Elliptic curve data - 204304.a2

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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': '204304a', 'Clabel': '204304a1', 'Cnumber': 1, 'abc_quality': 1.0575282282301526, 'absD': 61672141106660507648, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 904, 'ainvs': [0, 1, 0, -1025776, -131271468], 'analytic_rank': 0, 'bad_primes': [2, 113], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 204304, 'degree': 7354368, 'elladic_images': ['8.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4894222955768888473479406231', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [13997521, 7232], 'lmfdb_iso': '204304.a', 'lmfdb_label': '204304.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -5, 1], 'min_quad_twist_disc': -452, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.c.1', '226.6.0.?', '904.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 12769], [113, 6498, 16]], 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.56741879433922674636035724517', 'prec': 107}, 'szpiro_ratio': 4.345702173949407, '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, -2, 0, 4, 0, 0, 0, 1, 0, 4, 0, -2, 0, -8, 0, 2, 0, -2, 0], 'aplist': [0, -2, 4, 0, 4, -2, 2, -2, 4, 4, -8, 8, -6, 6, -12, 10, -6, -6, 2, -8, 14, 8, -16, 14, -2], 'class_deg': 2, 'class_size': 2, 'conductor': 204304, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '204304.a', 'trace_hash': 1941291089852523547}
• 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': '0.0068820095002845900303654532173', 'prec': 110}, 'conductor': 204304, 'gens': [], 'heights': [], 'lmfdb_label': '204304.a2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.15867292821226074520743239287', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.5387668513961719233189182859853498972', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-942, 0, 1]], 'xcoord_integral_points': [-942]}
• lmfdb_label 204304.a2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8944439
    {'degree': 2, 'field': [-28, -1, 1], 'lmfdb_label': '204304.a2', 'torsion': [2, 2]}
  • id: 8944440
    {'degree': 4, 'field': [34, -4, 10, 0, 1], 'lmfdb_label': '204304.a2', 'torsion': [4]}
  • id: 8944443
    {'degree': 8, 'field': [-38307, 0, -22600, 0, -678, 0, 0, 0, 1], 'lmfdb_label': '204304.a2', 'torsion': [6]}
  • id: 8944441
    {'degree': 8, 'field': [196, 0, -1053, 0, 933, 0, 51, 0, 1], 'lmfdb_label': '204304.a2', 'torsion': [2, 4]}
  • id: 8944442
    {'degree': 8, 'field': [784, 0, -512, 0, 105, 0, 14, 0, 1], 'lmfdb_label': '204304.a2', 'torsion': [2, 4]}
  • id: 8944445
    {'degree': 16, 'field': [2304, 0, 26628, 0, -87851, 0, 5124, 0, 3588, 0, -6762, 0, -636, 0, 0, 0, 1], 'lmfdb_label': '204304.a2', 'torsion': [2, 6]}
  • id: 8944444
    {'degree': 16, 'field': [163108, 786192, 1129528, -230544, 168368, -542424, 142932, -145248, 74917, -20880, 13920, -1968, 1338, -72, 68, 0, 1], 'lmfdb_label': '204304.a2', '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: 5059136
    {'conductor': 204304, 'conductor_valuation': 4, 'discriminant_valuation': 18, 'j_denominator_valuation': 6, 'kodaira_symbol': -14, 'lmfdb_label': '204304.a2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5059137
    {'conductor': 204304, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '204304.a2', 'prime': 113, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 2971909
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [458, 1, 223, 0], [793, 114, 112, 791], [453, 4, 2, 9], [901, 4, 900, 5]], 'adelic_image': '904.12.0.?', 'conductor': 204304, 'lmfdb_label': '204304.a2', 'prime': 0}
  • id: 755705
    {'conductor': 204304, 'elladic_image': '8.6.0.1', 'lmfdb_label': '204304.a2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 204304.a does not appear in ec_padic