{"id":"W4414268283","doi":"10.1007/s40316-025-00249-8","title":"Elliptic curves of conductor $$2^m p$$, quadratic twists, and Watkins’ conjecture","year":2025,"lang":"fr","type":"article","venue":"Annales mathématiques du Québec","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Regina","funders":"","keywords":"Elliptic curve; Modular elliptic curve; Conjecture; Modular curve; Surjective function; Degree (music); Schoof's algorithm; Twists of curves; Integer (computer science); Order (exchange)","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0009705536,0.0005348872,0.00108595,0.00022368,0.000110775,0.00007403273,0.0004071424,0.0003152543,0.001561409],"category_scores_gemma":[0.001900271,0.0004972199,0.0002458763,0.0004229574,0.001187493,0.0003395008,0.000226177,0.0004599871,0.0001417408],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001217778,"about_ca_system_score_gemma":0.000990278,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.004885725,"about_ca_topic_score_gemma":0.003784697,"domain_scores_codex":[0.9971257,0.0005422027,0.001097097,0.0004622192,0.0002923816,0.0004803836],"domain_scores_gemma":[0.9956186,0.002706215,0.0005180255,0.0006924297,0.0003047992,0.0001599268],"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":[0.00009025685,0.0008418435,0.003367445,0.04553783,0.0009983293,0.00006466315,0.01605727,0.000003539099,0.0005285788,0.8151184,0.1119497,0.005442081],"study_design_scores_gemma":[0.001627837,0.0006786138,0.005896106,0.02302884,0.001971145,0.0004079429,0.00301078,0.0007877687,0.02142861,0.6031985,0.3364573,0.001506497],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8231084,0.1476312,0.001702992,0.0203558,0.0005858548,0.0006348632,0.00007939232,0.0001293102,0.005772133],"genre_scores_gemma":[0.9485874,0.01179321,0.001985593,0.002262405,0.0001647562,0.00003998042,0.00002153349,0.00006215879,0.03508294],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2245076,"threshold_uncertainty_score":0.9997479,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01592491775328212,"score_gpt":0.2708997062021642,"score_spread":0.2549747884488821,"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."}}