Elliptic curve data - 304950.p2

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• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  abc_quality	double precision
  absD	numeric
  adelic_genus	integer
  adelic_index	integer
  adelic_level	bigint
  ainvs	numeric[]
  analytic_rank	smallint
  bad_primes	integer[]
  class_deg	smallint
  class_size	smallint
  cm	smallint
  conductor	integer
  degree	bigint
  elladic_images	text[]
  faltings_height	numeric
  faltings_index	smallint
  faltings_ratio	smallint
  iso_nlabel	smallint
  isogeny_degrees	smallint[]
  jinv	numeric[]
  lmfdb_iso	text
  lmfdb_label	text
  lmfdb_number	smallint
  manin_constant	smallint
  min_quad_twist_ainvs	numeric[]
  min_quad_twist_disc	smallint
  modell_images	text[]
  modm_images	text[]
  nonmax_primes	smallint[]
  nonmax_rad	integer
  num_bad_primes	smallint
  num_int_pts	integer
  optimality	smallint
  potential_good_reduction	boolean
  rank	smallint
  regulator	numeric
  semistable	boolean
  serre_invariants	integer[]
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '304950p', 'Clabel': '304950p1', 'Cnumber': 1, 'abc_quality': 0.9730763572648525, 'absD': 225712649671875000000000, 'adelic_genus': 3, 'adelic_index': 144, 'adelic_level': 731880, 'ainvs': [1, 1, 0, -5781000, 23473224000], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 19, 107], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 304950, 'degree': 35271936, 'elladic_images': ['9.36.0.4'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.1632508491363719318962796919', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 15, 'isogeny_degrees': [1, 3, 9], 'jinv': [-1367453954870275397761, 14445609579000000000], 'lmfdb_iso': '304950.p', 'lmfdb_label': '304950.p2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -231240, 187785792], 'min_quad_twist_disc': 5, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '9.36.0.d.1', '15.8.0-3.a.1.2', '45.72.0-9.d.1.2', '48792.8.0.?', '146376.72.0.?', '243960.16.0.?', '731880.144.3.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '12.295450617743574315282050675', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 152475], [3, 4, 2675], [5, 18, 12198], [19, 20, 16050], [107, 108, 2850]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.3585318929193217445959000253', 'prec': 100}, 'szpiro_ratio': 4.8528724560692975, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• ec_classdata •

  Column	Type
  anlist	smallint[]
  aplist	smallint[]
  class_deg	smallint
  class_size	smallint
  conductor	integer
  isogeny_matrix	smallint[]
  lmfdb_iso	text
  trace_hash	bigint

  
  {'anlist': [0, 1, -1, -1, 1, 0, 1, 1, -1, 1, 0, 3, -1, 4, -1, 0, 1, 0, -1, 1, 0], 'aplist': [-1, -1, 0, 1, 3, 4, 0, 1, 3, -6, 5, -2, 6, 10, -3, -9, -3, -10, 13, 0, 7, -10, 6, 18, 10], 'class_deg': 9, 'class_size': 3, 'conductor': 304950, 'isogeny_matrix': [[1, 9, 3], [9, 1, 3], [3, 3, 1]], 'lmfdb_iso': '304950.p', 'trace_hash': 738862016251578620}
• ec_mwbsd •

  Column	Type
  area	numeric
  conductor	integer
  gens	numeric[]
  heights	numeric[]
  lmfdb_label	text
  ngens	smallint
  rank_bounds	smallint[]
  real_period	numeric
  sha_an	numeric
  special_value	numeric
  tamagawa_product	integer
  torsion_generators	numeric[]
  xcoord_integral_points	numeric[]

  
  {'area': {'__RealLiteral__': 0, 'data': '0.0017882787780077633217142622988', 'prec': 110}, 'conductor': 304950, 'gens': [[1087135, 1132381415, 2]], 'heights': [{'__RealLiteral__': 0, 'data': '12.295450617743574315282050675', 'prec': 100}], 'lmfdb_label': '304950.p2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.084687039202331301446608745180', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.2475918508510721723895370135877384653', 'prec': 130}, 'tamagawa_product': 6, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 304950.p2 does not appear in ec_iwasawa
• ec_torsion_growth •

  Column	Type
  degree	smallint
  field	numeric[]
  lmfdb_label	text
  torsion	smallint[]

  
  
