Elliptic curve data - 7728.q2

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '7728e', 'Clabel': '7728e1', 'Cnumber': 1, 'abc_quality': 0.9294350221238309, 'absD': 613308423168, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 184, 'ainvs': [0, 1, 0, -1568, 44100], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 23], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 7728, 'degree': 10752, 'elladic_images': ['8.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.95392429261160433668058602165', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 16, 'isogeny_degrees': [1, 2], 'jinv': [-416618810500, 598934007], 'lmfdb_iso': '7728.q', 'lmfdb_label': '7728.q2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -1568, -44100], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.c.1', '46.6.0.a.1', '184.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 13, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.25932947822628291143160820671', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.37630164214498324549955925377', 'prec': 103}, 'szpiro_ratio': 3.902232015270709, '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, 1, 0, 0, 0, 1, 0, 1, 0, 2, 0, -6, 0, 0, 0, -6, 0, 6, 0], 'aplist': [0, 1, 0, 1, 2, -6, -6, 6, -1, 2, -8, 8, 6, -10, 8, -4, -8, 0, -14, 0, -2, 8, -14, -10, -2], 'class_deg': 2, 'class_size': 2, 'conductor': 7728, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '7728.q', 'trace_hash': 917054259110368016}
• 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': '0.14839931187460161955107302668', 'prec': 103}, 'conductor': 7728, 'gens': [[-14, 252, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.25932947822628291143160820671', 'prec': 103}], 'lmfdb_label': '7728.q2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.82306033836323639804958131215', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.1226513943156630194923802555487943955', 'prec': 130}, 'tamagawa_product': 96, 'torsion_generators': [[-50, 0, 1]], 'xcoord_integral_points': [-50, -14, 0, 22, 31, 112, 1102]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [1, 1, 0], '7': [2, 0], '11': [1, 0], '13': [1, 0], '17': [3, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '7728.q2'}
• ec_torsion_growth •

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

  
  
  • id: 404145
    {'degree': 2, 'field': [6, -1, 1], 'lmfdb_label': '7728.q2', 'torsion': [2, 2]}
  • id: 404146
    {'degree': 4, 'field': [-7, -8, -4, 0, 1], 'lmfdb_label': '7728.q2', 'torsion': [4]}
  • id: 404149
    {'degree': 8, 'field': [-972, 0, 596, 0, -108, 0, 0, 0, 1], 'lmfdb_label': '7728.q2', 'torsion': [6]}
  • id: 404148
    {'degree': 8, 'field': [62, -76, 134, -96, 39, -4, 2, 0, 1], 'lmfdb_label': '7728.q2', 'torsion': [2, 4]}
  • id: 404147
    {'degree': 8, 'field': [178929, -35109, 26910, -5399, 2010, -209, 46, -3, 1], 'lmfdb_label': '7728.q2', 'torsion': [2, 4]}
  • id: 404150
    {'degree': 16, 'field': [2693161, 10655176, 14658088, 6489472, -3705048, -4958984, -544064, 1024128, 210682, -57816, -19000, -192, 872, -40, -64, 0, 1], 'lmfdb_label': '7728.q2', 'torsion': [8]}
  • id: 404151
    {'degree': 16, 'field': [57793716, -43663824, 50600580, -15403776, 11664684, -5154784, 2431112, -707824, 303833, -94096, 29036, -6488, 1870, -392, 76, -8, 1], 'lmfdb_label': '7728.q2', 'torsion': [2, 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: 159450
    {'conductor': 7728, 'conductor_valuation': 4, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -6, 'lmfdb_label': '7728.q2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 159451
    {'conductor': 7728, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '7728.q2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
  • id: 159452
    {'conductor': 7728, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '7728.q2', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 159453
    {'conductor': 7728, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '7728.q2', 'prime': 23, '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: 1715012
    {'adelic_gens': [[1, 2, 2, 5], [25, 162, 160, 23], [10, 1, 87, 0], [3, 4, 8, 11], [93, 4, 2, 9], [181, 4, 180, 5], [1, 4, 0, 1], [1, 0, 4, 1]], 'adelic_image': '184.12.0.?', 'conductor': 7728, 'lmfdb_label': '7728.q2', 'prime': 0}
  • id: 37890
    {'conductor': 7728, 'elladic_image': '8.6.0.1', 'lmfdb_label': '7728.q2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 315213
    {'lmfdb_iso': '7728.q', 'p': 11, 'prec': 20, 'unit': 50653520731177119973, 'val': 1}
  • id: 315211
    {'lmfdb_iso': '7728.q', 'p': 13, 'prec': 20, 'unit': 519396250542957935120, 'val': 1}
  • id: 315214
    {'lmfdb_iso': '7728.q', 'p': 17, 'prec': 20, 'unit': 10366428860181616272831, 'val': 2}
  • id: 315215
    {'lmfdb_iso': '7728.q', 'p': 19, 'prec': 20, 'unit': 993981568082821355600018, 'val': 1}
  • id: 315221
    {'lmfdb_iso': '7728.q', 'p': 29, 'prec': 20, 'unit': 1095974489546482321707236193, 'val': 1}
  • id: 315222
    {'lmfdb_iso': '7728.q', 'p': 31, 'prec': 20, 'unit': 11333487141921467161084411057, 'val': 1}
  • id: 315208
    {'lmfdb_iso': '7728.q', 'p': 37, 'prec': 20, 'unit': 1734240657195234197990147497, 'val': 1}
  • id: 315209
    {'lmfdb_iso': '7728.q', 'p': 41, 'prec': 20, 'unit': 843689804206662826205024164220, 'val': 1}
  • id: 315210
    {'lmfdb_iso': '7728.q', 'p': 43, 'prec': 20, 'unit': 3143818516754149631113142780628, 'val': 1}
  • id: 315220
    {'lmfdb_iso': '7728.q', 'p': 47, 'prec': 20, 'unit': 25784911900397499853645856082862, 'val': 1}
  • id: 315216
    {'lmfdb_iso': '7728.q', 'p': 53, 'prec': 20, 'unit': 269157940341753568723969202208993, 'val': 1}
  • id: 315217
    {'lmfdb_iso': '7728.q', 'p': 59, 'prec': 20, 'unit': 2907508582205719657013296898210980, 'val': 1}
  • id: 315207
    {'lmfdb_iso': '7728.q', 'p': 67, 'prec': 20, 'unit': 25788771365309434303816351535779093, 'val': 1}
  • id: 315218
    {'lmfdb_iso': '7728.q', 'p': 73, 'prec': 20, 'unit': 107406828650274713644918283388183976, 'val': 1}
  • id: 315212
    {'lmfdb_iso': '7728.q', 'p': 79, 'prec': 20, 'unit': 324558705400423474699402249011615146, 'val': 1}
  • id: 315206
    {'lmfdb_iso': '7728.q', 'p': 83, 'prec': 20, 'unit': 2450500824838813257920253502693905369, 'val': 1}
  • id: 315219
    {'lmfdb_iso': '7728.q', 'p': 89, 'prec': 20, 'unit': 3661434632793051131783327668105975450, 'val': 1}
  • id: 315205
    {'lmfdb_iso': '7728.q', 'p': 97, 'prec': 20, 'unit': 17858571432456544787364586375810209645, 'val': 1}