Question: What served Nelson as his flagship from 6 June 1799 until the end of June 1801, and was one of two British-built 80-gun ships he other being designed by Sir Edward Hunt?
Context: The "Boyne"-class ships of the line were a class of two 98-gun second rates, ordered in 1783 and designed for the Royal Navy by Sir Edward Hunt. The "Connecticut" was a sailing frigate built by Seth Overton at Chatham, Conn. and launched 6 June 1799 at Middletown, Conn.  She sailed 15 Oct. 1799 under the command of Captain M. Tryon for the Guadaloupe Station, and cruised in the West Indies for a year during the Quasi-War with France, protecting American commerce from French privateers.  Connecticut's successful career was highlighted by the capture of four privateers and the recapture of seven American merchantmen.  Arriving at New London, Conn., 18 Oct. 1800, "Connecticut" was sold at New York in 1801. HMS "Royal Sovereign" was a 100-gun first rate ship of the line of the Royal Navy, which served as the flagship of Admiral Collingwood at the Battle of Trafalgar.  She was the third of seven Royal Navy ships to bear the name.  Designed by Sir Edward Hunt, she was launched at Plymouth Dockyard on 11 September 1786, at a cost of £67,458, and was the only ship built to her draught.  She was known by her crew as the "West Country Wagon" due to her poor manoeuvrability and speed. HMS "Courageux" was a 74-gun third rate ship of the line of the Royal Navy, launched on 26 March 1800 at Deptford.  She was designed by Sir John Henslow as one of the large class 74-gun ships, and was the only ship built to her draught.  Unlike the middling and common class 74-gun ships, which carried 18-pounder long guns, as a large 74-gun ship, "Courageux" carried 24-pounders on her upper gun deck. HMS "Caesar, also Cæsar", was an 80-gun third rate ship of the line of the Royal Navy, launched on 16 November 1793 at Plymouth.  She was designed by Sir Edward Hunt, and was the only ship built to her draught.  She was also one of only two British-built 80-gun ships of the period, the other being HMS Foudroyant (1798). The "Crown"-class ships of the line were a class of three 64-gun third rates, designed for the Royal Navy by Sir Edward Hunt. A fourth-rate was, in the British Royal Navy during the first half of the 18th century, a ship of the line mounting from 46 up to 60 guns.  While the number of guns stayed subsequently in the same range until 1817, after 1756 the ships of 50 guns and below were considered too weak to stand in the line of battle, although the remaining 60-gun ships were still classed as fit to be ships of the line.  However, the 50-gun ship continued to be used largely during the Seven Years' War, and during the time of the American Revolution a whole new group of 50-gun ships was constructed, not for the battlefleet, but to meet the needs of combat in the shallow waters off North America where the larger ships found it difficult to sail.  50-gun ships were also suitable as convoy escorts and for service on foreign stations, where larger enemy vessels were unlikely to be encountered.  Some saw service as flagships since, as two-deckers, they were able to accommodate a flag officer and his retinue, and they also had the physical presence of a flagship.  Their usefulness was declining, however, and during the French Revolutionary and Napoleonic Wars few 50s were built, although several remained in service, especially on distant stations such as the East Indies.  The 60-gun ships were also dying out, superseded initially by the 74-gun third-rates, although by 1793 there were still four 60-gun ships left in harbour service. The "Ganges"-class ships of the line were a class of six 74-gun third rates, designed for the Royal Navy by Sir Edward Hunt. The "Scipion" class was a class of three 74-gun ships built to a design by François-Guillaume Clairin-Deslauriers, the "ingénieur-constructeur en chef" at Rochefort Dockyard.  These were the shortest 74-gun ships built by France since the 1750s, and they were found to lack stability as a consequence.  The third ship - originally the "Pluton" - was 'girdled' (sheathed) with 32 cm of pine at Rochefort in 1799 to overcome her instability, and the design of two further ships ordered at the same dockyard in 1779 were lengthened. HMS "Foudroyant" was an 80-gun third rate of the Royal Navy, one of only two British-built 80-gun ships of the period (the other was HMS Caesar (1793)).  "Foudroyant" was built in the dockyard at Plymouth Dock (a.k.a. Devonport) and launched on 31 March 1798.  "Foudroyant" served Nelson as his flagship from 6 June 1799 until the end of June 1801.
Answer: HMS "Foudroyant"