{"id":"W4391160328","doi":"10.1016/j.indag.2024.01.004","title":"Ranks of elliptic curves in cyclic sextic extensions of <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\" id=\"d1e47\" altimg=\"si11.svg\"><mml:mi mathvariant=\"double-struck\">Q</mml:mi></mml:math>","year":2024,"lang":"en","type":"article","venue":"Indagationes Mathematicae","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Concordia University","funders":"Japan Society for the Promotion of Science; Chuo University","keywords":"Mathematics; Rank (graph theory); Elliptic curve; Conductor; Combinatorics; Cyclic group; Algebra over a field; Pure mathematics; Geometry; Abelian group","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":[0.001698333,0.0004402971,0.0006007461,0.0003596063,0.0002086921,0.0001192218,0.0006108694,0.0004782179,0.000316287],"category_scores_gemma":[0.001226945,0.0004548929,0.0004332526,0.0008447286,0.000459109,0.0004985347,0.0003400923,0.0005695109,0.0008040078],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002378123,"about_ca_system_score_gemma":0.0002676033,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004270787,"about_ca_topic_score_gemma":0.00003034506,"domain_scores_codex":[0.9961498,0.0001445324,0.001627324,0.0005801869,0.0009209147,0.000577237],"domain_scores_gemma":[0.9953485,0.002455646,0.0007773009,0.001118781,0.0001266624,0.0001730669],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.0001035769,0.0004240658,0.00001349136,0.006975543,0.0003184623,0.0001072877,0.003422104,0.0001014959,0.001993474,0.9859385,0.0002240705,0.0003778917],"study_design_scores_gemma":[0.001410737,0.0003088825,0.0002059324,0.008140894,0.0009787389,0.0006630293,0.002497972,0.652785,0.0161378,0.3158304,0.0002869118,0.0007537304],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9909194,0.0007368601,0.003899334,0.0003565263,0.0004787527,0.0002342189,0.00009773108,0.0001917348,0.00308543],"genre_scores_gemma":[0.9911973,0.0002254688,0.007513412,0.000119395,0.0001829839,0.0002093278,0.0001008532,0.0001556079,0.0002956729],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.6701081,"threshold_uncertainty_score":0.999974,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02808196848817398,"score_gpt":0.278880252162455,"score_spread":0.2507982836742811,"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."}}