This paper proposes a movable-antenna (MA) array empowered integrated sensing and communications (ISAC) system for low-altitude economy (LAE) applications. The system uses an unmanned aerial vehicle (UAV) as a low-altitude platform (LAP) to provide simultaneous information transmission and sensing. The goal is to maximize the achievable data rate while meeting the sensing beampattern threshold. To achieve this, the paper formulates a data rate maximization problem by jointly optimizing transmit information and sensing beamforming, and the positions of the MA array. Due to the non-convex nature of the problem, an efficient alternating optimization (AO)-based algorithm is proposed. The algorithm iteratively optimizes parts of the variables while fixing the others. Numerical results show that the proposed MA array-based scheme outperforms two benchmark schemes in terms of achievable data rate and beamforming gain. The system model considers a linear MA array with M antennas, where the positions of the antennas can be adjusted to optimize beamforming. The system uses a time interval divided into slots, with each slot having a fixed duration. The ULAP transmits information signals to ground nodes (GNs) and dedicated sensing signals to the ground target. The information and sensing signals are combined to improve both communication and sensing performance. The system also considers the constraints on antenna positions, power, and sensing beamforming gain. The problem formulation involves maximizing the overall data rate while ensuring the sensing beampattern gain. The problem is non-convex due to the coupling of information and sensing beamforming with the positions of the MA array. To solve this, the paper proposes an AO-based algorithm that first optimizes the positions of the MA array, then optimizes the transmit information and sensing beamforming. The algorithm uses particle swarm optimization (PSO) for the MA array position optimization and successive convex approximation (SCA) for the beamforming optimization. The results show that the proposed scheme achieves higher data rates and beamforming gains compared to fixed and random position schemes. The numerical results demonstrate that the proposed scheme outperforms the fixed-position antenna array (FPA) and random-position antenna array (RPA) schemes in terms of data rate and beamforming gain. The results also show that the proposed scheme is robust to changes in the number of antennas. The paper concludes that the MA array empowered ISAC system is effective for LAE applications, and future work can focus on further optimizing the mobility of the UAV for these applications.This paper proposes a movable-antenna (MA) array empowered integrated sensing and communications (ISAC) system for low-altitude economy (LAE) applications. The system uses an unmanned aerial vehicle (UAV) as a low-altitude platform (LAP) to provide simultaneous information transmission and sensing. The goal is to maximize the achievable data rate while meeting the sensing beampattern threshold. To achieve this, the paper formulates a data rate maximization problem by jointly optimizing transmit information and sensing beamforming, and the positions of the MA array. Due to the non-convex nature of the problem, an efficient alternating optimization (AO)-based algorithm is proposed. The algorithm iteratively optimizes parts of the variables while fixing the others. Numerical results show that the proposed MA array-based scheme outperforms two benchmark schemes in terms of achievable data rate and beamforming gain. The system model considers a linear MA array with M antennas, where the positions of the antennas can be adjusted to optimize beamforming. The system uses a time interval divided into slots, with each slot having a fixed duration. The ULAP transmits information signals to ground nodes (GNs) and dedicated sensing signals to the ground target. The information and sensing signals are combined to improve both communication and sensing performance. The system also considers the constraints on antenna positions, power, and sensing beamforming gain. The problem formulation involves maximizing the overall data rate while ensuring the sensing beampattern gain. The problem is non-convex due to the coupling of information and sensing beamforming with the positions of the MA array. To solve this, the paper proposes an AO-based algorithm that first optimizes the positions of the MA array, then optimizes the transmit information and sensing beamforming. The algorithm uses particle swarm optimization (PSO) for the MA array position optimization and successive convex approximation (SCA) for the beamforming optimization. The results show that the proposed scheme achieves higher data rates and beamforming gains compared to fixed and random position schemes. The numerical results demonstrate that the proposed scheme outperforms the fixed-position antenna array (FPA) and random-position antenna array (RPA) schemes in terms of data rate and beamforming gain. The results also show that the proposed scheme is robust to changes in the number of antennas. The paper concludes that the MA array empowered ISAC system is effective for LAE applications, and future work can focus on further optimizing the mobility of the UAV for these applications.