Elliptic curve data - 122304.dc2

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '122304ge', 'Clabel': '122304ge2', 'Cnumber': 2, 'abc_quality': 1.129325119818151, 'absD': 209940702773636417716224, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 2184, 'ainvs': [0, -1, 0, 14590623, 5074947585], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 122304, 'degree': 14376960, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.1642797188874277273629751070', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 80, 'isogeny_degrees': [1, 2], 'jinv': [3820420340137317041, 2334869460099072], 'lmfdb_iso': '122304.dc', 'lmfdb_label': '122304.dc2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 227979, -9826515], 'min_quad_twist_disc': -8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '56.6.0.b.1', '312.6.0.?', '1092.6.0.?', '2184.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 7], [3, 4, 3136], [5, 2, 40768], [7, 20, 2496], [13, 14, 9408]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.6380814107836814369607887390', 'prec': 100}, 'szpiro_ratio': 5.215971439985975, '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, -1, 0, 2, 0, 0, 0, 1, 0, -4, 0, 1, 0, -2, 0, -6, 0, 4, 0], 'aplist': [0, -1, 2, 0, -4, 1, -6, 4, 0, 4, 4, -12, -12, -8, 2, -8, 4, 10, -14, -8, 2, -16, 0, -4, 2], 'class_deg': 2, 'class_size': 2, 'conductor': 122304, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '122304.dc', 'trace_hash': 588007616931584354}
• 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': '0.0017846027495770399747179567979', 'prec': 110}, 'conductor': 122304, 'gens': [], 'heights': [], 'lmfdb_label': '122304.dc2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.061608994360978375840794209749', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.73930793233174051008953051699117775683', 'prec': 133}, 'tamagawa_product': 48, 'torsion_generators': [[-345, 0, 1]], 'xcoord_integral_points': [-345]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [6, 0], '7': 'a', '13': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '122304.dc2'}
• ec_torsion_growth •

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

  
  
  • id: 5587041
    {'degree': 2, 'field': [14, 0, 1], 'lmfdb_label': '122304.dc2', 'torsion': [2, 2]}
  • id: 5587042
    {'degree': 4, 'field': [142, 122, -39, -1, 1], 'lmfdb_label': '122304.dc2', 'torsion': [4]}
  • id: 5587045
    {'degree': 8, 'field': [-37632, 0, 7840, 0, -672, 0, 0, 0, 1], 'lmfdb_label': '122304.dc2', 'torsion': [6]}
  • id: 5587044
    {'degree': 8, 'field': [676, 0, 858, 0, 425, 0, 72, 0, 1], 'lmfdb_label': '122304.dc2', 'torsion': [2, 4]}
  • id: 5587043
    {'degree': 8, 'field': [3249, 0, -2748, 0, 580, 0, 52, 0, 1], 'lmfdb_label': '122304.dc2', 'torsion': [2, 4]}
  • id: 5587047
    {'degree': 16, 'field': [64, 0, 6400, 0, -11324, 0, 22704, 0, -12636, 0, 3300, 0, -404, 0, 16, 0, 1], 'lmfdb_label': '122304.dc2', 'torsion': [2, 6]}
  • id: 5587046
    {'degree': 16, 'field': [20884347, -68619096, 41384988, 110211192, -28859034, -7561008, -22164288, -3682224, 4703092, 1067976, 93484, -19656, 4458, 0, -8, 0, 1], 'lmfdb_label': '122304.dc2', '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: 3012544
    {'conductor': 122304, 'conductor_valuation': 6, 'discriminant_valuation': 31, 'j_denominator_valuation': 13, 'kodaira_symbol': -25, 'lmfdb_label': '122304.dc2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 3012545
    {'conductor': 122304, 'conductor_valuation': 1, 'discriminant_valuation': 10, 'j_denominator_valuation': 10, 'kodaira_symbol': 14, 'lmfdb_label': '122304.dc2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3012546
    {'conductor': 122304, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '122304.dc2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 3012547
    {'conductor': 122304, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '122304.dc2', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
• ec_galrep •

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

  
  
  • id: 2462163
    {'adelic_gens': [[1, 0, 4, 1], [2017, 4, 1850, 9], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [2181, 4, 2180, 5], [1457, 4, 730, 9], [628, 1, 935, 0], [2, 1, 1091, 0], [1913, 274, 272, 1911]], 'adelic_image': '2184.12.0.?', 'conductor': 122304, 'lmfdb_label': '122304.dc2', 'prime': 0}
  • id: 479686
    {'conductor': 122304, 'elladic_image': '2.3.0.1', 'lmfdb_label': '122304.dc2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 122304.dc does not appear in ec_padic