Elliptic curve data - 20160.dp1

Formats: - HTML - YAML - JSON - 2024-05-21T14:07:35.645769

• 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': '20160eo', 'Clabel': '20160eo3', 'Cnumber': 3, 'abc_quality': 0.9608739095359471, 'absD': 2508226560000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 840, 'ainvs': [0, 0, 0, -64812, -6350384], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 20160, 'degree': 65536, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4230647557467495320484214438', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 93, 'isogeny_degrees': [1, 2, 4], 'jinv': [157551496201, 13125], 'lmfdb_iso': '20160.dp', 'lmfdb_label': '20160.dp1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -113, -469], 'min_quad_twist_disc': 24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0-4.c.1.2', '40.12.0.ba.1', '42.6.0.a.1', '56.12.0-4.c.1.1', '84.12.0.?', '120.24.0.?', '168.24.0.?', '280.24.0.?', '840.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.16596215942722327777504935685', 'prec': 107}, 'szpiro_ratio': 4.525202194413618, '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, 0, 0, 6, 0, 0, 0, -2, 0, -8, 0], 'aplist': [0, 0, 1, -1, 0, 6, -2, -8, 8, -2, -4, 2, 6, 4, 8, 10, -4, 2, 4, -12, -2, -8, 4, 6, -18], '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.dp', 'trace_hash': 658218802600221608}
• 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': '0.058068640487153186034690784521', 'prec': 107}, 'conductor': 20160, 'gens': [], 'heights': [], 'lmfdb_label': '20160.dp1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.29921810608476893478756197857', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.3937448486781514783004958285546560624', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-148, 0, 1]], 'xcoord_integral_points': [-148]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '20160.dp1'}
• ec_torsion_growth •

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

  
  
  • id: 1030879
    {'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '20160.dp1', 'torsion': [2, 2]}
  • id: 1030880
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '20160.dp1', 'torsion': [4]}
  • id: 1030881
    {'degree': 2, 'field': [14, 0, 1], 'lmfdb_label': '20160.dp1', 'torsion': [4]}
  • id: 1030882
    {'degree': 4, 'field': [4, 0, 10, 0, 1], 'lmfdb_label': '20160.dp1', 'torsion': [2, 4]}
  • id: 1030886
    {'degree': 8, 'field': [-432, 0, 0, 0, 72, 0, 26, 0, 1], 'lmfdb_label': '20160.dp1', 'torsion': [6]}
  • id: 1030883
    {'degree': 8, 'field': [25, 0, 46, 0, 54, 0, -26, 0, 1], 'lmfdb_label': '20160.dp1', 'torsion': [2, 4]}
  • id: 1030884
    {'degree': 8, 'field': [70, -240, 384, -348, 164, -24, -6, 0, 1], 'lmfdb_label': '20160.dp1', 'torsion': [8]}
  • id: 1030885
    {'degree': 8, 'field': [4096, 0, -640, 0, 48, 0, -10, 0, 1], 'lmfdb_label': '20160.dp1', 'torsion': [8]}
  • id: 1030887
    {'degree': 16, 'field': [25, -1160, 26912, -53392, 54656, -39904, 29568, -21624, 12694, -6072, 2688, -976, 224, -64, 32, -8, 1], 'lmfdb_label': '20160.dp1', 'torsion': [4, 4]}
  • id: 1030890
    {'degree': 16, 'field': [2304, 0, 24960, 0, 37312, 0, 12480, 0, -24720, 0, -11440, 0, -552, 0, 0, 0, 1], 'lmfdb_label': '20160.dp1', 'torsion': [2, 6]}
  • id: 1030888
    {'degree': 16, 'field': [30625, 98000, 39830, -86100, -514, 23180, -1742, -9840, 6499, -1080, 174, 160, 64, -20, -12, 0, 1], 'lmfdb_label': '20160.dp1', 'torsion': [2, 8]}
  • id: 1030891
    {'degree': 16, 'field': [998001, 0, 2937822, 0, 1641301, 0, 496644, 0, 96066, 0, 12266, 0, 996, 0, 48, 0, 1], 'lmfdb_label': '20160.dp1', 'torsion': [12]}
  • id: 1030889
    {'degree': 16, 'field': [10758400, 0, -5527040, 0, 2014336, 0, -366848, 0, 67504, 0, -6464, 0, 424, 0, -8, 0, 1], 'lmfdb_label': '20160.dp1', 'torsion': [2, 8]}
  • id: 1030892
    {'degree': 16, 'field': [48149721, 0, 11757312, 0, 1876932, 0, 794016, 0, 157410, 0, 12816, 0, 757, 0, 52, 0, 1], 'lmfdb_label': '20160.dp1', 'torsion': [12]}
• 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: 457735
    {'conductor': 20160, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '20160.dp1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 457736
    {'conductor': 20160, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '20160.dp1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 457737
    {'conductor': 20160, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '20160.dp1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 457738
    {'conductor': 20160, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '20160.dp1', 'prime': 7, '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: 1798748
    {'adelic_gens': [[101, 102, 302, 725], [833, 8, 832, 9], [517, 524, 478, 99], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [248, 3, 365, 2], [337, 8, 508, 33], [7, 6, 834, 835], [272, 837, 275, 838]], 'adelic_image': '840.48.0.?', 'conductor': 20160, 'lmfdb_label': '20160.dp1', 'prime': 0}
  • id: 93955
    {'conductor': 20160, 'elladic_image': '4.6.0.1', 'lmfdb_label': '20160.dp1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 20160.dp does not appear in ec_padic