Elliptic curve data - 81120.bw1

Formats: - HTML - YAML - JSON - 2024-04-25T07:10:31.827869

• 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': '81120u', 'Clabel': '81120u4', 'Cnumber': 4, 'abc_quality': 0.9113907960857873, 'absD': 3855268884480, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1560, 'ainvs': [0, 1, 0, -175985, -28474497], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 81120, 'degree': 258048, 'elladic_images': ['4.12.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5996771257102330092433846543', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 2, 'iso_nlabel': 48, 'isogeny_degrees': [1, 2, 4], 'jinv': [30488290624, 195], 'lmfdb_iso': '81120.bw', 'lmfdb_label': '81120.bw1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -1041, 13281], 'min_quad_twist_disc': -52, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '104.24.0.?', '120.24.0.?', '780.24.0.?', '1560.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '19.099534960810457449147331217', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.37594473358048066820059118794', 'prec': 107}, 'szpiro_ratio': 4.2329622252631935, '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, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, -4, 0], 'aplist': [0, 1, 1, 0, 0, 0, 2, -4, -4, -6, 8, 6, 2, -4, 0, 6, 0, -2, 8, 0, -6, 4, -12, -6, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 81120, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '81120.bw', 'trace_hash': 68482071992267504}
• 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': '0.040788534614254310698718270401', 'prec': 107}, 'conductor': 81120, 'gens': [[174153897, 2232660296931, 308]], 'heights': [{'__RealLiteral__': 0, 'data': '19.099534960810457449147331217', 'prec': 100}], 'lmfdb_label': '81120.bw1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.23309373590268222821707583800', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.9039639160383978604292959431204764103', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-243, 0, 1]], 'xcoord_integral_points': [-243]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [2, 0], '7': [1, 1, 0], '11': [1, 1, 0], '13': 'a', '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '81120.bw1'}
• ec_torsion_growth •

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

  
  
