Prosthetic aortic valve comprising: an annular stent (5010) that includes: (1) a flow inlet portion of the ring (5200) configured for disposal, in use, adjacent to a patient's native aortic valve ring, (2 ) an aortic flow outlet portion (5100) configured for disposal, in use, in the patient's native aorta downstream from at least a portion of the patient's native waltzalva (20), and (3) a plurality of connection filaments (5284a, 5284b) which constitute substantially the only connection between the flow inlet portion of the ring (5200) and the aortic flow outlet portion (5100), defining the flow inlet portion of the ring (5200) a plurality of commissure points (5236) that are spaced apart in the annular direction around the flow inlet portion of the ring (5200), the commissure points (5236) being the characteristics of the flow inlet portion of the ring (5100) that are closer to the aortic flow outlet portion (5100), each of the connecting filaments (5284a, 5284b) being connected to the flow inlet portion of the ring (5200) only at points that are farther from the aortic flow outlet portion than the tips (5236) of the commissures and each of the connecting filaments (5284a, 5284b) being adjacent to an associated one of the commissure points (5236), at least one being of the connection filaments (5284a, 5284b) positioned for disposal, in use, adjacent to each side of each of the commissure tips (5236) of the patient's native aortic valve and each of the connection filaments (5284a , 5284b), in use, bulges radially outward into the waltz (20) between the flow inlet portion of the ring (5200) and the outlet portion of the aortic flow (5100)； and a plurality of valve leaflets (5500) supported by the flow inlet portion of the ring (5200), characterized in that the connecting filaments (5284a, 5284b) that are adjacent to each side of each of the tips (5236) The commissure of the patient's native aortic valve is spaced apart from each other by a distance that is less than
