Elliptic curve data - 123200.fp3

Formats: - HTML - YAML - JSON - 2025-10-15T12:42:27.516574

• 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': '123200s', 'Clabel': '123200s3', 'Cnumber': 3, 'abc_quality': 1.0659265883154396, 'absD': 115539436859000000, 'adelic_genus': 3, 'adelic_index': 144, 'adelic_level': 27720, 'ainvs': [0, 1, 0, 44067, -15946987], 'analytic_rank': 0, 'bad_primes': [2, 5, 7, 11], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 123200, 'degree': 933120, 'elladic_images': ['9.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.9549051657797283969291599111', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 9, 'iso_nlabel': 145, 'isogeny_degrees': [1, 3, 9], 'jinv': [9463555063808, 115539436859], 'lmfdb_iso': '123200.fp', 'lmfdb_label': '123200.fp3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, 441, -15815], 'min_quad_twist_disc': 40, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '9.12.0.a.1', '22.2.0.a.1', '63.36.0.e.2', '66.8.0.a.1', '120.8.0.?', '198.24.1.?', '360.24.0.?', '1320.16.0.?', '1386.72.3.?', '2520.72.0.?', '3960.48.1.?', '27720.144.3.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 275], [3, 2, 11200], [5, 14, 4928], [7, 8, 17600], [11, 12, 11200]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.80361261928270555492016418376', 'prec': 103}, 'szpiro_ratio': 3.9836447190329416, '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, 0, 1, 0, 0, 0, -1, 0, -2, 0, 1, 0, -4, 0, 0, 0, 6, 0, -2, 0], 'aplist': [0, 1, 0, -1, 1, -4, 6, -2, -3, 6, 5, 11, 6, 8, 0, -6, 9, 10, 5, 9, -2, -10, 12, -3, 1], 'class_deg': 9, 'class_size': 3, 'conductor': 123200, 'isogeny_matrix': [[1, 3, 9], [3, 1, 3], [9, 3, 1]], 'lmfdb_iso': '123200.fp', 'trace_hash': 1861690920370914857}
• 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': '0.020044302472760550171235422019', 'prec': 107}, 'conductor': 123200, 'gens': [], 'heights': [], 'lmfdb_label': '123200.fp3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.16326945660556817445643144753', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.9388502189002271402157660555601833476', 'prec': 130}, 'tamagawa_product': 18, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 2], '5': 'a', '7': [0, 0], '11': [1, 0], '13': [0, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0, 0]}, 'iwp0': 0, 'lmfdb_label': '123200.fp3'}
• ec_torsion_growth •

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

  
  
  • id: 5622270
    {'degree': 2, 'field': [30, 0, 1], 'lmfdb_label': '123200.fp3', 'torsion': [3]}
  • id: 5622271
    {'degree': 3, 'field': [1, 1, -1, 1], 'lmfdb_label': '123200.fp3', 'torsion': [2]}
  • id: 5622273
    {'degree': 6, 'field': [-951, -420, 300, -14, -30, 0, 1], 'lmfdb_label': '123200.fp3', 'torsion': [3]}
  • id: 5622272
    {'degree': 6, 'field': [1, -1, 2, -3, 2, -1, 1], 'lmfdb_label': '123200.fp3', 'torsion': [2, 2]}
  • id: 5622275
    {'degree': 6, 'field': [6750, 0, 0, 0, -30, 0, 1], 'lmfdb_label': '123200.fp3', 'torsion': [6]}
  • id: 5622274
    {'degree': 6, 'field': [79255, 7770, 3141, -70, 48, 0, 1], 'lmfdb_label': '123200.fp3', 'torsion': [9]}
  • id: 5622276
    {'degree': 12, 'field': [-171875, 0, -262500, 0, -153125, 0, -17500, 0, 75, 0, 0, 0, 1], 'lmfdb_label': '123200.fp3', 'torsion': [4]}
  • id: 5622277
    {'degree': 12, 'field': [904401, -399420, 461700, 152628, 55590, 29400, 7294, 0, 600, -28, 30, 0, 1], 'lmfdb_label': '123200.fp3', 'torsion': [3, 3]}
  • id: 5622278
    {'degree': 12, 'field': [989049, 297900, -571500, -80070, 151350, 6000, -19961, 0, 1500, -10, -60, 0, 1], 'lmfdb_label': '123200.fp3', 'torsion': [9]}
  • id: 5622279
    {'degree': 12, 'field': [59459521, -22223102, 3410825, 782870, -682666, 86322, 16071, -6258, 854, 170, -55, -2, 1], 'lmfdb_label': '123200.fp3', 'torsion': [2, 6]}
  • id: 5622280
    {'degree': 18, 'field': [-5719601, -46346580, -36029700, -40585342, -10756710, -8811600, -4664235, -2437680, 13200, -297360, -17940, -8400, 985, -420, 300, -42, 30, 0, 1], 'lmfdb_label': '123200.fp3', 'torsion': [6]}
  • id: 5622281
    {'degree': 18, 'field': [148207027375, -278997783750, 287412134625, -141572275950, 18723894795, 7918361010, 381388866, -1159978050, -108685476, 78182300, 14463495, -1568700, -613965, 28350, 16875, -210, -216, 0, 1], 'lmfdb_label': '123200.fp3', 'torsion': [18]}
• 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: 3034342
    {'conductor': 123200, 'conductor_valuation': 6, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '123200.fp3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 3034343
    {'conductor': 123200, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '123200.fp3', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 3034344
    {'conductor': 123200, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '123200.fp3', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3034345
    {'conductor': 123200, 'conductor_valuation': 1, 'discriminant_valuation': 9, 'j_denominator_valuation': 9, 'kodaira_symbol': 13, 'lmfdb_label': '123200.fp3', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 9}
• ec_galrep •

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

  
  
  • id: 2467956
    {'adelic_gens': [[27719, 11070, 0, 5389], [1, 18, 10, 181], [13859, 0, 0, 27719], [1, 18, 0, 1], [20789, 0, 0, 27719], [10, 9, 81, 73], [5543, 0, 0, 27719], [27703, 18, 27702, 19], [22169, 11070, 26550, 16169], [1, 0, 18, 1], [4409, 11070, 10575, 16469], [9719, 11070, 9720, 11069]], 'adelic_image': '27720.144.3.?', 'conductor': 123200, 'lmfdb_label': '123200.fp3', 'prime': 0}
  • id: 482756
    {'conductor': 123200, 'elladic_image': '9.12.0.1', 'lmfdb_label': '123200.fp3', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 123200.fp does not appear in ec_padic