Elliptic curve data - 31200.ba3

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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': '31200c', 'Clabel': '31200c1', 'Cnumber': 1, 'abc_quality': 1.0447549090132258, 'absD': 2927948765625000000, 'adelic_genus': 3, 'adelic_index': 192, 'adelic_level': 1040, 'ainvs': [0, -1, 0, -406758, 56638512], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 31200, 'degree': 589824, 'elladic_images': ['8.24.0.30'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2419368884896600097282092022', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 26, 'isogeny_degrees': [1, 2], 'jinv': [7442744143086784, 2927948765625], 'lmfdb_iso': '31200.ba', 'lmfdb_label': '31200.ba3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -16270, -446600], 'min_quad_twist_disc': -20, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.a.1', '8.24.0-4.a.1.4', '20.24.0-4.a.1.1', '40.48.0-40.a.1.2', '80.96.0.?', '104.48.0.?', '520.96.1.?', '1040.192.3.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '11.583356174235201471568439773', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 25], [3, 4, 10400], [5, 18, 1248], [13, 14, 2400]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.0906443419926371677192134749', 'prec': 100}, 'szpiro_ratio': 4.8667068815905665, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, 0, 0, 4, 0, 1, 0, 0, 0, -1, 0, 0, 0, -2, 0, -8, 0], 'aplist': [0, -1, 0, 4, 0, -1, -2, -8, 4, 6, 8, -6, -6, -4, 4, -6, -8, -10, 4, -8, 14, 0, 12, -6, 6], 'class_deg': 4, 'class_size': 4, 'conductor': 31200, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '31200.ba', 'trace_hash': 69585011459255886}
• 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': '0.011289594965433257320290707835', 'prec': 107}, 'conductor': 31200, 'gens': [[10919, 12157894, 13]], 'heights': [{'__RealLiteral__': 0, 'data': '11.583356174235201471568439773', 'prec': 100}], 'lmfdb_label': '31200.ba3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.23096147344752609208531207752', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.3506180189377218044259309070605031252', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[147, 0, 1], [552, 0, 1]], 'xcoord_integral_points': [-698, 147, 552]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '5': 'a', '7': [1, 0], '11': [1, 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': '31200.ba3'}
• ec_torsion_growth •

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

  
  
  • id: 1555429
    {'degree': 4, 'field': [1, 0, 3, 0, 1], 'lmfdb_label': '31200.ba3', 'torsion': [2, 4]}
  • id: 1555427
    {'degree': 4, 'field': [4, 0, -6, 0, 1], 'lmfdb_label': '31200.ba3', 'torsion': [2, 4]}
  • id: 1555428
    {'degree': 4, 'field': [9, 0, -4, 0, 1], 'lmfdb_label': '31200.ba3', 'torsion': [2, 4]}
  • id: 1555431
    {'degree': 8, 'field': [-11275, -27980, -27514, 4964, 520, -136, -2, -4, 1], 'lmfdb_label': '31200.ba3', 'torsion': [2, 6]}
  • id: 1555430
    {'degree': 8, 'field': [1, 0, 0, 0, 7, 0, 0, 0, 1], 'lmfdb_label': '31200.ba3', 'torsion': [4, 4]}
  • id: 1555433
    {'degree': 16, 'field': [81, 0, -720, 0, 2284, 0, -3360, 0, 2066, 0, -240, 0, -76, 0, 0, 0, 1], 'lmfdb_label': '31200.ba3', 'torsion': [2, 8]}
  • id: 1555434
    {'degree': 16, 'field': [1934521, -3899536, 5260892, -5586848, 4700880, -3233264, 1943884, -937768, 417610, -144752, 48556, -11968, 3024, -496, 92, -8, 1], 'lmfdb_label': '31200.ba3', 'torsion': [2, 8]}
  • id: 1555432
    {'degree': 16, 'field': [7983717921, 1533890376, -3202448852, -362152352, 528693148, 1651568, -44291604, 7249824, 2323428, -525248, 6684, 21576, -1812, 104, 52, -8, 1], 'lmfdb_label': '31200.ba3', '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: 727718
    {'conductor': 31200, 'conductor_valuation': 5, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '31200.ba3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 727719
    {'conductor': 31200, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '31200.ba3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 727720
    {'conductor': 31200, 'conductor_valuation': 2, 'discriminant_valuation': 12, 'j_denominator_valuation': 6, 'kodaira_symbol': -10, 'lmfdb_label': '31200.ba3', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 727721
    {'conductor': 31200, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '31200.ba3', '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: 1872412
    {'adelic_gens': [[783, 2, 518, 1039], [779, 1032, 0, 909], [1, 0, 8, 1], [1, 8, 0, 1], [561, 8, 164, 33], [1, 4, 4, 17], [829, 1038, 834, 1], [1033, 8, 1032, 9]], 'adelic_image': '1040.192.3.?', 'conductor': 31200, 'lmfdb_label': '31200.ba3', 'prime': 0}
  • id: 139713
    {'conductor': 31200, 'elladic_image': '8.24.0.30', 'lmfdb_label': '31200.ba3', 'modell_image': '2Cs', 'prime': 2}
• ec_padic •

