Elliptic curve data - 80223.o4

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

  
  {'Ciso': '80223n', 'Clabel': '80223n1', 'Cnumber': 1, 'abc_quality': 0.8949580184960225, 'absD': 38908550134295127, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 3432, 'ainvs': [1, 0, 1, 74775, 5309599], 'analytic_rank': 0, 'bad_primes': [3, 11, 13, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 80223, 'degree': 460800, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8709980792621496300449536490', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 14, 'isogeny_degrees': [1, 2, 4], 'jinv': [26100282937247, 21962862207], 'lmfdb_iso': '80223.o', 'lmfdb_label': '80223.o4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 618, -3933], 'min_quad_twist_disc': -11, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0.ba.1', '44.12.0-4.c.1.2', '52.12.0-4.c.1.2', '264.24.0.?', '286.6.0.?', '312.24.0.?', '572.24.0.?', '3432.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.67205044286296435801398186002', 'prec': 103}, 'szpiro_ratio': 4.00974771977342, '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, 0, -3, 1, 2, 0, -1, -1, 0, 2, -1, 1, 1, -4, -2], 'aplist': [1, 1, 2, 0, 0, -1, 1, -4, 0, -2, -4, -10, 6, 8, -8, -10, -4, 2, 8, 8, 6, -12, -4, 6, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 80223, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '80223.o', 'trace_hash': 335121325633275979}
• 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': '0.023706733470257996319048310113', 'prec': 107}, 'conductor': 80223, 'gens': [], 'heights': [], 'lmfdb_label': '80223.o4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.23581914056104877239021521954', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.8298296867325852686825826344482235485', 'prec': 130}, 'tamagawa_product': 48, 'torsion_generators': [[-67, 33, 1]], 'xcoord_integral_points': [-67]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [6, 0], '3': [3, 0], '11': 'a', '13': [0, 0], '17': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '80223.o4'}
• ec_torsion_growth •

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

  
  
  • id: 3777722
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '80223.o4', 'torsion': [4]}
  • id: 3777723
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '80223.o4', 'torsion': [4]}
  • id: 3777721
    {'degree': 2, 'field': [36, -1, 1], 'lmfdb_label': '80223.o4', 'torsion': [2, 2]}
  • id: 3777724
    {'degree': 4, 'field': [36, 0, -1, 0, 1], 'lmfdb_label': '80223.o4', 'torsion': [2, 4]}
  • id: 3777728
    {'degree': 8, 'field': [-513, -2961, 2655, -201, 123, -188, -27, 0, 1], 'lmfdb_label': '80223.o4', 'torsion': [6]}
  • id: 3777726
    {'degree': 8, 'field': [41616, 0, -15672, 0, 2065, 0, -83, 0, 1], 'lmfdb_label': '80223.o4', 'torsion': [8]}
  • id: 3777727
    {'degree': 8, 'field': [558009, 152388, -6417, 6696, 4404, 246, -41, -2, 1], 'lmfdb_label': '80223.o4', 'torsion': [8]}
  • id: 3777725
    {'degree': 8, 'field': [5687878, 2923022, 441401, 16276, 5036, 1196, 38, -2, 1], 'lmfdb_label': '80223.o4', 'torsion': [2, 4]}
  • id: 3777733
    {'degree': 16, 'field': [-6488829, 50768019, -63082710, 26072174, -17165848, 6480006, -4884242, 2709586, -1161336, 347160, -93918, 13278, -2122, -70, 30, -8, 1], 'lmfdb_label': '80223.o4', 'torsion': [12]}
  • id: 3777734
    {'degree': 16, 'field': [165807, -66582, 202716, -463386, 737151, -685804, 366230, -129520, 47972, -12382, 4826, -1760, 718, -224, 52, -8, 1], 'lmfdb_label': '80223.o4', 'torsion': [12]}
  • id: 3777732
    {'degree': 16, 'field': [15116544, 0, 14188800, 0, 22489120, 0, -1104672, 0, 39309, 0, -6437, 0, 426, 0, 0, 0, 1], 'lmfdb_label': '80223.o4', 'torsion': [2, 6]}
  • id: 3777730
    {'degree': 16, 'field': [514155625, 0, -175358723, 0, 38108953, 0, -5415098, 0, 497278, 0, -32474, 0, 1681, 0, -59, 0, 1], 'lmfdb_label': '80223.o4', 'torsion': [2, 8]}
  • id: 3777731
    {'degree': 16, 'field': [1906304436, -3293454168, 3341022444, -1680811560, 399096621, 68865570, -7904075, -17634546, 6936190, -786454, -6191, -5566, 2926, -178, -11, -6, 1], 'lmfdb_label': '80223.o4', 'torsion': [2, 8]}
  • id: 3777729
    {'degree': 16, 'field': [26975984333281, 0, 0, 0, 80207188546, 0, 0, 0, 56587731, 0, 0, 0, 14050, 0, 0, 0, 1], 'lmfdb_label': '80223.o4', 'torsion': [4, 4]}
• 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: 1952399
    {'conductor': 80223, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '80223.o4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
  • id: 1952400
    {'conductor': 80223, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '80223.o4', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1952401
    {'conductor': 80223, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '80223.o4', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1952402
    {'conductor': 80223, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '80223.o4', 'prime': 17, '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: 2193111
    {'adelic_gens': [[1145, 8, 1148, 33], [1291, 1290, 442, 2155], [3425, 8, 3424, 9], [3116, 3431, 2473, 3426], [1, 0, 8, 1], [433, 432, 2158, 439], [7, 6, 3426, 3427], [268, 1, 2399, 6], [1, 8, 0, 1], [1, 4, 4, 17]], 'adelic_image': '3432.48.0.?', 'conductor': 80223, 'lmfdb_label': '80223.o4', 'prime': 0}
  • id: 329634
    {'conductor': 80223, 'elladic_image': '4.6.0.1', 'lmfdb_label': '80223.o4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 80223.o does not appear in ec_padic