Aragorn is quoted as saying (emphasis mine) :
'For the Sword that was Broken is the Sword of Elendil that broke beneath him when he fell. It has been treasured by his heirs when all other heirlooms were lost; for it was spoken of old among us that it should be made again when the Ring, Isildur's Bane, was found. Now you have seen the sword that you have sought, what would you ask?'
The Lord of the Rings: The Fellowship of the Ring : Chapter 2 The Council of Elrond
But we know from the appendices that many years prior to this Elrond told Aragorn this:
"Here is the ring of Barahir," he said, "the token of our kinship from afar; and here also are the shards of Narsil. With these you may yet do great deeds; for I foretell that the span of your life shall be greater than the measure of Men, unless evil befalls you or you fail at the test. But the test will be hard and long. The Sceptre of Annúminas I withhold, for you have yet to earn it."
The Lord of the Rings : Appendix A (v) : Here Follows a Part of The Tale of Aragorn and Arwen
Why would Aragorn say that all other heirlooms are lost when he knows that others exist?