Elliptic curve data - 1056.d1

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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': '1056a', 'Clabel': '1056a1', 'Cnumber': 1, 'abc_quality': 0.9631437603910471, 'absD': 19008, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 264, 'ainvs': [0, -1, 0, -98, 408], 'analytic_rank': 1, 'bad_primes': [2, 3, 11], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 1056, 'degree': 96, 'elladic_images': ['8.6.0.4'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.17531452818576905752585812190', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 3, 'isogeny_degrees': [1, 2], 'jinv': [1643032000, 297], 'lmfdb_iso': '1056.d', 'lmfdb_label': '1056.d1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -98, 408], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.d.1', '66.6.0.a.1', '264.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.1396448857938216224381539763', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 33], [3, 4, 352], [11, 12, 96]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.52188811846574171223447418263', 'prec': 107}, 'szpiro_ratio': 3.6451888483927957, '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, -2, 0, 1, 0, -1, 0, 4, 0, 0, 0, -2, 0, 0, 0], 'aplist': [0, -1, 0, -2, -1, 4, -2, 0, -2, -2, -4, 6, -6, -12, -6, 0, 0, 0, 4, -10, 2, 2, -4, -14, -2], 'class_deg': 2, 'class_size': 2, 'conductor': 1056, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '1056.d', 'trace_hash': 1418902645715003956}
• 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': '1.4199605029061967787930937793', 'prec': 100}, 'conductor': 1056, 'gens': [[4, 8, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.1396448857938216224381539763', 'prec': 100}], 'lmfdb_label': '1056.d1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '3.7463399240971830705033830371', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.1347485674712842829797156692071595615', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [[6, 0, 1]], 'xcoord_integral_points': [4, 6, 7]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [1, 1, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [3, 0], '19': [1, 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': '1056.d1'}
• ec_torsion_growth •

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

  
  
  • id: 51813
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '1056.d1', 'torsion': [2, 2]}
  • id: 51814
    {'degree': 4, 'field': [9, -8, 0, 0, 1], 'lmfdb_label': '1056.d1', 'torsion': [4]}
  • id: 51817
    {'degree': 8, 'field': [-27, 0, 144, 0, -18, 0, 0, 0, 1], 'lmfdb_label': '1056.d1', 'torsion': [6]}
  • id: 51816
    {'degree': 8, 'field': [36, 0, 204, 0, 13, 0, 10, 0, 1], 'lmfdb_label': '1056.d1', 'torsion': [2, 4]}
  • id: 51815
    {'degree': 8, 'field': [58, -206, 203, 22, -50, 44, -10, -4, 1], 'lmfdb_label': '1056.d1', 'torsion': [2, 4]}
  • id: 51819
    {'degree': 16, 'field': [-17798, 23364, -31228, 12896, 24676, 1612, -13662, -6112, 1047, 2444, 864, -152, -134, -52, 2, 0, 1], 'lmfdb_label': '1056.d1', 'torsion': [2, 6]}
  • id: 51818
    {'degree': 16, 'field': [8937, -182016, 1179600, 373392, 515548, -21424, -13248, -76448, 10954, 5472, -1808, 48, 372, -16, -32, 0, 1], 'lmfdb_label': '1056.d1', '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: 14945
    {'conductor': 1056, 'conductor_valuation': 5, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '1056.d1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 14946
    {'conductor': 1056, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '1056.d1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 14947
    {'conductor': 1056, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '1056.d1', 'prime': 11, '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: 1671222
    {'adelic_gens': [[178, 1, 175, 0], [1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [26, 1, 119, 0], [261, 4, 260, 5], [169, 100, 32, 231], [133, 4, 2, 9]], 'adelic_image': '264.12.0.?', 'conductor': 1056, 'lmfdb_label': '1056.d1', 'prime': 0}
  • id: 5001
    {'conductor': 1056, 'elladic_image': '8.6.0.4', 'lmfdb_label': '1056.d1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 24209
    {'lmfdb_iso': '1056.d', 'p': 7, 'prec': 20, 'unit': 4398307268659957, 'val': 1}
  • id: 24212
    {'lmfdb_iso': '1056.d', 'p': 13, 'prec': 20, 'unit': 1189459215130711576310, 'val': 1}
  • id: 24214
    {'lmfdb_iso': '1056.d', 'p': 17, 'prec': 20, 'unit': 9330464128849991788708, 'val': 2}
  • id: 24217
    {'lmfdb_iso': '1056.d', 'p': 23, 'prec': 20, 'unit': 31352505545610925766857397, 'val': 1}
  • id: 24221
    {'lmfdb_iso': '1056.d', 'p': 29, 'prec': 20, 'unit': 203862601242334282526707434, 'val': 1}
  • id: 24222
    {'lmfdb_iso': '1056.d', 'p': 31, 'prec': 20, 'unit': 8582641788105920395778948407, 'val': 1}
  • id: 24208
    {'lmfdb_iso': '1056.d', 'p': 37, 'prec': 20, 'unit': 589639170786669721877657731145, 'val': 1}
  • id: 24210
    {'lmfdb_iso': '1056.d', 'p': 41, 'prec': 20, 'unit': 3895592935444367187296219074672, 'val': 1}
  • id: 24211
    {'lmfdb_iso': '1056.d', 'p': 43, 'prec': 20, 'unit': 4767867320231892581709197309620, 'val': 1}
  • id: 24213
    {'lmfdb_iso': '1056.d', 'p': 47, 'prec': 20, 'unit': 33002513099175376467609893449416, 'val': 1}
  • id: 24207
    {'lmfdb_iso': '1056.d', 'p': 67, 'prec': 20, 'unit': 33914352564830437595724050039458333, 'val': 1}
  • id: 24219
    {'lmfdb_iso': '1056.d', 'p': 71, 'prec': 20, 'unit': 139121918173068749099542426053831980, 'val': 1}
  • id: 24216
    {'lmfdb_iso': '1056.d', 'p': 73, 'prec': 20, 'unit': 211887844906857404417941339733498164, 'val': 1}
  • id: 24220
    {'lmfdb_iso': '1056.d', 'p': 79, 'prec': 20, 'unit': 976555493939184901322331749830153878, 'val': 1}
  • id: 24215
    {'lmfdb_iso': '1056.d', 'p': 83, 'prec': 20, 'unit': 666027621655379838052628288653605703, 'val': 1}
  • id: 24218
    {'lmfdb_iso': '1056.d', 'p': 89, 'prec': 20, 'unit': 4974419930164831222101007344342663300, 'val': 1}
  • id: 24206
    {'lmfdb_iso': '1056.d', 'p': 97, 'prec': 20, 'unit': 7047150304660359577507113336755761406, 'val': 1}