Elliptic curve data - 45864.bz1

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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': '45864bh', 'Clabel': '45864bh1', 'Cnumber': 1, 'abc_quality': 0.7942083638864892, 'absD': 11363667968016, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1092, 'ainvs': [0, 0, 0, -19551, -1039633], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 13], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 45864, 'degree': 120960, 'elladic_images': ['2.2.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3109745182968645062064451949', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 51, 'isogeny_degrees': [1], 'jinv': [12291328, 169], 'lmfdb_iso': '45864.bz', 'lmfdb_label': '45864.bz1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -44, -127], 'min_quad_twist_disc': 21, 'modell_images': ['2Cn'], 'modm_images': ['2.2.0.a.1', '14.6.0.a.1', '156.4.0.?', '1092.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.5982141460646618451902981157', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 441], [3, 6, 5096], [7, 26, 936], [13, 14, 3528]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.76665411892738097936715662634', 'prec': 107}, 'szpiro_ratio': 3.843685194949415, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 3, 0, 0, 0, 0, 0, 3, 0, -1, 0, 0, 0, -7, 0, -1, 0], 'aplist': [0, 0, 3, 0, 3, -1, -7, -1, -1, 2, 9, -3, -10, 4, -3, 1, 11, -1, -7, -8, -7, -11, 4, -1, 2], 'class_deg': 1, 'class_size': 1, 'conductor': 45864, 'isogeny_matrix': [[1]], 'lmfdb_iso': '45864.bz', 'trace_hash': 1512275766031563348}
• 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': '0.072661105573569246270804285414', 'prec': 107}, 'conductor': 45864, 'gens': [[-343, 637, 2]], 'heights': [{'__RealLiteral__': 0, 'data': '1.5982141460646618451902981157', 'prec': 100}], 'lmfdb_label': '45864.bz1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.40408129860323499405142499004', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.7497013710544262147574833351123735992', 'prec': 130}, 'tamagawa_product': 12, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [5, 0], '7': 'a', '11': [1, 0], '13': [1, 0], '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, 0]}, 'iwp0': 0, 'lmfdb_label': '45864.bz1'}
• ec_torsion_growth •

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

  
  
  • id: 2239383
    {'degree': 3, 'field': [1, -2, -1, 1], 'lmfdb_label': '45864.bz1', 'torsion': [2, 2]}
  • id: 2239384
    {'degree': 8, 'field': [-7203, 0, -36, 0, -78, 0, 16, 0, 1], 'lmfdb_label': '45864.bz1', 'torsion': [3]}
  • id: 2239385
    {'degree': 12, 'field': [-6791, 8380, 704, -444, -5122, 3570, -468, -132, 33, -22, 16, -6, 1], 'lmfdb_label': '45864.bz1', 'torsion': [2, 4]}
• 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: 1093078
    {'conductor': 45864, 'conductor_valuation': 3, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '45864.bz1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1093079
    {'conductor': 45864, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '45864.bz1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1093080
    {'conductor': 45864, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '45864.bz1', 'prime': 7, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 3}
  • id: 1093081
    {'conductor': 45864, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '45864.bz1', 'prime': 13, '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: 1969701
    {'adelic_gens': [[1, 0, 4, 1], [1, 2, 2, 5], [1, 4, 0, 1], [913, 732, 918, 739], [727, 0, 0, 1091], [955, 732, 120, 739], [3, 2, 1084, 1087], [1089, 4, 1088, 5], [464, 363, 621, 1091]], 'adelic_image': '1092.12.0.?', 'conductor': 45864, 'lmfdb_label': '45864.bz1', 'prime': 0}
  • id: 198716
    {'conductor': 45864, 'elladic_image': '2.2.0.1', 'lmfdb_label': '45864.bz1', 'modell_image': '2Cn', 'prime': 2}
• ec_padic •

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

  
  
  • id: 2296207
    {'lmfdb_iso': '45864.bz', 'p': 5, 'prec': 20, 'unit': 3244353833371, 'val': 2}
  • id: 2296214
    {'lmfdb_iso': '45864.bz', 'p': 11, 'prec': 20, 'unit': 49193761652839866947, 'val': 1}
  • id: 2296215
    {'lmfdb_iso': '45864.bz', 'p': 17, 'prec': 20, 'unit': 215279830384095753455658, 'val': 1}
  • id: 2296216
    {'lmfdb_iso': '45864.bz', 'p': 19, 'prec': 20, 'unit': 953054221511550604790720, 'val': 1}
  • id: 2296220
    {'lmfdb_iso': '45864.bz', 'p': 23, 'prec': 20, 'unit': 42613791893792398534352906, 'val': 1}
  • id: 2296212
    {'lmfdb_iso': '45864.bz', 'p': 29, 'prec': 20, 'unit': 5981447779257262080077753107, 'val': 1}
  • id: 2296209
    {'lmfdb_iso': '45864.bz', 'p': 31, 'prec': 20, 'unit': 3570698899698452001787305862, 'val': 1}
  • id: 2296224
    {'lmfdb_iso': '45864.bz', 'p': 37, 'prec': 20, 'unit': 91850372243427930211419102348, 'val': 1}
  • id: 2296210
    {'lmfdb_iso': '45864.bz', 'p': 41, 'prec': 20, 'unit': 1919793326292368522360648461456, 'val': 1}
  • id: 2296211
    {'lmfdb_iso': '45864.bz', 'p': 43, 'prec': 20, 'unit': 7016428961681118861128095473369, 'val': 1}
  • id: 2296222
    {'lmfdb_iso': '45864.bz', 'p': 47, 'prec': 20, 'unit': 52218624818463350914015981565865, 'val': 1}
  • id: 2296217
    {'lmfdb_iso': '45864.bz', 'p': 53, 'prec': 20, 'unit': 10314948885823495613350335257512494, 'val': -1}
  • id: 2296218
    {'lmfdb_iso': '45864.bz', 'p': 59, 'prec': 20, 'unit': 1651490784369481500407475362911317, 'val': 1}
  • id: 2296223
    {'lmfdb_iso': '45864.bz', 'p': 61, 'prec': 20, 'unit': 6703402839153703850578943485514722, 'val': 1}
  • id: 2296206
    {'lmfdb_iso': '45864.bz', 'p': 67, 'prec': 20, 'unit': 25409590528399874311065721164610802, 'val': 1}
  • id: 2296208
    {'lmfdb_iso': '45864.bz', 'p': 71, 'prec': 20, 'unit': 2029985382932145178979107543431115, 'val': 1}
  • id: 2296219
    {'lmfdb_iso': '45864.bz', 'p': 73, 'prec': 20, 'unit': 979540880098088328460172070643245, 'val': 2}
  • id: 2296213
    {'lmfdb_iso': '45864.bz', 'p': 79, 'prec': 20, 'unit': 1055971545573662550205513541987367163, 'val': 1}
  • id: 2296205
    {'lmfdb_iso': '45864.bz', 'p': 83, 'prec': 20, 'unit': 663392965838349623826298700090085136, 'val': 1}
  • id: 2296221
    {'lmfdb_iso': '45864.bz', 'p': 89, 'prec': 20, 'unit': 9363205419837405872718671149338871408, 'val': 1}
  • id: 2296204
    {'lmfdb_iso': '45864.bz', 'p': 97, 'prec': 20, 'unit': 228902889515597315926378073118062723, 'val': 1}