An electrochemical storage device has an anode chamber filled with anode material during operation, and a cathode chamber filled with cathode material. The anode chamber is separated from the cathode chamber by solid body electrolyte guiding ions, and the anode chamber is limited on one side by the solid body electrolyte, on another side by a wall at least partially surrounding the solid body electrolyte. The wall is surrounded by a head part of the device, by a base part arranged opposite the head part and/or by a lateral part arranged between the head and base part. The wall has an electrical conductive wall section as an anode to the anode chamber, an at least partially flat, electrical conductive line section electrically connected to the wall section by a surface, and conductivity per surface of the line section greater than conductivity of the wall per surface of the wall section.