  • id: 3814105
    {'degree': 2, 'field': [-195, 0, 1], 'lmfdb_label': '81120.bw1', 'torsion': [2, 2]}
  • id: 3814106
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '81120.bw1', 'torsion': [4]}
  • id: 3814107
    {'degree': 2, 'field': [49, -1, 1], 'lmfdb_label': '81120.bw1', 'torsion': [4]}
  • id: 3814108
    {'degree': 4, 'field': [-32955, 0, 0, 0, 1], 'lmfdb_label': '81120.bw1', 'torsion': [2, 4]}
  • id: 3814109
    {'degree': 4, 'field': [2401, 0, -97, 0, 1], 'lmfdb_label': '81120.bw1', 'torsion': [2, 4]}
  • id: 3814113
    {'degree': 8, 'field': [-727, -1616, 1460, 108, 42, -48, 4, -4, 1], 'lmfdb_label': '81120.bw1', 'torsion': [6]}
  • id: 3814111
    {'degree': 8, 'field': [38025, 0, 0, 0, 286, 0, 0, 0, 1], 'lmfdb_label': '81120.bw1', 'torsion': [8]}
  • id: 3814112
    {'degree': 8, 'field': [50625, 0, 0, 0, 330, 0, 0, 0, 1], 'lmfdb_label': '81120.bw1', 'torsion': [8]}
  • id: 3814110
    {'degree': 8, 'field': [91298025, 0, 0, 0, 18915, 0, 0, 0, 1], 'lmfdb_label': '81120.bw1', 'torsion': [4, 4]}
  • id: 3814114
    {'degree': 16, 'field': [1, 0, -8, 0, 12508, 0, -49976, 0, -124730, 0, -49976, 0, 12508, 0, -8, 0, 1], 'lmfdb_label': '81120.bw1', 'torsion': [2, 8]}
  • id: 3814117
    {'degree': 16, 'field': [9, 0, -37488, 0, -99740, 0, -74976, 0, 30, 0, 12496, 0, -12, 0, 0, 0, 1], 'lmfdb_label': '81120.bw1', 'torsion': [2, 6]}
  • id: 3814118
    {'degree': 16, 'field': [4112784, 0, 0, 0, 1941472, 0, 0, 0, 20280, 0, 0, 0, -312, 0, 0, 0, 1], 'lmfdb_label': '81120.bw1', 'torsion': [12]}
  • id: 3814119
    {'degree': 16, 'field': [5489649, 0, -1047648, 0, 2486740, 0, -522816, 0, 32790, 0, -224, 0, -12, 0, 0, 0, 1], 'lmfdb_label': '81120.bw1', 'torsion': [12]}
  • id: 3814115
    {'degree': 16, 'field': [83501161, -20171524, 38674656, -1020852, -2062132, 3649496, -1475352, 110308, 101181, -99496, 36732, -10508, 2618, -396, 84, -8, 1], 'lmfdb_label': '81120.bw1', 'torsion': [2, 8]}
  • id: 3814116
    {'degree': 16, 'field': [120391105, -52691500, 40956780, 3471940, -3050304, 4853760, -1606508, 208084, 54009, -95224, 36424, -10572, 2622, -388, 84, -8, 1], 'lmfdb_label': '81120.bw1', 'torsion': [2, 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: 1973790
    {'conductor': 81120, 'conductor_valuation': 5, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '81120.bw1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1973791
    {'conductor': 81120, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '81120.bw1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1973792
    {'conductor': 81120, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '81120.bw1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1973793
    {'conductor': 81120, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '81120.bw1', 'prime': 13, '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: 2198687
    {'adelic_gens': [[203, 198, 1370, 587], [628, 1, 1271, 6], [1, 0, 8, 1], [1, 8, 0, 1], [712, 1557, 835, 1558], [1, 4, 4, 17], [524, 1, 1063, 6], [7, 6, 1554, 1555], [1553, 8, 1552, 9], [192, 967, 983, 996]], 'adelic_image': '1560.48.0.?', 'conductor': 81120, 'lmfdb_label': '81120.bw1', 'prime': 0}
  • id: 332676
    {'conductor': 81120, 'elladic_image': '4.12.0.8', 'lmfdb_label': '81120.bw1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 4180064
    {'lmfdb_iso': '81120.bw', 'p': 17, 'prec': 20, 'unit': 165095652235518519830222, 'val': 1}
  • id: 4180056
    {'lmfdb_iso': '81120.bw', 'p': 19, 'prec': 20, 'unit': 1489099981758105629182835, 'val': 1}
  • id: 4180068
    {'lmfdb_iso': '81120.bw', 'p': 23, 'prec': 20, 'unit': 49764417789484324600827851, 'val': 1}
  • id: 4180062
    {'lmfdb_iso': '81120.bw', 'p': 29, 'prec': 20, 'unit': 3848273353872671589368133299, 'val': 1}
  • id: 4180071
    {'lmfdb_iso': '81120.bw', 'p': 31, 'prec': 20, 'unit': 18628536080268429385073559457, 'val': 1}
  • id: 4180059
    {'lmfdb_iso': '81120.bw', 'p': 37, 'prec': 20, 'unit': 370950069750158456082518338672, 'val': 1}
  • id: 4180060
    {'lmfdb_iso': '81120.bw', 'p': 41, 'prec': 20, 'unit': 3354511284011915365225985166586, 'val': 1}
  • id: 4180061
    {'lmfdb_iso': '81120.bw', 'p': 43, 'prec': 20, 'unit': 5034158582551802661095637324802, 'val': 1}
  • id: 4180066
    {'lmfdb_iso': '81120.bw', 'p': 53, 'prec': 20, 'unit': 473344920501198953333331759518838, 'val': 1}
  • id: 4180070
    {'lmfdb_iso': '81120.bw', 'p': 61, 'prec': 20, 'unit': 1070399459931678539220975264296440, 'val': 1}
  • id: 4180058
    {'lmfdb_iso': '81120.bw', 'p': 67, 'prec': 20, 'unit': 32788108252455909816210092884434469, 'val': 1}
  • id: 4180067
    {'lmfdb_iso': '81120.bw', 'p': 73, 'prec': 20, 'unit': 186486849617483580728611770081853742, 'val': 1}
  • id: 4180063
    {'lmfdb_iso': '81120.bw', 'p': 79, 'prec': 20, 'unit': 316772977926817939892724045634988911, 'val': 1}
  • id: 4180065
    {'lmfdb_iso': '81120.bw', 'p': 83, 'prec': 20, 'unit': 2160586418474136486969719565944581021, 'val': 1}
  • id: 4180069
    {'lmfdb_iso': '81120.bw', 'p': 89, 'prec': 20, 'unit': 6900936188487357318005885166541035075, 'val': 1}
  • id: 4180057
    {'lmfdb_iso': '81120.bw', 'p': 97, 'prec': 20, 'unit': 35285348074718544667456201443386705141, 'val': 1}