Elliptic curve data - 73008.bs4

Formats: - HTML - YAML - JSON - 2024-05-23T00:00:21.055109

• 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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '73008bi', 'Clabel': '73008bi3', 'Cnumber': 3, 'absD': 389144910016512, 'ainvs': [0, 0, 0, 0, 949104], 'analytic_rank': 0, 'bad_primes': [2, 3, 13], 'class_deg': 27, 'class_size': 4, 'cm': -3, 'conductor': 73008, 'degree': 147744, 'elladic_images': ['27.972.55.16'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4784636473637580310005405741', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 44, 'isogeny_degrees': [1, 3, 9], 'jinv': [0, 1], 'lmfdb_iso': '73008.bs', 'lmfdb_label': '73008.bs4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 1, 0, 0], 'min_quad_twist_disc': 156, 'modell_images': ['3Cs'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.3211174284280379149898691958', 'prec': 103}, 'szpiro_ratio': 3.6656995946487823, '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, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7, 0], 'aplist': [0, 0, 0, -1, 0, 0, 0, -7, 0, 0, -4, -11, 0, -8, 0, 0, 0, -1, 5, 0, 7, -17, 0, 0, 19], 'class_deg': 27, 'class_size': 4, 'conductor': 73008, 'isogeny_matrix': [[1, 27, 9, 3], [27, 1, 3, 9], [9, 3, 1, 3], [3, 9, 3, 1]], 'lmfdb_iso': '73008.bs', 'trace_hash': 945875648724699090}
• 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': '0.051978386308094196415681429618', 'prec': 107}, 'conductor': 73008, 'gens': [], 'heights': [], 'lmfdb_label': '73008.bs4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.42433290228560317770948065726', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.42433290228560317770948065725812546493', 'prec': 133}, 'tamagawa_product': 1, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [0, 0, 0], '7': [0, 0], '11': [0, 0, 0], '13': 'a', '17': [0, 0, 0], '19': [0, 0], '23': [0, 0, 0], '29': [0, 0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0, 0], '43': [0, 0], '47': [0, 0, 0]}, 'iwp0': 0, 'lmfdb_label': '73008.bs4'}
• ec_torsion_growth •

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

  
  
  • id: 3460069
    {'degree': 2, 'field': [-39, 0, 1], 'lmfdb_label': '73008.bs4', 'torsion': [3]}
  • id: 3460070
    {'degree': 2, 'field': [13, 0, 1], 'lmfdb_label': '73008.bs4', 'torsion': [3]}
  • id: 3460071
    {'degree': 3, 'field': [-2, 0, 0, 1], 'lmfdb_label': '73008.bs4', 'torsion': [2]}
  • id: 3460072
    {'degree': 4, 'field': [169, 0, -13, 0, 1], 'lmfdb_label': '73008.bs4', 'torsion': [3, 3]}
  • id: 3460074
    {'degree': 6, 'field': [-6591, 0, 1521, 0, -78, 0, 1], 'lmfdb_label': '73008.bs4', 'torsion': [9]}
  • id: 3460075
    {'degree': 6, 'field': [-1511, 546, 507, -38, -39, 0, 1], 'lmfdb_label': '73008.bs4', 'torsion': [6]}
  • id: 3460073
    {'degree': 6, 'field': [1, -3, 0, 5, 0, -3, 1], 'lmfdb_label': '73008.bs4', 'torsion': [2, 2]}
  • id: 3460076
    {'degree': 6, 'field': [686, 0, 0, -38, 0, 0, 1], 'lmfdb_label': '73008.bs4', 'torsion': [6]}
  • id: 3460077
    {'degree': 12, 'field': [-10202, -56400, -86004, 4316, 45150, -32832, 13260, -2412, 258, 2, 18, -6, 1], 'lmfdb_label': '73008.bs4', 'torsion': [4]}
  • id: 3460080
    {'degree': 12, 'field': [469225, -427440, 185277, -50544, 17352, -7512, 2963, -498, 6, -18, 15, -6, 1], 'lmfdb_label': '73008.bs4', 'torsion': [6, 6]}
  • id: 3460078
    {'degree': 12, 'field': [4826809, 0, 0, 0, 0, 0, -2197, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '73008.bs4', 'torsion': [3, 9]}
  • id: 3460079
    {'degree': 12, 'field': [101362989, 0, 23391459, 0, 599781, 0, -131820, 0, 3042, 0, -39, 0, 1], 'lmfdb_label': '73008.bs4', 'torsion': [7]}
  • id: 3460082
    {'degree': 18, 'field': [-380956967, 494367042, 195384681, -183402324, -136485708, 47965152, 45280548, -12510792, -6273006, 1955180, 292098, -140868, 10848, 2496, -1248, 168, 9, -6, 1], 'lmfdb_label': '73008.bs4', 'torsion': [18]}
  • id: 3460081
    {'degree': 18, 'field': [10705928273, 1125874152, 7308193581, 492070890, 2253548817, 86803470, 405847458, 7712406, 46860489, 329584, 3601260, 3042, 184545, -234, 6084, -6, 117, 0, 1], 'lmfdb_label': '73008.bs4', '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: 1771916
    {'conductor': 73008, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '73008.bs4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1771917
    {'conductor': 73008, 'conductor_valuation': 3, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '73008.bs4', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1771918
    {'conductor': 73008, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '73008.bs4', 'prime': 13, 'reduction_type': 0, '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

  
  {'conductor': 73008, 'elladic_image': '27.972.55.16', 'lmfdb_label': '73008.bs4', 'modell_image': '3Cs', 'prime': 3}
• lmfdb_iso 73008.bs does not appear in ec_padic