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

  
  
  • id: 1514102
    {'lmfdb_iso': '31200.ba', 'p': 7, 'prec': 20, 'unit': 9875475689593153, 'val': 1}
  • id: 1514107
    {'lmfdb_iso': '31200.ba', 'p': 17, 'prec': 20, 'unit': 157438487291487001580590, 'val': 1}
  • id: 1514098
    {'lmfdb_iso': '31200.ba', 'p': 19, 'prec': 20, 'unit': 672226900019515100084229, 'val': 1}
  • id: 1514111
    {'lmfdb_iso': '31200.ba', 'p': 23, 'prec': 20, 'unit': 52064413203501178683742823, 'val': 1}
  • id: 1514105
    {'lmfdb_iso': '31200.ba', 'p': 29, 'prec': 20, 'unit': 1669797413489367807218861575, 'val': 1}
  • id: 1514116
    {'lmfdb_iso': '31200.ba', 'p': 31, 'prec': 20, 'unit': 21228338394966995488398253384, 'val': 1}
  • id: 1514101
    {'lmfdb_iso': '31200.ba', 'p': 37, 'prec': 20, 'unit': 246694169526478801066985622348, 'val': 1}
  • id: 1514103
    {'lmfdb_iso': '31200.ba', 'p': 41, 'prec': 20, 'unit': 299017484415593980097943971592, 'val': 1}
  • id: 1514104
    {'lmfdb_iso': '31200.ba', 'p': 43, 'prec': 20, 'unit': 6865658812324134792498877525371, 'val': 1}
  • id: 1514106
    {'lmfdb_iso': '31200.ba', 'p': 47, 'prec': 20, 'unit': 2343164551908244213599198036252, 'val': 1}
  • id: 1514109
    {'lmfdb_iso': '31200.ba', 'p': 53, 'prec': 20, 'unit': 40107818826132184682005918933316, 'val': 1}
  • id: 1514114
    {'lmfdb_iso': '31200.ba', 'p': 59, 'prec': 20, 'unit': 682903485282569106912433040670874, 'val': 1}
  • id: 1514115
    {'lmfdb_iso': '31200.ba', 'p': 61, 'prec': 20, 'unit': 1666559760775136536894642906199634, 'val': 1}
  • id: 1514100
    {'lmfdb_iso': '31200.ba', 'p': 67, 'prec': 20, 'unit': 47720107088210847455746795246808677, 'val': 1}
  • id: 1514113
    {'lmfdb_iso': '31200.ba', 'p': 71, 'prec': 20, 'unit': 90919758114012960399564885102272963, 'val': 1}
  • id: 1514110
    {'lmfdb_iso': '31200.ba', 'p': 73, 'prec': 20, 'unit': 238256252894908814863405282741315634, 'val': 1}
  • id: 1514108
    {'lmfdb_iso': '31200.ba', 'p': 83, 'prec': 20, 'unit': 97395555992081315464159580348716719, 'val': 1}
  • id: 1514112
    {'lmfdb_iso': '31200.ba', 'p': 89, 'prec': 20, 'unit': 7643003112036856813933221860731717772, 'val': 1}
  • id: 1514099
    {'lmfdb_iso': '31200.ba', 'p': 97, 'prec': 20, 'unit': 13850129057844042089774539328439266096, 'val': 1}