Elliptic curve data - 20160.g4

Formats: - HTML - YAML - JSON - 2024-05-16T17:40:48.549435

• 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': '20160dx', 'Clabel': '20160dx4', 'Cnumber': 4, 'abc_quality': 1.0178067640963724, 'absD': 7715736000000000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 120, 'ainvs': [0, 0, 0, 320532, 113937392], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 20160, 'degree': 294912, 'elladic_images': ['8.12.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3084408555212286205311472546', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 6, 'isogeny_degrees': [1, 2, 4], 'jinv': [152461584507448, 322998046875], 'lmfdb_iso': '20160.g', 'lmfdb_label': '20160.g4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 8904, 524520], 'min_quad_twist_disc': 24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.4', '12.12.0-4.c.1.2', '24.24.0-24.v.1.3', '40.24.0-40.bb.1.3', '120.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '6.3210226717479693482507580037', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.89270073548724213806198448432', 'prec': 103}, 'szpiro_ratio': 5.107772892464205, '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, -1, 0, -1, 0, 0, 0, -4, 0, -2, 0, 0, 0, 2, 0, 0, 0], 'aplist': [0, 0, -1, -1, -4, -2, 2, 0, 4, 2, 8, -10, -2, -4, -4, 10, 4, 2, -4, 0, -6, 8, -4, 6, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 20160, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '20160.g', 'trace_hash': 401954531116927126}
• 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': '0.0098835678791210886208001235231', 'prec': 110}, 'conductor': 20160, 'gens': [[1237, 49023, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '6.3210226717479693482507580037', 'prec': 100}], 'lmfdb_label': '20160.g4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.16229502431787702831619915667', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.1034821129007548405607489111756980975', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-284, 0, 1]], 'xcoord_integral_points': [-284, 1237]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [3, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 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': '20160.g4'}
• ec_torsion_growth •

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

  
  
