Several versions of the orbital elements for the Comet Hyakutake, "the great comet of 1996," are now available on my Web site. I also obtained the elements for the solar probe Ulysses, which unexpectedly encountered the comet's tail when the comet was at perihelion on May 1st, 1996. Ulysses is in a polar orbit around the sun which has a semi-major axis of more than 3AU. The comet's perihelion was only 0.2 AU.
The comet was also observed by the SOHO probe. Unfortunately, SOHO's location isn't easily described by Keplerian orbital elements, since it is stationed near Earth's L1 Lagrange point.
See http://www.lns.cornell.edu/~seb/celestia/index.html#3.3.2
and http://www.lns.cornell.edu/~seb/celestia/index.html#3.4.2