An indexable cutting insert configured for turning operation, comprising: a flank face having a generally parallelogram shape and a plurality of side faces, wherein the flank face is bounded by a plurality of edges, each edge joining the flank face with one of the side faces; wherein the plurality of side faces comprises a first side face, a second side face, a third side face, and a fourth side face, the first side face and the third side face intersecting a longitudinal direction of the cutting insert, the second side face and the fourth side face extending along the longitudinal direction of the cutting insert, the first and second side faces (102, 103) intersecting at an obtuse angle, the third and fourth side faces (104, 105) intersecting at the same obtuse angle, the first and fourth side faces (102, 105) intersecting at an acute angle, the second and third side faces (103, 104) intersecting at the same acute angle; wherein the plurality of edges comprises a first cutting edge and a second cutting edge; wherein the first cutting edge has a shape corresponding to a portion of a first bent curve and the second cutting edge has a shape corresponding to a portion of a second bent curve, the second bent curve being obtainable by a translation of the first bent curve along a width direction of the cutting insert; wherein the cutting insert has a two-fold rotational symmetry with respect to an axis of symmetry that is perpendicular to the width direction, the longitudinal direction of the cutting insert being perpendicular to the width direction and the axis of symmetry, and wherein the cutting insert further comprises a groove provided at the flank face of the cutting insert and extending along the longitudinal direction of the cutting insert to reach the edges (106, 108) intersecting the longitudinal direction of the cutting insert, and the groove being arranged between the first cutting edge and the second cutting edge. a flank face having a generally parallelogram shape and a plurality of side faces, wherein the flank face is bounded by a plurality of edges, each edge joining the flank face with one of the side faces; wherein the plurality of side faces comprises a first side face, a second side face, a third side face, and a fourth side face, the first side face and the third side face intersecting a longitudinal direction of the cutting insert, the second side face and the fourth side face extending along the longitudinal direction of the cutting insert, the first and second side faces (102, 103) intersecting at an obtuse angle, the third and fourth side faces (104, 105) intersecting at the same obtuse angle, the first and fourth side faces (102, 105) intersecting at an acute angle, the second and third side faces (103, 104) intersecting at the same acute angle; wherein the plurality of edges comprises a first cutting edge and a second cutting edge; wherein the first cutting edge has a shape corresponding to a portion of a first bent curve and the second cutting edge has a shape corresponding to a portion of a second bent curve, the second bent curve being obtainable by a translation of the first bent curve along a width direction of the cutting insert; wherein the cutting insert has a two-fold rotational symmetry with respect to an axis of symmetry that is perpendicular to the width direction, the longitudinal direction of the cutting insert being perpendicular to the width direction and the axis of symmetry, and wherein the cutting insert further comprises a groove provided at the flank face of the cutting insert and extending along the longitudinal direction of the cutting insert to reach the edges (106, 108) intersecting the longitudinal direction of the cutting insert, and the groove being arranged between the first cutting edge and the second cutting edge.