that time period were called the "Diggers" who advocated the abolition of private ownership of land.

No, this is not correct.

Levellers didn't call themselves levellers initially, that was a pejorative term assigned to them by their political opponents which they eventually adopted because more people knew them by that name than their original name "Agitators."

Levellers were populists who opposed common ownership of property and originally called for freedom of religion and equality for all under the law. Later they called for excluding anyone didn't own land from the electorate.

The communistic faction during that time period were called the "Diggers" who advocated the abolition of private ownership of land.

No, this is not correct.

Levellers didn't call themselves levellers initially, that was a pejorative term assigned to them by their political opponents which they eventually adopted because more people knew them by that name than their original name "Agitators."

Levellers were populists who opposed common ownership of property and originally called for freedom of religion and equality for all under the law. These tenets were later changed for political expediency by excluding anyone didn't own land from the electorate.

The communistic faction during that time period were called the "Diggers" who advocated the abolition of private ownership of land.