Intersomatic cage intended to be inserted into an intervertebral disc space between two vertebrae, namely a lower vertebra and an upper vertebra, having a lower face intended to be situated towards the lower vertebra once the cage has been positioned in the intervertebral disc space, an upper face intended to be directed towards the upper vertebra once the cage has been positioned in the intervertebral disc space, at least one side face extending between the upper and lower faces and laterally delimiting the cage, characterized in that the upper face and/or the lower face have in cross section, in a plane defined by the vertical axis and the medio-lateral axis at at least one point along the antero-posterior axis, an inwardly curved shape with their convexity directed towards the outside of the cage, especially in the shape of an arc of a circle, and the greatest thickness of the cage in the vertical direction is greater than the greatest thickness of the cage in the medio-lateral direction.
