When did the ice battle with the crusaders take place on Lake Chudskoye?

The Russian chronicles and the story “The Life of Alexander Nevsky” mainly testify about the Battle of the Ice, which happened on April 5, 1242 on the lake that had the name Chudskoye. By right, it is the story that is considered to be the main source, since it colorfully sets out battle scenes, as well as individual realities. It should be noted that historians did not separate historically authentic news from literary fiction, and also did not take into account the time and place of origin of the Battle of the Ice in the stories.