Elliptic curve data - 66066.bi2

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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': '66066ba', 'Clabel': '66066ba1', 'Cnumber': 1, 'abc_quality': 0.9269344000478278, 'absD': 123594186171456, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 8008, 'ainvs': [1, 0, 1, -26260, -1550254], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 11, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 66066, 'degree': 304128, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4557261301222261218639506789', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 34, 'isogeny_degrees': [1, 2], 'jinv': [849278123, 52416], 'lmfdb_iso': '66066.bi', 'lmfdb_label': '66066.bi2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -217, 1145], 'min_quad_twist_disc': -11, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '88.6.0.?', '728.6.0.?', '2002.6.0.?', '8008.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 1001], [3, 4, 11011], [7, 8, 9438], [11, 32, 546], [13, 14, 5082]], 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.34269532447655178618250700457', 'prec': 107}, 'szpiro_ratio': 3.7970264706585906, '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, 1, 1, 2, -1, 1, -1, 1, -2, 0, 1, 1, -1, 2, 1, -2, -1, 2, 2], 'aplist': [-1, 1, 2, 1, 0, 1, -2, 2, -4, 10, 4, -4, -12, 6, 0, 2, 4, 14, -12, 6, 8, -16, -6, 6, -2], 'class_deg': 2, 'class_size': 2, 'conductor': 66066, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '66066.bi', 'trace_hash': 1096535123351747093}
• 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': '0.054396674350900881038832860698', 'prec': 107}, 'conductor': 66066, 'gens': [], 'heights': [], 'lmfdb_label': '66066.bi2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.37648951743475075743627842215', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.0119161394780060594902273772289467043', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-111, 55, 1]], 'xcoord_integral_points': [-111]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 0], '3': [7, 0], '7': [1, 0], '11': 'a', '13': [3, 0]}, 'iwp0': 3, 'lmfdb_label': '66066.bi2'}
• ec_torsion_growth •

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

  
  
  • id: 3149146
    {'degree': 2, 'field': [-250, -1, 1], 'lmfdb_label': '66066.bi2', 'torsion': [2, 2]}
  • id: 3149147
    {'degree': 4, 'field': [75, -50, 51, -2, 1], 'lmfdb_label': '66066.bi2', 'torsion': [4]}
  • id: 3149149
    {'degree': 8, 'field': [-314851250, -42796250, 7128275, -817950, 19037, 8634, -583, -2, 1], 'lmfdb_label': '66066.bi2', 'torsion': [2, 4]}
  • id: 3149150
    {'degree': 8, 'field': [-1452, 0, 1331, 0, -132, 0, 0, 0, 1], 'lmfdb_label': '66066.bi2', 'torsion': [6]}
  • id: 3149148
    {'degree': 8, 'field': [719104, 0, 27328, 0, 5924, 0, 70, 0, 1], 'lmfdb_label': '66066.bi2', 'torsion': [2, 4]}
  • id: 3149151
    {'degree': 16, 'field': [309900816, 0, -2361728, 0, 12974384, 0, 3582912, 0, 231468, 0, 2592, 0, 972, 0, -64, 0, 1], 'lmfdb_label': '66066.bi2', 'torsion': [8]}
  • id: 3149152
    {'degree': 16, 'field': [17960288256, 0, -5170853028, 0, 411766273, 0, -14486604, 0, 202836, 0, 8206, 0, 1212, 0, 0, 0, 1], 'lmfdb_label': '66066.bi2', 'torsion': [2, 6]}
• 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: 1595618
    {'conductor': 66066, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '66066.bi2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1595619
    {'conductor': 66066, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '66066.bi2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1595620
    {'conductor': 66066, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '66066.bi2', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1595621
    {'conductor': 66066, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '66066.bi2', 'prime': 11, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1595622
    {'conductor': 66066, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '66066.bi2', 'prime': 13, '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: 2101174
    {'adelic_gens': [[1, 2, 2, 5], [5009, 3004, 1000, 7007], [1, 4, 0, 1], [1460, 1, 3639, 0], [8005, 4, 8004, 5], [6866, 1, 4575, 0], [1850, 1, 3079, 0], [4005, 4, 2, 9], [1, 0, 4, 1], [3, 4, 8, 11]], 'adelic_image': '8008.12.0.?', 'conductor': 66066, 'lmfdb_label': '66066.bi2', 'prime': 0}
  • id: 276397
    {'conductor': 66066, 'elladic_image': '2.3.0.1', 'lmfdb_label': '66066.bi2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 66066.bi does not appear in ec_padic