  • id: 12887784
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '304950.p2', 'torsion': [9]}
  • id: 12887785
    {'degree': 3, 'field': [-454, 93, 0, 1], 'lmfdb_label': '304950.p2', 'torsion': [2]}
  • id: 12887788
    {'degree': 6, 'field': [-22999, -1485, 1398, 173, -84, -3, 1], 'lmfdb_label': '304950.p2', 'torsion': [18]}
  • id: 12887787
    {'degree': 6, 'field': [3456, -144, -68, 102, 5, -3, 1], 'lmfdb_label': '304950.p2', 'torsion': [3]}
  • id: 12887786
    {'degree': 6, 'field': [2382264, 628200, 74526, 1104, -239, -2, 1], 'lmfdb_label': '304950.p2', 'torsion': [2, 2]}
  • id: 12887789
    {'degree': 12, 'field': [-1789103375706, 41420688206, 15494093887, -17088670676, -1811609377, -129539582, -25573299, -708776, -99073, -1154, 63, 0, 1], 'lmfdb_label': '304950.p2', 'torsion': [4]}
  • id: 12887790
    {'degree': 12, 'field': [220900, 0, 48935, 0, 16251, 0, 1183, 0, 93, 0, -7, 0, 1], 'lmfdb_label': '304950.p2', 'torsion': [3, 9]}
  • id: 12887791
    {'degree': 12, 'field': [24151666876, -9577200552, 2982739002, -368201752, -24480121, 19230326, -2040295, -259990, 45516, 1350, -355, -2, 1], 'lmfdb_label': '304950.p2', 'torsion': [2, 18]}
  • id: 12887792
    {'degree': 18, 'field': [-7599142163541292902481, 1649916295135107252321, 444411613450833400833, -26875427901356977952, -19123236672139816800, 201147672335087676, 34920775730577624, -1987849513324878, -119565313803423, -25919170425, 520402744893, -11034030198, -172498634, 19058466, 2340300, 11358, -3543, -9, 1], 'lmfdb_label': '304950.p2', 'torsion': [27]}
  • id: 12887793
    {'degree': 18, 'field': [241722918055824, 280363788803076, 247987516503298, 41506371894939, 5807247732744, 304607519403, 188400560829, 5914531137, 2057438535, 135090450, -81638903, -23804931, 527718, 163959, 14415, -1041, -93, 0, 1], 'lmfdb_label': '304950.p2', 'torsion': [6]}
• ec_localdata •

  Column	Type
  conductor	integer
  conductor_valuation	smallint
  discriminant_valuation	smallint
  j_denominator_valuation	smallint
  kodaira_symbol	smallint
  lmfdb_label	text
  prime	integer
  reduction_type	smallint
  root_number	smallint
  tamagawa_number	smallint

  
  
  • id: 7552400
    {'conductor': 304950, 'conductor_valuation': 1, 'discriminant_valuation': 9, 'j_denominator_valuation': 9, 'kodaira_symbol': 13, 'lmfdb_label': '304950.p2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 7552401
    {'conductor': 304950, 'conductor_valuation': 1, 'discriminant_valuation': 9, 'j_denominator_valuation': 9, 'kodaira_symbol': 13, 'lmfdb_label': '304950.p2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 7552402
    {'conductor': 304950, 'conductor_valuation': 2, 'discriminant_valuation': 15, 'j_denominator_valuation': 9, 'kodaira_symbol': -13, 'lmfdb_label': '304950.p2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 7552403
    {'conductor': 304950, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '304950.p2', 'prime': 19, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 7552404
    {'conductor': 304950, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '304950.p2', 'prime': 107, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 3580594
    {'adelic_gens': [[365942, 182979, 548865, 447058], [1, 18, 0, 1], [731863, 18, 731862, 19], [548911, 18, 0, 1], [1, 18, 10, 181], [10, 9, 81, 73], [577810, 9, 577791, 731872], [731870, 731871, 585513, 8], [1, 0, 18, 1], [540370, 9, 465111, 731872], [10, 9, 365931, 731872]], 'adelic_image': '731880.144.3.?', 'conductor': 304950, 'lmfdb_label': '304950.p2', 'prime': 0}
  • id: 1073263
    {'conductor': 304950, 'elladic_image': '9.36.0.4', 'lmfdb_label': '304950.p2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 304950.p does not appear in ec_padic