Battery module and battery

A battery module comprising:

• a plurality of individual electrical cells which are arranged within a common housing, wherein an end side of the common housing has mechanical connecting elements for connecting the battery module to a temperature-control element which is provided outside the battery module in order to thereby enable good heat transfer between the battery module and the temperature-control element,
• wherein the mechanical connecting elements are provided as corresponding upper and lower cutouts in the end side of the housing,
• wherein the battery module has a step in an upper or in a lower region of the end side, two electrical pole contacts of the battery module being arranged on said step in a horizontal direction in such a way that said electrical pole contacts are positioned either above or below the or each upper or lower cutout, and the electrical pole contacts being arranged at least partially outside of the common housing of the battery module, wherein the two electrical pole contacts are spaced apart from each other, positioned on opposite sides of the step and disposed on the end side of the common housing,
• wherein the battery module has two electrical pole connectors that are respectively connected to the electrical pole contacts and extend from the housing for connecting to further battery modules, wherein one of the two electrical pole connectors is configured to be connected to an adjacent battery module arranged beside the battery module, and the other of the two electrical pole connectors is configured to be connected to an opposing battery module arranged opposite the battery module, wherein said other of the two electrical pole connectors has an elongated and straight body that extends at an acute angle with respect to said one of the two electrical pole connectors and said battery module.