Background: Cardiovascular diseases are the leading cause of death worldwide, and the 12-lead electrocardiogram (ECG) is the most widely used tool for their diagnosis. An ECG carries a cardiac rhythm and a variable number of coexisting abnormalities, yet most automatic methods treat all diagnostic labels as one flat set and rely on large models unsuited to resource-constrained devices. Objective: To classify the cardiac rhythm, detect multiple coexisting abnormalities and determine whether an abnormal rhythm and an abnormality occur together, with a single compact model suitable for deployment. Methods: On the Chapman–Shaoxing database (10,646 recordings), the labels were merged into four rhythm groups and four abnormality groups, and each recording was represented by a 12 × 24 mean amplitude spectrum. FL-Net, a compact dual-stream frequency–lead attention network, processes this representation directly and feeds a multi-task head with three outputs, rhythm, abnormality and co-occurrence, coupled by a logical consistency loss and trained end-to-end. Results: In 10-fold cross-validation, FL-Net trained with the multi-task objective achieved a precision of 0.8264, a recall of 0.7203, an F1-score of 0.7694 and an AUC of 0.8551, outperforming Binary Relevance, Classifier Chains, Label Powerset and its own single-task variant, and reached an F1-score of 0.8924 on the co-occurrence task. FL-Net has 1.94M parameters and an inference latency of 3.6 ms. Structural and electrical abnormalities remained the most difficult categories. Conclusion: Jointly modeling rhythm, abnormalities and their co-occurrence in a single compact network yields an accurate and efficient framework for ECG-based cardiac diagnosis.