Battery module comprising • a plurality of battery cells that comprise in each case a first connection and a second connection, • connection connecting elements for electrically connecting the plurality of battery cells, wherein each connection connecting element connects a first connection of a first battery cell (2-i) to a second connection of a second battery cell (2-(i+1)), which second connection is adjacent to said first connection, and wherein the connection connecting elements are embodied in a planar manner owing to their low material thickness in relation to their width; • a first terminal connection and a second terminal connection for connecting the battery module to external circuitry, • a first terminal connection connecting element for electrically connecting the first terminal connection to a first terminal of the battery module, wherein the first terminal is embodied by way of a first connection of a battery cell of the plurality of battery cells, and • a second terminal connection connecting element for electrically connecting the second terminal connection to a second terminal of the battery module, wherein the second terminal is embodied by way of a second connection of a battery cell of the plurality of battery cells, wherein the first terminal connection connecting element is embodied in a planar manner, and wherein the second terminal connection connecting element is likewise embodied in a planar manner and arranged in such a manner that the surface thereof extends at a spaced disposition from and parallel to the surfaces of the connection connecting elements and parallel to the surface of the first terminal connection connecting element and covers the surfaces of the connection connecting elements and the surface of the first terminal connection connecting element at least partially, and that during the operation of the battery module a current flows through the second terminal connection connecting element, the direction of said current being opposite to a current flow direction in the connection connecting elements and in the first terminal connection connecting element, as a result of which the resulting magnetic fields are largely balanced. • a plurality of battery cells that comprise in each case a first connection and a second connection, • connection connecting elements for electrically connecting the plurality of battery cells, wherein each connection connecting element connects a first connection of a first battery cell (2-i) to a second connection of a second battery cell (2-(i+1)), which second connection is adjacent to said first connection, and wherein the connection connecting elements are embodied in a planar manner owing to their low material thickness in relation to their width; • a first terminal connection and a second terminal connection for connecting the battery module to external circuitry, • a first terminal connection connecting element for electrically connecting the first terminal connection to a first terminal of the battery module, wherein the first terminal is embodied by way of a first connection of a battery cell of the plurality of battery cells, and • a second terminal connection connecting element for electrically connecting the second terminal connection to a second terminal of the battery module, wherein the second terminal is embodied by way of a second connection of a battery cell of the plurality of battery cells,