Elliptic curve data - 80325.bt3

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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': '80325a', 'Clabel': '80325a1', 'Cnumber': 1, 'abc_quality': 1.1009571968779495, 'absD': 83639786283703125, 'adelic_genus': 3, 'adelic_index': 144, 'adelic_level': 10710, 'ainvs': [0, 0, 1, -492750, -132404594], 'analytic_rank': 1, 'bad_primes': [3, 5, 7, 17], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 80325, 'degree': 715392, 'elladic_images': ['9.36.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0843497676966429593180774663', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 45, 'isogeny_degrees': [1, 3], 'jinv': [31363160518656000, 198257271191], 'lmfdb_iso': '80325.bt', 'lmfdb_label': '80325.bt3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 1, -177390, 28599392], 'min_quad_twist_disc': -15, 'modell_images': ['3Cs'], 'modm_images': ['3.12.0.a.1', '9.36.0.c.1', '15.24.0-3.a.1.1', '45.72.0-9.c.1.1', '714.24.1.?', '2142.72.3.?', '3570.48.1.?', '10710.144.3.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '16.100633901878249565972009872', 'prec': 100}, 'semistable': False, 'serre_invariants': [[3, 2, 25], [5, 14, 3213], [7, 8, 11475], [17, 18, 4725]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.0049777393125653491688864905', 'prec': 100}, 'szpiro_ratio': 4.5101481797657765, '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, -2, 0, 0, -1, 0, 0, 0, 0, 0, 4, 0, 0, 4, -1, 0, 2, 0], 'aplist': [0, 0, 0, -1, 0, 4, -1, 2, 9, 9, 5, -2, 0, 1, -9, 0, -9, -1, -5, 9, 7, -10, 0, 9, 1], 'class_deg': 9, 'class_size': 3, 'conductor': 80325, 'isogeny_matrix': [[1, 9, 3], [9, 1, 3], [3, 3, 1]], 'lmfdb_iso': '80325.bt', 'trace_hash': 1185756068171253326}
• 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': '0.015472368313454875109053992544', 'prec': 107}, 'conductor': 80325, 'gens': [[-77512090, 16209323787, 451]], 'heights': [{'__RealLiteral__': 0, 'data': '16.100633901878249565972009872', 'prec': 100}], 'lmfdb_label': '80325.bt3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.18026369919444223565911668676', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.8047196530560391316348660910378314536', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 13, 0], '3': 'a', '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, 1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '80325.bt3'}
• ec_torsion_growth •

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

  
  
  • id: 3780604
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '80325.bt3', 'torsion': [3]}
  • id: 3780605
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '80325.bt3', 'torsion': [3]}
  • id: 3780606
    {'degree': 3, 'field': [-12, -24, 0, 1], 'lmfdb_label': '80325.bt3', 'torsion': [2]}
  • id: 3780607
    {'degree': 4, 'field': [1, 1, 2, -1, 1], 'lmfdb_label': '80325.bt3', 'torsion': [3, 3]}
  • id: 3780609
    {'degree': 6, 'field': [-601, -87, 540, 77, -48, -3, 1], 'lmfdb_label': '80325.bt3', 'torsion': [6]}
  • id: 3780608
    {'degree': 6, 'field': [121, -495, 450, 89, -42, -3, 1], 'lmfdb_label': '80325.bt3', 'torsion': [2, 2]}
  • id: 3780610
    {'degree': 6, 'field': [2764, 228, 600, 47, -33, -3, 1], 'lmfdb_label': '80325.bt3', 'torsion': [6]}
  • id: 3780612
    {'degree': 12, 'field': [47716, 86052, 160704, 5044, 84576, -13104, 19211, -2853, 1830, -175, 72, -3, 1], 'lmfdb_label': '80325.bt3', 'torsion': [3, 6]}
  • id: 3780613
    {'degree': 12, 'field': [327184, 0, -605808, 0, 330636, 0, -52993, 0, 3495, 0, -99, 0, 1], 'lmfdb_label': '80325.bt3', 'torsion': [2, 6]}
  • id: 3780614
    {'degree': 12, 'field': [6985449, 0, 2938347, 0, 135126, 0, -33033, 0, 2310, 0, -69, 0, 1], 'lmfdb_label': '80325.bt3', 'torsion': [2, 6]}
  • id: 3780611
    {'degree': 12, 'field': [165273661, 2221177596, 548791104, -238430074, -28358157, -5310444, 1003920, 63204, 9213, -1696, -36, -6, 1], 'lmfdb_label': '80325.bt3', 'torsion': [4]}
  • id: 3780615
    {'degree': 18, 'field': [-425701, -285159, 1293336, -671640, -782352, 1436004, -1247151, 790710, -329841, 68581, -1530, -4248, 3285, -1320, 162, 0, 21, -9, 1], 'lmfdb_label': '80325.bt3', 'torsion': [9]}
  • id: 3780616
    {'degree': 18, 'field': [6859, 0, 0, 1905, 0, 0, 789, 0, 0, 479, 0, 0, 51, 0, 0, -3, 0, 0, 1], 'lmfdb_label': '80325.bt3', 'torsion': [9]}
• 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: 1954068
    {'conductor': 80325, 'conductor_valuation': 3, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '80325.bt3', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1954069
    {'conductor': 80325, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '80325.bt3', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1954070
    {'conductor': 80325, 'conductor_valuation': 1, 'discriminant_valuation': 9, 'j_denominator_valuation': 9, 'kodaira_symbol': 13, 'lmfdb_label': '80325.bt3', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1954071
    {'conductor': 80325, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '80325.bt3', 'prime': 17, '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: 2193604
    {'adelic_gens': [[10693, 18, 10692, 19], [1, 18, 0, 1], [1261, 2160, 7065, 8731], [4283, 0, 0, 10709], [1, 9, 9, 82], [6431, 2160, 1935, 6871], [1, 6, 6, 37], [6121, 2160, 7965, 8731], [1, 0, 18, 1], [1, 12, 0, 1]], 'adelic_image': '10710.144.3.?', 'conductor': 80325, 'lmfdb_label': '80325.bt3', 'prime': 0}
  • id: 329846
    {'conductor': 80325, 'elladic_image': '9.36.0.3', 'lmfdb_label': '80325.bt3', 'modell_image': '3Cs', 'prime': 3}
• ec_padic •

