Elliptic curve data - 61200.gb4

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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': '61200fr', 'Clabel': '61200fr4', 'Cnumber': 4, 'abc_quality': 1.0569023051760313, 'absD': 13483584000000000000000000, 'adelic_genus': 9, 'adelic_index': 384, 'adelic_level': 2040, 'ainvs': [0, 0, 0, 58721325, -34850960750], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 17], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 61200, 'degree': 13271040, 'elladic_images': ['4.6.0.5', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.5112223484330561924889106841', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 6, 'iso_nlabel': 157, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [479958568556831351, 289000000000000], 'lmfdb_iso': '61200.gb', 'lmfdb_label': '61200.gb4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 16311, -159988], 'min_quad_twist_disc': 60, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.a.1', '6.12.0.a.1', '12.24.0.d.1', '24.48.0.bh.2', '30.24.0-6.a.1.3', '60.48.0-12.d.1.6', '68.12.0.d.1', '120.96.0.?', '204.48.1.?', '408.192.3.?', '680.24.0.?', '1020.96.1.?', '2040.384.9.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 225], [3, 2, 6800], [5, 18, 2448], [17, 18, 3600]], 'sha': 9, 'sha_primes': [3], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.4640500673220058500736762776', 'prec': 100}, 'szpiro_ratio': 5.922620322532638, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
• 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, 0, 0, 0, 0, 2, 0, 0, 0, 6, 0, -2, 0, 0, 0, 1, 0, -8, 0], 'aplist': [0, 0, 0, 2, 6, -2, 1, -8, 6, 6, -2, -2, 6, -4, -12, 6, 0, 2, 8, -6, -2, 10, -12, -6, -2], 'class_deg': 6, 'class_size': 4, 'conductor': 61200, 'isogeny_matrix': [[1, 3, 6, 2], [3, 1, 2, 6], [6, 2, 1, 3], [2, 6, 3, 1]], 'lmfdb_iso': '61200.gb', 'trace_hash': 1291091331386752531}
• 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': '0.00089164302928555638448555939800', 'prec': 113}, 'conductor': 61200, 'gens': [], 'heights': [], 'lmfdb_label': '61200.gb4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.041134998606080086571636315628', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '9.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.9617198996377662331578147251816702581', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[590, 0, 1]], 'xcoord_integral_points': [590]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': 'a', '17': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '61200.gb4'}
• ec_torsion_growth •

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

  
  
  • id: 2934508
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '61200.gb4', 'torsion': [2, 2]}
  • id: 2934509
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '61200.gb4', 'torsion': [6]}
  • id: 2934510
    {'degree': 4, 'field': [-59, 31, 2, -1, 1], 'lmfdb_label': '61200.gb4', 'torsion': [4]}
  • id: 2934511
    {'degree': 4, 'field': [1, 0, 3, 0, 1], 'lmfdb_label': '61200.gb4', 'torsion': [2, 6]}
  • id: 2934512
    {'degree': 6, 'field': [-1500, 0, -275, 0, -5, 0, 1], 'lmfdb_label': '61200.gb4', 'torsion': [6]}
  • id: 2934513
    {'degree': 8, 'field': [289, 0, 172, 0, 23, 0, -4, 0, 1], 'lmfdb_label': '61200.gb4', 'torsion': [2, 4]}
  • id: 2934515
    {'degree': 8, 'field': [361, 0, 909, 0, 212, 0, 21, 0, 1], 'lmfdb_label': '61200.gb4', 'torsion': [12]}
  • id: 2934514
    {'degree': 8, 'field': [3481, 0, 1197, 0, -52, 0, -3, 0, 1], 'lmfdb_label': '61200.gb4', 'torsion': [2, 4]}
  • id: 2934516
    {'degree': 12, 'field': [1089, 0, 36276, 0, 12760, 0, 3062, 0, 384, 0, 32, 0, 1], 'lmfdb_label': '61200.gb4', 'torsion': [3, 6]}
  • id: 2934517
    {'degree': 12, 'field': [9216, 0, 2112, 0, 1600, 0, 176, 0, 81, 0, -1, 0, 1], 'lmfdb_label': '61200.gb4', 'torsion': [2, 6]}
  • id: 2934519
    {'degree': 16, 'field': [-911264, 3072992, -3748272, 1874976, -28904, -426216, 211012, -33080, -5562, 5286, -2063, 438, -96, -32, 2, -4, 1], 'lmfdb_label': '61200.gb4', 'torsion': [8]}
  • id: 2934520
    {'degree': 16, 'field': [16, 0, 48, 0, 156, 0, -228, 0, 101, 0, 12, 0, 51, 0, -12, 0, 1], 'lmfdb_label': '61200.gb4', 'torsion': [2, 12]}
  • id: 2934521
    {'degree': 16, 'field': [3481, 0, 6004, 0, 1034, 0, -1764, 0, -181, 0, 324, 0, 74, 0, 16, 0, 1], 'lmfdb_label': '61200.gb4', 'torsion': [2, 12]}
  • id: 2934518
    {'degree': 16, 'field': [28561, 0, -66924, 0, 90918, 0, -44256, 0, 13883, 0, -192, 0, 342, 0, -12, 0, 1], 'lmfdb_label': '61200.gb4', 'torsion': [4, 4]}
  • id: 2934522
    {'degree': 18, 'field': [915031044, 3262024440, 7031022768, 8790546192, 6384104460, 2469761220, 240821060, -168886980, -44263830, 10181540, 4599468, -211140, -251979, -5796, 8205, 442, -135, -6, 1], 'lmfdb_label': '61200.gb4', '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: 1475177
    {'conductor': 61200, 'conductor_valuation': 4, 'discriminant_valuation': 24, 'j_denominator_valuation': 12, 'kodaira_symbol': -20, 'lmfdb_label': '61200.gb4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1475178
    {'conductor': 61200, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '61200.gb4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1475179
    {'conductor': 61200, 'conductor_valuation': 2, 'discriminant_valuation': 18, 'j_denominator_valuation': 12, 'kodaira_symbol': -16, 'lmfdb_label': '61200.gb4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 1475180
    {'conductor': 61200, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '61200.gb4', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
• ec_galrep •

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

  
  
  • id: 2069747
    {'adelic_gens': [[2017, 24, 2016, 25], [13, 24, 1332, 733], [679, 2016, 1700, 2039], [1021, 24, 6, 145], [1529, 2016, 765, 2039], [1687, 18, 1554, 1099], [15, 16, 314, 335], [1, 24, 0, 1], [1, 0, 24, 1], [807, 2036, 1348, 55]], 'adelic_image': '2040.384.9.?', 'conductor': 61200, 'lmfdb_label': '61200.gb4', 'prime': 0}
  • id: 258094
    {'conductor': 61200, 'elladic_image': '4.6.0.5', 'lmfdb_label': '61200.gb4', 'modell_image': '2B', 'prime': 2}
  • id: 258095
    {'conductor': 61200, 'elladic_image': '3.4.0.1', 'lmfdb_label': '61200.gb4', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 61200.gb does not appear in ec_padic