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ECC2K-108, solved on April 4th 2000.
ECC2-97, solved on September 22nd 1999.
ECCp-79, solved on December 6th 1997.
ECC2-79, solved on December 16th 1997.
ECCp-89, solved on January 12th 1998.
ECC2-89, solved on February 7th 1998.
ECCp-97, solved on March 16th 1998 in association with British Telecom Labs.
ECC2K-95, solved on May 21st 1998.
Here are two papers about counting points: on elliptic curves and on hyperelliptic curves.
Please note: These pages are no longer maintained (since circa December 2000).