  • id: 1030142
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '20160.g4', 'torsion': [4]}
  • id: 1030143
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '20160.g4', 'torsion': [4]}
  • id: 1030141
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '20160.g4', 'torsion': [2, 2]}
  • id: 1030144
    {'degree': 4, 'field': [4, 0, 2, 0, 1], 'lmfdb_label': '20160.g4', 'torsion': [2, 4]}
  • id: 1030148
    {'degree': 8, 'field': [-243, 0, -84, 0, 30, 0, 12, 0, 1], 'lmfdb_label': '20160.g4', 'torsion': [6]}
  • id: 1030146
    {'degree': 8, 'field': [196, 0, -200, 0, 72, 0, -20, 0, 1], 'lmfdb_label': '20160.g4', 'torsion': [8]}
  • id: 1030147
    {'degree': 8, 'field': [86436, 0, 8232, 0, 1078, 0, -28, 0, 1], 'lmfdb_label': '20160.g4', 'torsion': [8]}
  • id: 1030145
    {'degree': 8, 'field': [90553, -49896, 7064, -336, 606, -168, 8, 0, 1], 'lmfdb_label': '20160.g4', 'torsion': [2, 4]}
  • id: 1030153
    {'degree': 16, 'field': [81, 0, -1340, 0, -572, 0, 180, 0, 362, 0, 164, 0, 36, 0, 4, 0, 1], 'lmfdb_label': '20160.g4', 'torsion': [12]}
  • id: 1030154
    {'degree': 16, 'field': [144, 0, -96, 0, -80, 0, -96, 0, 156, 0, -16, 0, 12, 0, 0, 0, 1], 'lmfdb_label': '20160.g4', 'torsion': [12]}
  • id: 1030150
    {'degree': 16, 'field': [2401, -7448, 12768, -2620, -10254, 10116, -1628, -1912, 1521, -764, 208, 48, -24, -20, 12, -4, 1], 'lmfdb_label': '20160.g4', 'torsion': [2, 8]}
  • id: 1030152
    {'degree': 16, 'field': [2500, 0, -2944, 0, 2656, 0, -968, 0, 572, 0, -128, 0, 52, 0, -4, 0, 1], 'lmfdb_label': '20160.g4', 'torsion': [2, 6]}
  • id: 1030149
    {'degree': 16, 'field': [466948881, 0, -266827932, 0, 76236552, 0, -14521248, 0, 1707111, 0, -98784, 0, 3528, 0, -84, 0, 1], 'lmfdb_label': '20160.g4', 'torsion': [4, 4]}
  • id: 1030151
    {'degree': 16, 'field': [1475789056, 0, -1054135040, 0, 342593888, 0, -56471520, 0, 5349428, 0, -288120, 0, 8918, 0, -140, 0, 1], 'lmfdb_label': '20160.g4', '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: 457503
    {'conductor': 20160, 'conductor_valuation': 6, 'discriminant_valuation': 15, 'j_denominator_valuation': 0, 'kodaira_symbol': -9, 'lmfdb_label': '20160.g4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 457504
    {'conductor': 20160, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '20160.g4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 457505
    {'conductor': 20160, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '20160.g4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 457506
    {'conductor': 20160, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '20160.g4', 'prime': 7, '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: 1798911
    {'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [113, 108, 110, 47], [76, 119, 17, 114], [104, 37, 71, 42], [113, 8, 112, 9], [7, 6, 114, 115], [97, 8, 28, 33], [1, 4, 4, 17]], 'adelic_image': '120.48.0.?', 'conductor': 20160, 'lmfdb_label': '20160.g4', 'prime': 0}
  • id: 94128
    {'conductor': 20160, 'elladic_image': '8.12.0.8', 'lmfdb_label': '20160.g4', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 937327
    {'lmfdb_iso': '20160.g', 'p': 11, 'prec': 20, 'unit': 6780516633810221491, 'val': 1}
  • id: 937332
    {'lmfdb_iso': '20160.g', 'p': 13, 'prec': 20, 'unit': 1443113413103238248613, 'val': 1}
  • id: 937334
    {'lmfdb_iso': '20160.g', 'p': 17, 'prec': 20, 'unit': 229259723930153241170013, 'val': 1}
  • id: 937339
    {'lmfdb_iso': '20160.g', 'p': 23, 'prec': 20, 'unit': 59997615443349163991689229, 'val': 1}
  • id: 937331
    {'lmfdb_iso': '20160.g', 'p': 29, 'prec': 20, 'unit': 32829960379003718285826008, 'val': 1}
  • id: 937343
    {'lmfdb_iso': '20160.g', 'p': 31, 'prec': 20, 'unit': 16274117169853179185395524531, 'val': 1}
  • id: 937328
    {'lmfdb_iso': '20160.g', 'p': 37, 'prec': 20, 'unit': 489172807954519873352939249757, 'val': 1}
  • id: 937329
    {'lmfdb_iso': '20160.g', 'p': 41, 'prec': 20, 'unit': 351796711663665190491452725302, 'val': 1}
  • id: 937330
    {'lmfdb_iso': '20160.g', 'p': 43, 'prec': 20, 'unit': 5518630931956437371471616568966, 'val': 1}
  • id: 937341
    {'lmfdb_iso': '20160.g', 'p': 47, 'prec': 20, 'unit': 380990168732597647284170122570, 'val': 1}
  • id: 937336
    {'lmfdb_iso': '20160.g', 'p': 53, 'prec': 20, 'unit': 181837414761801102623329586717441, 'val': 1}
  • id: 937337
    {'lmfdb_iso': '20160.g', 'p': 59, 'prec': 20, 'unit': 2065410095750099824540813611668541, 'val': 1}
  • id: 937342
    {'lmfdb_iso': '20160.g', 'p': 61, 'prec': 20, 'unit': 1179130964202024286721024010565626, 'val': 1}
  • id: 937335
    {'lmfdb_iso': '20160.g', 'p': 67, 'prec': 20, 'unit': 7329240798956816497840065609847412, 'val': 1}
  • id: 937338
    {'lmfdb_iso': '20160.g', 'p': 73, 'prec': 20, 'unit': 149097438316155596765613391137542644, 'val': 1}
  • id: 937333
    {'lmfdb_iso': '20160.g', 'p': 79, 'prec': 20, 'unit': 914906810066664127924543024833451828, 'val': 1}
  • id: 937326
    {'lmfdb_iso': '20160.g', 'p': 83, 'prec': 20, 'unit': 722767105917963511486510605304029133, 'val': 1}
  • id: 937340
    {'lmfdb_iso': '20160.g', 'p': 89, 'prec': 20, 'unit': 1947231964307191744007320008646575632, 'val': 1}
  • id: 937325
    {'lmfdb_iso': '20160.g', 'p': 97, 'prec': 20, 'unit': 5922660193401432538661757287922497679, 'val': 1}