The following statements are true of the 1800 elections
1. The House of Representatives decided who would win the presidency.
This happened because there was a tie at the Electoral College.
2. Hamilton influenced the decision of who would win the presidency.
Hamilton wrote to his Federalist colleagues that were members of the House of representative, warning them that a Burr presidency would prove disastrous for the nation
3. Jefferson was elected.
It is not true that the Federalists won the election, because Jefferson who won the election was Democratic-Republican. John Adams, who flagged for the Federalists lost at the electoral college.
It is also not true that Aaron Burr and Alexander Hamilton tied in the electoral college. It was Aaron Burr and Thomas Jefferson that ties with 73 votes each at the Electoral college.