Elliptic curve data - 12480.dg2

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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': '12480cz', 'Clabel': '12480cz2', 'Cnumber': 2, 'abc_quality': 0.9882017545674919, 'absD': 15575040000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 312, 'ainvs': [0, 1, 0, -625, -625], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 12480, 'degree': 12288, 'elladic_images': ['8.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.64532022521202749368162070811', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 84, 'isogeny_degrees': [1, 2], 'jinv': [1650587344, 950625], 'lmfdb_iso': '12480.dg', 'lmfdb_label': '12480.dg2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -156, 0], 'min_quad_twist_disc': -8, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '8.12.0-2.a.1.1', '12.12.0.a.1', '24.24.0-12.a.1.2', '52.12.0.b.1', '104.24.0.?', '156.24.0.?', '312.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 1], [3, 4, 4160], [5, 6, 2496], [13, 14, 960]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.16335148544124203397181676692', 'prec': 107}, 'szpiro_ratio': 3.279139354209638, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, 1, 0, 4, 0, 1, 0, 4, 0, -1, 0, 1, 0, -6, 0, 0, 0], 'aplist': [0, 1, 1, 4, 4, -1, -6, 0, 8, -6, 4, 2, -10, -4, 8, 2, 12, 2, -16, 8, -6, 16, 4, -2, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 12480, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '12480.dg', 'trace_hash': 143688211491743498}
• 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': '0.27509454224277930566446530512', 'prec': 103}, 'conductor': 12480, 'gens': [], 'heights': [], 'lmfdb_label': '12480.dg2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.0394420827204784373034491720', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.1577683308819137492137966879816728087', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[-1, 0, 1], [25, 0, 1]], 'xcoord_integral_points': [-25, -1, 25]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [1, 0], '13': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '12480.dg2'}
• ec_torsion_growth •

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

  
  
  • id: 644931
    {'degree': 4, 'field': [-1, 10, -9, -2, 1], 'lmfdb_label': '12480.dg2', 'torsion': [2, 4]}
  • id: 644933
    {'degree': 4, 'field': [1, 0, 4, 0, 1], 'lmfdb_label': '12480.dg2', 'torsion': [2, 4]}
  • id: 644932
    {'degree': 4, 'field': [64, 0, 10, 0, 1], 'lmfdb_label': '12480.dg2', 'torsion': [2, 4]}
  • id: 644934
    {'degree': 8, 'field': [-3888, 0, 5472, 0, -216, 0, 0, 0, 1], 'lmfdb_label': '12480.dg2', 'torsion': [2, 6]}
  • id: 644935
    {'degree': 16, 'field': [6561, 0, 0, 0, -2511, 0, 0, 0, 880, 0, 0, 0, -31, 0, 0, 0, 1], 'lmfdb_label': '12480.dg2', 'torsion': [4, 4]}
  • id: 644937
    {'degree': 16, 'field': [14400, 0, -49536, 0, 36672, 0, 41808, 0, 17344, 0, 2600, 0, 225, 0, 20, 0, 1], 'lmfdb_label': '12480.dg2', 'torsion': [2, 8]}
  • id: 644938
    {'degree': 16, 'field': [171396, 0, 427896, 0, 204228, 0, 72024, 0, 7813, 0, -952, 0, -138, 0, 8, 0, 1], 'lmfdb_label': '12480.dg2', 'torsion': [2, 8]}
  • id: 644936
    {'degree': 16, 'field': [455625, 0, -57500, 0, -601400, 0, -46500, 0, 119366, 0, -24868, 0, 2424, 0, -92, 0, 1], 'lmfdb_label': '12480.dg2', 'torsion': [2, 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: 270523
    {'conductor': 12480, 'conductor_valuation': 6, 'discriminant_valuation': 14, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '12480.dg2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 270524
    {'conductor': 12480, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '12480.dg2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 270525
    {'conductor': 12480, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '12480.dg2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 270526
    {'conductor': 12480, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '12480.dg2', '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: 1746856
    {'adelic_gens': [[1, 0, 4, 1], [145, 2, 0, 1], [1, 4, 0, 1], [159, 308, 160, 307], [309, 310, 262, 157], [309, 4, 308, 5], [233, 308, 310, 303], [155, 0, 0, 311]], 'adelic_image': '312.48.0.?', 'conductor': 12480, 'lmfdb_label': '12480.dg2', 'prime': 0}
  • id: 59486
    {'conductor': 12480, 'elladic_image': '8.12.0.1', 'lmfdb_label': '12480.dg2', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 12480.dg does not appear in ec_padic