In order to adapt an intervertebral implant better to the contours of the lower and upper faces of the vertebrae spaced apart by the implant, which faces face the vertebral implant, the intervertebral implant according to the invention has a support portion (1.1) and a proximal contact portion (1.3) contiguous thereto in the longitudinal direction, an upper face (1.6) and a lower face (1.7) are symmetrical to a horizontal central plane (L-Q), in particular the height of the support portion between the transition (U) of said support portion to the contact portion (1.3) and a distal end face (1.2) remote from the contact portion (1.3) being greater than the height at the transition (U) and at the distal end face (1.2).