{"id":"W3175243575","doi":"10.1112/s0010437x21007193","title":"Large families of elliptic curves ordered by conductor","year":2021,"lang":"en","type":"article","venue":"Compositio Mathematica","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo; University of Toronto","funders":"","keywords":"Mathematics; Supersingular elliptic curve; Quotient; Schoof's algorithm; Elliptic curve; Conductor; Hessian form of an elliptic curve; Bounded function; Edwards curve; Sato–Tate conjecture; Discriminant; Modular elliptic curve; Counting points on elliptic curves; Pure mathematics; Combinatorics; Mathematical analysis; Quarter period; Geometry","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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0004095993,0.0002190467,0.0005976093,0.00005797924,0.0001024865,0.0000223815,0.0002580674,0.00008962481,0.002634548],"category_scores_gemma":[0.0005635154,0.0002028219,0.0001598387,0.0003330914,0.0001335441,0.0001086035,0.0001315302,0.0001511716,0.0001486672],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001975278,"about_ca_system_score_gemma":0.00005692453,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":8.444087e-7,"about_ca_topic_score_gemma":7.865612e-7,"domain_scores_codex":[0.99836,0.0001650418,0.0005742952,0.0002555785,0.0003347918,0.0003103361],"domain_scores_gemma":[0.9977463,0.001094708,0.0002200471,0.0006282469,0.000216474,0.00009414985],"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":[0.00002639994,0.002003602,0.00007555383,0.007225506,0.0003615273,0.00003687892,0.002492133,3.190084e-7,0.07801901,0.8347478,0.07491986,0.00009144649],"study_design_scores_gemma":[0.0008790377,0.00007513451,0.00002783834,0.001419321,0.0002472885,0.0001310275,0.00235022,0.0001157959,0.2459648,0.7454121,0.002967268,0.0004101259],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9282227,0.005094646,0.02370085,0.0007964648,0.0002131136,0.0004636382,0.0002352076,0.0002179851,0.04105539],"genre_scores_gemma":[0.9808788,0.0002781516,0.01407607,0.000422245,0.00004426463,0.00003173029,0.00009583048,0.00005355304,0.004119398],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1679458,"threshold_uncertainty_score":0.9982772,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02650699646489148,"score_gpt":0.2902589599390332,"score_spread":0.2637519634741417,"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."}}