Elliptic curve data - 107712.ec2

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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': '107712ez', 'Clabel': '107712ez1', 'Cnumber': 1, 'abc_quality': 1.025647102928615, 'absD': 225821121470005248, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 4488, 'ainvs': [0, 0, 0, -152364, -1131568], 'analytic_rank': 1, 'bad_primes': [2, 3, 11, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 107712, 'degree': 737280, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0193989841595872654113820404', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 106, 'isogeny_degrees': [1, 2], 'jinv': [2046931732873, 1181672448], 'lmfdb_iso': '107712.ec', 'lmfdb_label': '107712.ec2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -264, -192], 'min_quad_twist_disc': 24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '66.6.0.a.1', '136.6.0.?', '4488.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.4169086895813529039781817273', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 99], [3, 8, 1088], [11, 12, 9792], [17, 18, 6336]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.43037206898561445558791123975', 'prec': 103}, 'szpiro_ratio': 4.092068786716447, '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, 2, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, -2, 0], 'aplist': [0, 0, 2, 2, 1, 0, 1, -2, -6, 2, 0, -2, -2, -10, 4, 4, -6, 10, -12, 6, -4, 2, 12, 2, -6], 'class_deg': 2, 'class_size': 2, 'conductor': 107712, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '107712.ec', 'trace_hash': 1374574105422551790}
• 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': '0.017618637853184208327237169041', 'prec': 107}, 'conductor': 107712, 'gens': [[496, 6732, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.4169086895813529039781817273', 'prec': 100}], 'lmfdb_label': '107712.ec2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.26374382164464025184031058329', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.9688219050804467135463889056597047576', 'prec': 130}, 'tamagawa_product': 96, 'torsion_generators': [[394, 0, 1]], 'xcoord_integral_points': [394, 496, 3466]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [5, 0], '7': [1, 0], '11': [2, 0], '13': [1, 1, 0], '17': [2, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '107712.ec2'}
• ec_torsion_growth •

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

  
  
  • id: 4973312
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '107712.ec2', 'torsion': [2, 2]}
  • id: 4973313
    {'degree': 4, 'field': [-30, -68, -30, 0, 1], 'lmfdb_label': '107712.ec2', 'torsion': [4]}
  • id: 4973316
    {'degree': 8, 'field': [-972, 0, -270, 0, 108, 0, 0, 0, 1], 'lmfdb_label': '107712.ec2', 'torsion': [6]}
  • id: 4973314
    {'degree': 8, 'field': [2896, -4264, 2645, -1594, 667, 124, 23, -2, 1], 'lmfdb_label': '107712.ec2', 'torsion': [2, 4]}
  • id: 4973315
    {'degree': 8, 'field': [4114, 8228, -9614, -1760, 1739, 136, -86, -4, 1], 'lmfdb_label': '107712.ec2', 'torsion': [2, 4]}
  • id: 4973318
    {'degree': 16, 'field': [36864, 0, 53760, 0, -88064, 0, -13440, 0, -17484, 0, -2590, 0, 492, 0, 0, 0, 1], 'lmfdb_label': '107712.ec2', 'torsion': [2, 6]}
  • id: 4973317
    {'degree': 16, 'field': [21974466564, 19564566768, -16251198120, -6410657232, 2673922480, 613394984, -164963372, -31909024, 5589125, 1517192, -230240, -37784, 4538, 784, -92, -8, 1], 'lmfdb_label': '107712.ec2', 'torsion': [8]}
• 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: 2648641
    {'conductor': 107712, 'conductor_valuation': 6, 'discriminant_valuation': 28, 'j_denominator_valuation': 10, 'kodaira_symbol': -22, 'lmfdb_label': '107712.ec2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 2648642
    {'conductor': 107712, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '107712.ec2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 2648643
    {'conductor': 107712, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '107712.ec2', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 2648644
    {'conductor': 107712, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '107712.ec2', '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: 2370594
    {'adelic_gens': [[1498, 1, 1495, 0], [1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [1057, 4, 2114, 9], [2245, 4, 2, 9], [3929, 562, 560, 3927], [818, 1, 4079, 0], [4485, 4, 4484, 5]], 'adelic_image': '4488.12.0.?', 'conductor': 107712, 'lmfdb_label': '107712.ec2', 'prime': 0}
  • id: 429178
    {'conductor': 107712, 'elladic_image': '2.3.0.1', 'lmfdb_label': '107712.ec2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 5618508
    {'lmfdb_iso': '107712.ec', 'p': 5, 'prec': 20, 'unit': 2589193248604, 'val': 2}
  • id: 5618494
    {'lmfdb_iso': '107712.ec', 'p': 7, 'prec': 20, 'unit': 8253511304919199, 'val': 1}
  • id: 5618490
    {'lmfdb_iso': '107712.ec', 'p': 19, 'prec': 20, 'unit': 300448872109135610770536, 'val': 1}
  • id: 5618503
    {'lmfdb_iso': '107712.ec', 'p': 23, 'prec': 20, 'unit': 62878650191142671283777388, 'val': 1}
  • id: 5618497
    {'lmfdb_iso': '107712.ec', 'p': 29, 'prec': 20, 'unit': 846684175156014118666367130, 'val': 1}
  • id: 5618493
    {'lmfdb_iso': '107712.ec', 'p': 37, 'prec': 20, 'unit': 530540465429057669728502093889, 'val': 1}
  • id: 5618495
    {'lmfdb_iso': '107712.ec', 'p': 41, 'prec': 20, 'unit': 357249816850107214045928883388, 'val': 1}
  • id: 5618496
    {'lmfdb_iso': '107712.ec', 'p': 43, 'prec': 20, 'unit': 4764780745229642312293197805537, 'val': 1}
  • id: 5618506
    {'lmfdb_iso': '107712.ec', 'p': 47, 'prec': 20, 'unit': 46069264314383315082163474959240, 'val': 1}
  • id: 5618501
    {'lmfdb_iso': '107712.ec', 'p': 53, 'prec': 20, 'unit': 154265468476533105138044568490647, 'val': 1}
  • id: 5618499
    {'lmfdb_iso': '107712.ec', 'p': 59, 'prec': 20, 'unit': 10336704097535874290912640109869, 'val': 2}
  • id: 5618507
    {'lmfdb_iso': '107712.ec', 'p': 61, 'prec': 20, 'unit': 204002551440543998100411882280289, 'val': 1}
  • id: 5618492
    {'lmfdb_iso': '107712.ec', 'p': 67, 'prec': 20, 'unit': 7933707042246674101159020214777382, 'val': 1}
  • id: 5618505
    {'lmfdb_iso': '107712.ec', 'p': 71, 'prec': 20, 'unit': 140195684036389080015651428625013975, 'val': 1}
  • id: 5618502
    {'lmfdb_iso': '107712.ec', 'p': 73, 'prec': 20, 'unit': 176805891235646485394694639392803758, 'val': 1}
  • id: 5618498
    {'lmfdb_iso': '107712.ec', 'p': 79, 'prec': 20, 'unit': 1016842207685873683825644304165129352, 'val': 1}
  • id: 5618500
    {'lmfdb_iso': '107712.ec', 'p': 83, 'prec': 20, 'unit': 68591516882301749898398399592009716, 'val': 1}
  • id: 5618504
    {'lmfdb_iso': '107712.ec', 'p': 89, 'prec': 20, 'unit': 7269366309196411103741950635719334778, 'val': 1}
  • id: 5618491
    {'lmfdb_iso': '107712.ec', 'p': 97, 'prec': 20, 'unit': 11368654204052472651665671364584407379, 'val': 1}