{'fraction_non_alphanumeric': 0.010958904109589041, 'fraction_numerical': 0.0, 'mean_word_length': 5.0, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
On the Birch and Swinnerton-Dyer conjecture

In this paper we prove that if the Birch and Swinnerton-Dyer conjecture holds for products of a finite number of modular elliptic curves defined over totally real number fields, then the Birch and SwinnertonDyer conjecture holds for products of a finite number of elliptic curves defined over totally real number fields.