Elliptic curve data - 20475.p2

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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': '20475k', 'Clabel': '20475k2', 'Cnumber': 2, 'abc_quality': 0.9080898841024813, 'absD': 2546795671875, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1092, 'ainvs': [1, -1, 1, 2320, -64178], 'analytic_rank': 1, 'bad_primes': [3, 5, 7, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 20475, 'degree': 27648, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0652015805093074024015159987', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 15, 'isogeny_degrees': [1, 2], 'jinv': [4492125, 8281], 'lmfdb_iso': '20475.p', 'lmfdb_label': '20475.p2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, 10, 16], 'min_quad_twist_disc': -15, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '6.6.0.a.1', '364.6.0.?', '1092.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.0091132825772501181598593578', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 75], [3, 2, 2275], [5, 14, 819], [7, 8, 2925], [13, 14, 1575]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.56347659220882505344529759561', 'prec': 107}, 'szpiro_ratio': 3.59060675774077, '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, -1, 0, -1, 0, 0, 1, 3, 0, 0, 0, 0, 1, -1, 0, -1, 2, 0, -4, 0], 'aplist': [-1, 0, 0, 1, 0, 1, 2, -4, 6, 4, 0, 10, -12, 4, -10, -12, 14, -10, 0, -8, -2, 0, -6, 0, 2], 'class_deg': 2, 'class_size': 2, 'conductor': 20475, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '20475.p', 'trace_hash': 818723013866059421}
• 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': '0.11878939294450890051613832743', 'prec': 103}, 'conductor': 20475, 'gens': [[70, 626, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.0091132825772501181598593578', 'prec': 100}], 'lmfdb_label': '20475.p2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.42529189388843304814016612253', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.4178383719347410367427259974651444684', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[91, -95, 2]], 'xcoord_integral_points': [70, 104]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 1], '3': 'a', '5': 'a', '7': [4, 0], '11': [1, 1, 0], '13': [2, 0], '17': [1, 0], '19': [1, 0], '23': [3, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '20475.p2'}
• ec_torsion_growth •

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

  
  
  • id: 1045652
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '20475.p2', 'torsion': [2, 2]}
  • id: 1045653
    {'degree': 4, 'field': [-1200, 0, 45, 0, 1], 'lmfdb_label': '20475.p2', 'torsion': [4]}
  • id: 1045654
    {'degree': 8, 'field': [256, 0, -128, 0, 3, 0, 7, 0, 1], 'lmfdb_label': '20475.p2', 'torsion': [2, 4]}
  • id: 1045656
    {'degree': 8, 'field': [945, 1890, 756, 117, -9, -27, -12, 0, 1], 'lmfdb_label': '20475.p2', 'torsion': [6]}
  • id: 1045655
    {'degree': 8, 'field': [1440000, 0, 54000, 0, 3225, 0, -45, 0, 1], 'lmfdb_label': '20475.p2', 'torsion': [2, 4]}
  • id: 1045658
    {'degree': 16, 'field': [8379, -7191, -3843, 8883, 13698, -17568, 2682, 7794, -4299, -1509, 1458, -57, -207, 57, 9, -6, 1], 'lmfdb_label': '20475.p2', 'torsion': [2, 6]}
  • id: 1045657
    {'degree': 16, 'field': [38416, 0, -2711072, 0, -14113519, 0, -70616, 0, 6883, 0, 39728, 0, -2461, 0, 104, 0, 1], 'lmfdb_label': '20475.p2', 'torsion': [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: 465189
    {'conductor': 20475, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '20475.p2', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 465190
    {'conductor': 20475, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '20475.p2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 465191
    {'conductor': 20475, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '20475.p2', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 465192
    {'conductor': 20475, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '20475.p2', '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: 1800993
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [368, 1, 727, 0], [821, 274, 272, 819], [925, 4, 758, 9], [1089, 4, 1088, 5], [157, 4, 314, 9]], 'adelic_image': '1092.12.0.?', 'conductor': 20475, 'lmfdb_label': '20475.p2', 'prime': 0}
  • id: 95416
    {'conductor': 20475, 'elladic_image': '2.3.0.1', 'lmfdb_label': '20475.p2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 953295
    {'lmfdb_iso': '20475.p', 'p': 17, 'prec': 20, 'unit': 182995068147940040440442, 'val': 1}
  • id: 953287
    {'lmfdb_iso': '20475.p', 'p': 19, 'prec': 20, 'unit': 999720459222186290513889, 'val': 1}
  • id: 953299
    {'lmfdb_iso': '20475.p', 'p': 23, 'prec': 20, 'unit': 1252499283119892869397902, 'val': 2}
  • id: 953293
    {'lmfdb_iso': '20475.p', 'p': 29, 'prec': 20, 'unit': 2459787383342306323546920389, 'val': 1}
  • id: 953289
    {'lmfdb_iso': '20475.p', 'p': 37, 'prec': 20, 'unit': 146025040912701485168310216898, 'val': 1}
  • id: 953291
    {'lmfdb_iso': '20475.p', 'p': 41, 'prec': 20, 'unit': 40132984625738071005468593443, 'val': 1}
  • id: 953292
    {'lmfdb_iso': '20475.p', 'p': 43, 'prec': 20, 'unit': 7791142044453022872348431242529, 'val': 1}
  • id: 953294
    {'lmfdb_iso': '20475.p', 'p': 47, 'prec': 20, 'unit': 2448923040868584755620163075823, 'val': 1}
  • id: 953297
    {'lmfdb_iso': '20475.p', 'p': 53, 'prec': 20, 'unit': 286675441036641748310692678132133, 'val': 1}
  • id: 953300
    {'lmfdb_iso': '20475.p', 'p': 59, 'prec': 20, 'unit': 1217321093484048702022176168387906, 'val': 1}
  • id: 953301
    {'lmfdb_iso': '20475.p', 'p': 61, 'prec': 20, 'unit': 3920456869211136236756636429752864, 'val': 1}
  • id: 953290
    {'lmfdb_iso': '20475.p', 'p': 71, 'prec': 20, 'unit': 31835293508316821681312688124754318, 'val': 1}
  • id: 953298
    {'lmfdb_iso': '20475.p', 'p': 73, 'prec': 20, 'unit': 34684467742778751195839398844805061, 'val': 1}
  • id: 953296
    {'lmfdb_iso': '20475.p', 'p': 83, 'prec': 20, 'unit': 10966672373376688870926326855388439, 'val': 1}
  • id: 953288
    {'lmfdb_iso': '20475.p', 'p': 97, 'prec': 20, 'unit': 25569530267122459377654130359732872789, 'val': 1}