Coriolis mass flowmeter or density meter comprising: at least two measuring tubes (110a, 110b) which are curved in the rest position, wherein the measuring tubes have measuring tube axes which are in mirror symmetry to a first mirror plane which extends between the measuring tubes (110a, 110b), at least one actuator arrangement and at least one sensor arrangement (142a, 142b); a collector (120a, 120b) on both the inlet side and the outlet side, wherein the measuring tubes are grouped in terms of flow with a collector on the inlet side and on the outlet side, a carrier body, which connects the collector on the inlet side and the collector on the outlet side in a rigid manner; and at least a first plate-like coupler (132a, 134a) and a second plate-like coupler (132b, 134b) on both the inlet side and the outlet side, wherein the measuring tubes are interconnected in pairs by means of the couplers in order to form an oscillator, wherein the couplers each have two tube openings for the measuring tubes that are connected by means of the couplers, wherein the measuring tubes are at least partially connected to the couplers along their circumference, wherein the actuator arrangement is configured to excite a flexural vibration useful mode between the two measuring tubes of the oscillator, the sensor arrangement (142a, 142b) is configured to measure vibrations of the oscillator, wherein on the inlet side and on the outlet side at least the first coupler (132a, 134a) and the second coupler (132b, 134b) each have an opening between the measuring tubes (110a, 110b), which are connected via the coupler, said opening being surrounded by a closed perimeter and designed to influence the vibration properties of the oscillator, characterized in that on both the inlet side and the outlet side a first of the couplers and a second of the couplers have coupler-specific coupler normal planes which are parallel to the largest principal axis of inertia of the individual coupler, which are perpendicular to the first mirror plane, and which touch a connecting line of the measuring tube axes (12a, 12b) inside the opening of the coupler in question, wherein said connecting line is perpendicular to the first mirror plane, wherein the first coupler has a first center of mass which is spaced away from its coupler-specific coupler normal plane by a first distance, wherein the second coupler has a first center of mass, which is spaced away from its coupler-specific coupler normal plane by a second distance, wherein the first distance is different from the second distance, wherein the difference is not less than 5 %, particularly not less than 10 % of the smaller of the two distances. at least two measuring tubes (110a, 110b) which are curved in the rest position, wherein the measuring tubes have measuring tube axes which are in mirror symmetry to a first mirror plane which extends between the measuring tubes (110a, 110b), at least one actuator arrangement and at least one sensor arrangement (142a, 142b); a collector (120a, 120b) on both the inlet side and the outlet side, wherein the measuring tubes are grouped in terms of flow with a collector on the inlet side and on the outlet side, a carrier body, which connects the collector on the inlet side and the collector on the outlet side in a rigid manner; and at least a first plate-like coupler (132a, 134a) and a second plate-like coupler (132b, 134b) on both the inlet side and the outlet side, wherein the measuring tubes are interconnected in pairs by means of the couplers in order to form an oscillator, wherein the couplers each have two tube openings for the measuring tubes that are connected by means of the couplers, wherein the measuring tubes are at least partially connected to the couplers along their circumference, wherein the actuator arrangement is configured to excite a flexural vibration useful mode between the two measuring tubes of the oscillator, the sensor arrangement (142a, 142b) is configured to measure vibrations of the oscillator, wherein on the inlet side and on the outlet side at least the first coupler (132a, 134a) and the second coupler (132b, 134b) each have an opening between the measuring tubes (110a, 110b), which are connected via the coupler, said opening being surrounded by a closed perimeter and designed to influence the vibration properties of the oscillator, characterized in that on both the inlet side and the outlet side a first of the couplers and a second of the couplers have coupler-specific coupler normal planes which are parallel to the largest principal axis of inertia of the individual coupler, which are perpendicular to the first mirror plane, and which touch a connecting line of the measuring tube axes (12a, 12b) inside the opening of the coupler in question, wherein said connecting line is perpendicular to the first mirror plane, wherein the first coupler has a first center of mass which is spaced away from its coupler-specific coupler normal plane by a first distance, wherein the second coupler has a first center of mass, which is spaced away from its coupler-specific coupler normal plane by a second distance, wherein the first distance is different from the second distance, wherein the difference is not less than 5 %, particularly not less than 10 % of the smaller of the two distances.