Elliptic curve data - 82368.cg3

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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': '82368s', 'Clabel': '82368s2', 'Cnumber': 2, 'abc_quality': 1.033360901289125, 'absD': 48216610930685902848, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 3432, 'ainvs': [0, 0, 0, -1037100, -231611344], 'analytic_rank': 0, 'bad_primes': [2, 3, 11, 13], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 82368, 'degree': 1769472, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4755454895822021523163776603', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 58, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [645532578015625, 252306960048], 'lmfdb_iso': '82368.cg', 'lmfdb_label': '82368.cg3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -1801, 16604], 'min_quad_twist_disc': -24, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '12.24.0.h.1', '24.48.0-12.h.1.1', '572.6.0.?', '1716.48.1.?', '3432.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.88651857440822934249290685965', 'prec': 103}, 'szpiro_ratio': 4.697379970312376, '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, 0, 0, 0, 0, 0, -4, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 4, 0], 'aplist': [0, 0, 0, -4, -1, -1, 0, 4, 0, 0, -10, -2, 6, 10, 0, 6, 0, -2, -2, -12, -10, -10, -12, -12, -10], 'class_deg': 6, 'class_size': 4, 'conductor': 82368, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '82368.cg', 'trace_hash': 882491304301652050}
• 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': '0.0070756852914275086828948884748', 'prec': 110}, 'conductor': 82368, 'gens': [], 'heights': [], 'lmfdb_label': '82368.cg3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.15467898283550486694942800726', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.61871593134201946779771202905536516477', 'prec': 133}, 'tamagawa_product': 16, 'torsion_generators': [[-236, 0, 1]], 'xcoord_integral_points': [-236]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '11': [0, 0], '13': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '82368.cg3'}
• ec_torsion_growth •

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

  
  
  • id: 3868862
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '82368.cg3', 'torsion': [2, 2]}
  • id: 3868863
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '82368.cg3', 'torsion': [6]}
  • id: 3868865
    {'degree': 4, 'field': [1, 0, 4, 0, 1], 'lmfdb_label': '82368.cg3', 'torsion': [2, 6]}
  • id: 3868864
    {'degree': 4, 'field': [192, 0, -14, 0, 1], 'lmfdb_label': '82368.cg3', 'torsion': [4]}
  • id: 3868866
    {'degree': 6, 'field': [-242, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '82368.cg3', 'torsion': [6]}
  • id: 3868868
    {'degree': 8, 'field': [-8418, 16944, -6768, -1212, 520, 8, 18, -4, 1], 'lmfdb_label': '82368.cg3', 'torsion': [2, 4]}
  • id: 3868867
    {'degree': 8, 'field': [2304, 0, -1344, 0, 721, 0, -28, 0, 1], 'lmfdb_label': '82368.cg3', 'torsion': [2, 4]}
  • id: 3868869
    {'degree': 8, 'field': [2304, 0, 390, 0, 265, 0, 26, 0, 1], 'lmfdb_label': '82368.cg3', 'torsion': [12]}
  • id: 3868870
    {'degree': 12, 'field': [36, 0, -96, 0, 244, 0, -20, 0, -12, 0, -2, 0, 1], 'lmfdb_label': '82368.cg3', 'torsion': [3, 6]}
  • id: 3868871
    {'degree': 12, 'field': [169, 0, 32, 0, -45, 0, -44, 0, -9, 0, -4, 0, 1], 'lmfdb_label': '82368.cg3', 'torsion': [2, 6]}
  • id: 3868873
    {'degree': 16, 'field': [2304, -18432, 67680, -143088, 188422, -151188, 56166, 19652, -34831, 18332, -1462, -1972, 996, -336, 68, -8, 1], 'lmfdb_label': '82368.cg3', 'torsion': [2, 12]}
  • id: 3868874
    {'degree': 16, 'field': [9801, -11664, 20466, 14796, 42522, 28548, 8718, 5760, -953, -408, 194, -312, 60, -12, -4, 0, 1], 'lmfdb_label': '82368.cg3', 'torsion': [2, 12]}
  • id: 3868872
    {'degree': 16, 'field': [14017536, 0, -283855104, 0, 1428442704, 0, 133189992, 0, 5589897, 0, 25668, 0, 4531, 0, 46, 0, 1], 'lmfdb_label': '82368.cg3', 'torsion': [8]}
  • id: 3868875
    {'degree': 18, 'field': [8111314944, 0, -1762041600, 0, -647113536, 0, 151517412, 0, 57016872, 0, 6661224, 0, 421218, 0, 13716, 0, 198, 0, 1], 'lmfdb_label': '82368.cg3', 'torsion': [18]}
• 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: 2005664
    {'conductor': 82368, 'conductor_valuation': 6, 'discriminant_valuation': 22, 'j_denominator_valuation': 4, 'kodaira_symbol': -16, 'lmfdb_label': '82368.cg3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2005665
    {'conductor': 82368, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '82368.cg3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2005666
    {'conductor': 82368, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '82368.cg3', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2005667
    {'conductor': 82368, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '82368.cg3', '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: 2206786
    {'adelic_gens': [[1, 6, 6, 37], [937, 12, 474, 73], [1, 12, 0, 1], [1727, 3420, 1728, 3419], [578, 11, 561, 1696], [11, 2, 3382, 3423], [2430, 1847, 2431, 1858], [3421, 3430, 1766, 1725], [1715, 0, 0, 3431], [2507, 3420, 3030, 3359], [1, 0, 12, 1], [3421, 12, 3420, 13]], 'adelic_image': '3432.96.1.?', 'conductor': 82368, 'lmfdb_label': '82368.cg3', 'prime': 0}
  • id: 337142
    {'conductor': 82368, 'elladic_image': '2.3.0.1', 'lmfdb_label': '82368.cg3', 'modell_image': '2B', 'prime': 2}
  • id: 337143
    {'conductor': 82368, 'elladic_image': '3.4.0.1', 'lmfdb_label': '82368.cg3', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 82368.cg does not appear in ec_padic