{"id":"W2062092454","doi":"10.4153/cmb-2002-036-3","title":"Surjectivity of mod <i>ℓ</i> Representations Attached to Elliptic Curves and Congruence Primes","year":2002,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Congruence (geometry); Mod; Elliptic curve; Pure mathematics; Projective test; Prime (order theory); Dihedral group; Discrete mathematics; Combinatorics; Geometry; Group (periodic table)","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009885065,0.0006713284,0.0005790623,0.002361377,0.002537633,0.005540354,0.0006817449,0.000818539,0.008769479],"category_scores_gemma":[0.002782652,0.0005802031,0.0006757546,0.00118085,0.004894146,0.005700516,0.004404851,0.003521783,0.0007127125],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001324987,"about_ca_system_score_gemma":0.0004320553,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007468755,"about_ca_topic_score_gemma":0.0004425792,"domain_scores_codex":[0.9990964,0.0001219307,0.00004327426,0.000215455,0.0002836073,0.0002393922],"domain_scores_gemma":[0.9979966,0.0005586043,0.0004381237,0.0002889093,0.0002015593,0.0005161433],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00005164841,0.00003845878,0.0007879434,0.00001724668,0.00000553397,0.0003598107,0.0008340807,0.0004466484,0.001507413,0.9912747,0.0004045152,0.004272086],"study_design_scores_gemma":[0.00003354369,0.000079956,0.001423074,0.00002298643,0.00001361664,0.0005880615,0.0005503726,0.002719772,0.003668112,0.9862352,0.004636401,0.00002887109],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8589301,0.0002442983,0.03220639,0.0007405434,0.0001968157,0.00005059,0.0001089122,0.0002283535,0.107294],"genre_scores_gemma":[0.9879749,0.0001761496,0.002814338,0.00006979795,0.0001550842,0.00001829603,0.00008592584,0.0000473514,0.008658226],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.008769479,"threshold_uncertainty_score":0.02933687,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03682768751988836,"score_gpt":0.2801028965922097,"score_spread":0.2432752090723214,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}