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

  
  
  • id: 4137483
    {'lmfdb_iso': '80325.bt', 'p': 13, 'prec': 20, 'unit': 437892263480010012169, 'val': 1}
  • id: 4137486
    {'lmfdb_iso': '80325.bt', 'p': 19, 'prec': 20, 'unit': 1527821315498888690374968, 'val': 1}
  • id: 4137487
    {'lmfdb_iso': '80325.bt', 'p': 23, 'prec': 20, 'unit': 57358715284127317581112505, 'val': 1}
  • id: 4137482
    {'lmfdb_iso': '80325.bt', 'p': 29, 'prec': 20, 'unit': 1887652616202784328345657150, 'val': 1}
  • id: 4137491
    {'lmfdb_iso': '80325.bt', 'p': 31, 'prec': 20, 'unit': 19303981673802741251194637763, 'val': 1}
  • id: 4137478
    {'lmfdb_iso': '80325.bt', 'p': 37, 'prec': 20, 'unit': 197180523049043916200170607377, 'val': 1}
  • id: 4137481
    {'lmfdb_iso': '80325.bt', 'p': 43, 'prec': 20, 'unit': 148192423005265955922901972980893, 'val': -1}
  • id: 4137489
    {'lmfdb_iso': '80325.bt', 'p': 47, 'prec': 20, 'unit': 6033975876469434686407001488501, 'val': 1}
  • id: 4137485
    {'lmfdb_iso': '80325.bt', 'p': 59, 'prec': 20, 'unit': 4133204701018899743728728140771975, 'val': 1}
  • id: 4137490
    {'lmfdb_iso': '80325.bt', 'p': 61, 'prec': 20, 'unit': 2282425156563655282722148163531914, 'val': 1}
  • id: 4137477
    {'lmfdb_iso': '80325.bt', 'p': 67, 'prec': 20, 'unit': 29995141914622192672494837851915977, 'val': 1}
  • id: 4137479
    {'lmfdb_iso': '80325.bt', 'p': 71, 'prec': 20, 'unit': 45220352616582233671281926602799936, 'val': 1}
  • id: 4137480
    {'lmfdb_iso': '80325.bt', 'p': 73, 'prec': 20, 'unit': 134888680046166506517198831016491138, 'val': 1}
  • id: 4137484
    {'lmfdb_iso': '80325.bt', 'p': 79, 'prec': 20, 'unit': 38386319753190201503887766888676330, 'val': 1}
  • id: 4137488
    {'lmfdb_iso': '80325.bt', 'p': 89, 'prec': 20, 'unit': 2104511269404131432831024670420465025, 'val': 1}
  • id: 4137476
    {'lmfdb_iso': '80325.bt', 'p': 97, 'prec': 20, 'unit': 448310854192918596300881151227834972720, 'val': -1}