To calculate the capacitor C1 in a low-frequency common emitter (CE) amplifier circuit with a cutoff frequency of 25Hz, the input impedance at the junction of three resistors must be determined. The impedance seen by C1 is influenced by the transistor's beta (β) and the emitter resistor, with an estimated impedance of around 10k ohms for calculations. The discussion emphasizes that the AC current gain, rather than the DC working point, is crucial for accurate calculations. Additionally, it is noted that the base and collector currents are provided, eliminating the need to guess β. Understanding these parameters is essential for correctly sizing C1 in the amplifier design.