Elliptic curve data - 27735.c2

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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': '27735i', 'Clabel': '27735i2', 'Cnumber': 2, 'abc_quality': 1.193542791263003, 'absD': 42603490011855645, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 2580, 'ainvs': [1, 0, 0, 4584, -9929619], 'analytic_rank': 1, 'bad_primes': [3, 5, 43], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 27735, 'degree': 266112, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8698254986821987478533338338', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 2, 'isogeny_degrees': [1, 2], 'jinv': [1685159, 6739605], 'lmfdb_iso': '27735.c', 'lmfdb_label': '27735.c2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 3, 126], 'min_quad_twist_disc': -43, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '20.6.0.a.1', '516.6.0.?', '2580.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.5818629196563305616056030167', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 9245], [3, 4, 9245], [5, 6, 5547], [43, 968, 15]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.010774559164582463883087422873', 'prec': 110}, 'szpiro_ratio': 4.471483256059972, '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, -1, 1, -1, -1, -1, -4, 3, 1, 1, -2, -1, 2, 4, -1, -1, 0, -1, -6, 1], 'aplist': [-1, 1, -1, -4, -2, 2, 0, -6, 0, -10, 8, 4, -10, 0, 0, 12, -6, 10, 12, -4, 8, -16, -12, 10, 6], 'class_deg': 2, 'class_size': 2, 'conductor': 27735, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '27735.c', 'trace_hash': 1074224676366448808}
• 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': '0.023762394822731117888130989674', 'prec': 107}, 'conductor': 27735, 'gens': [[2820, 148359, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.5818629196563305616056030167', 'prec': 100}], 'lmfdb_label': '27735.c2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.16733887708130359562927825063', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.5922762505188779254589616780610890516', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [[831, -831, 2]], 'xcoord_integral_points': [2820]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [6, 1], '3': [2, 0], '5': [3, 0], '7': [1, 0], '11': [3, 0], '13': [1, 0], '17': [1, 1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': 'a', '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '27735.c2'}
• ec_torsion_growth •

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

  
  
  • id: 1388131
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '27735.c2', 'torsion': [2, 2]}
  • id: 1388132
    {'degree': 4, 'field': [-20, 0, 7, 0, 1], 'lmfdb_label': '27735.c2', 'torsion': [4]}
  • id: 1388135
    {'degree': 8, 'field': [-237, 180, -228, 95, -44, -7, 7, -4, 1], 'lmfdb_label': '27735.c2', 'torsion': [6]}
  • id: 1388134
    {'degree': 8, 'field': [900, 0, 1560, 0, 229, 0, 34, 0, 1], 'lmfdb_label': '27735.c2', 'torsion': [2, 4]}
  • id: 1388133
    {'degree': 8, 'field': [2958400, 0, -86000, 0, -2395, 0, 40, 0, 1], 'lmfdb_label': '27735.c2', 'torsion': [2, 4]}
  • id: 1388137
    {'degree': 16, 'field': [204309, -1091520, 2394282, -3456810, 3973860, -3031432, 1598471, -559192, 213800, -57460, 20237, -5576, 1627, -350, 70, -8, 1], 'lmfdb_label': '27735.c2', 'torsion': [2, 6]}
  • id: 1388136
    {'degree': 16, 'field': [4100625, 0, -6014250, 0, -321975, 0, 384750, 0, -1673640, 0, -8550, 0, -159, 0, 66, 0, 1], 'lmfdb_label': '27735.c2', '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: 640653
    {'conductor': 27735, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '27735.c2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 640654
    {'conductor': 27735, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '27735.c2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 640655
    {'conductor': 27735, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '27735.c2', 'prime': 43, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 1848944
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1936, 649, 645, 1936], [1, 2, 2, 5], [1, 4, 0, 1], [1721, 4, 862, 9], [1034, 1, 2063, 0], [1981, 4, 1382, 9], [2577, 4, 2576, 5]], 'adelic_image': '2580.12.0.?', 'conductor': 27735, 'lmfdb_label': '27735.c2', 'prime': 0}
  • id: 125365
    {'conductor': 27735, 'elladic_image': '2.3.0.1', 'lmfdb_label': '27735.c2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 1329102
    {'lmfdb_iso': '27735.c', 'p': 7, 'prec': 20, 'unit': 8410570015073305, 'val': 1}
  • id: 1329104
    {'lmfdb_iso': '27735.c', 'p': 11, 'prec': 20, 'unit': 4435513835806989550, 'val': 2}
  • id: 1329106
    {'lmfdb_iso': '27735.c', 'p': 13, 'prec': 20, 'unit': 1031177528561424024752, 'val': 1}
  • id: 1329098
    {'lmfdb_iso': '27735.c', 'p': 19, 'prec': 20, 'unit': 512287947776778143399649, 'val': 1}
  • id: 1329105
    {'lmfdb_iso': '27735.c', 'p': 29, 'prec': 20, 'unit': 2042566208900505932310970145, 'val': 1}
  • id: 1329115
    {'lmfdb_iso': '27735.c', 'p': 31, 'prec': 20, 'unit': 3814806406967174229050129608, 'val': 1}
  • id: 1329101
    {'lmfdb_iso': '27735.c', 'p': 37, 'prec': 20, 'unit': 98028011560992169489056447483, 'val': 1}
  • id: 1329103
    {'lmfdb_iso': '27735.c', 'p': 41, 'prec': 20, 'unit': 695167927678941915451249035903, 'val': 1}
  • id: 1329109
    {'lmfdb_iso': '27735.c', 'p': 53, 'prec': 20, 'unit': 306597295579306539210190571534349, 'val': 1}
  • id: 1329113
    {'lmfdb_iso': '27735.c', 'p': 59, 'prec': 20, 'unit': 3613474961219994818256791448627623, 'val': 1}
  • id: 1329114
    {'lmfdb_iso': '27735.c', 'p': 61, 'prec': 20, 'unit': 306288652161222566596613539368841, 'val': 1}
  • id: 1329100
    {'lmfdb_iso': '27735.c', 'p': 67, 'prec': 20, 'unit': 4307555117121279037055499452627017, 'val': 1}
  • id: 1329112
    {'lmfdb_iso': '27735.c', 'p': 71, 'prec': 20, 'unit': 141498861826209454295490665239924302, 'val': 1}
  • id: 1329110
    {'lmfdb_iso': '27735.c', 'p': 73, 'prec': 20, 'unit': 80890025606846821166372108298740117, 'val': 1}
  • id: 1329107
    {'lmfdb_iso': '27735.c', 'p': 79, 'prec': 20, 'unit': 496781080547349026652939805700630490, 'val': 1}
  • id: 1329108
    {'lmfdb_iso': '27735.c', 'p': 83, 'prec': 20, 'unit': 1326455164233476072568029183693770295, 'val': 1}
  • id: 1329111
    {'lmfdb_iso': '27735.c', 'p': 89, 'prec': 20, 'unit': 6823995210310599104756777407243696502, 'val': 1}
  • id: 1329099
    {'lmfdb_iso': '27735.c', 'p': 97, 'prec': 20, 'unit': 55681130462194239038297415900410801963, 'val': 1}