Elliptic curve data - 12240.t2

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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': '12240ba', 'Clabel': '12240ba1', 'Cnumber': 1, 'abc_quality': 1.0101758145655084, 'absD': 29557614182400000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 120, 'ainvs': [0, 0, 0, -144843, 22772858], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 12240, 'degree': 76800, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.9043239049169962561153772069', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 19, 'isogeny_degrees': [1, 2], 'jinv': [-3038732943445107, 267267200000], 'lmfdb_iso': '12240.t', 'lmfdb_label': '12240.t2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -81474, 9627668], 'min_quad_twist_disc': 12, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '24.6.0.d.1', '30.6.0.a.1', '40.6.0.e.1', '120.12.0.?'], '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, 'serre_invariants': [[2, 2, 15], [3, 6, 1360], [5, 6, 2448], [17, 18, 720]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.93652365219002352384933377621', 'prec': 103}, 'szpiro_ratio': 5.0364391969414735, '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, -1, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, -4, 0], 'aplist': [0, 0, -1, 2, -2, 0, -1, -4, -8, 6, -4, 0, 4, 4, -8, -2, -6, 2, 16, 8, 10, -4, -4, 12, -2], 'class_deg': 2, 'class_size': 2, 'conductor': 12240, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '12240.t', 'trace_hash': 598389009750307809}
• 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': '0.022178147764014743842910452843', 'prec': 107}, 'conductor': 12240, 'gens': [], 'heights': [], 'lmfdb_label': '12240.t2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.36432089000902807634976494937', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4572835600361123053990597974745544619', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-443, 0, 1]], 'xcoord_integral_points': [-443]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [0, 0], '17': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '12240.t2'}
• ec_torsion_growth •

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

  
  
  • id: 631829
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '12240.t2', 'torsion': [2, 2]}
  • id: 631830
    {'degree': 4, 'field': [-6, -12, -6, 0, 1], 'lmfdb_label': '12240.t2', 'torsion': [4]}
  • id: 631833
    {'degree': 8, 'field': [-75, 0, 0, 0, 30, 0, 4, 0, 1], 'lmfdb_label': '12240.t2', 'torsion': [6]}
  • id: 631832
    {'degree': 8, 'field': [1, 0, -2, 0, 18, 0, -2, 0, 1], 'lmfdb_label': '12240.t2', 'torsion': [2, 4]}
  • id: 631831
    {'degree': 8, 'field': [16, 0, -17, 0, 9, 0, 7, 0, 1], 'lmfdb_label': '12240.t2', 'torsion': [2, 4]}
  • id: 631835
    {'degree': 16, 'field': [452464, 197064, 38426, -54172, 10114, -18614, 23550, -8716, 7017, -2134, 816, -368, 214, -28, 26, 0, 1], 'lmfdb_label': '12240.t2', 'torsion': [2, 6]}
  • id: 631834
    {'degree': 16, 'field': [11458225, 32171040, 5885356, -67623792, 14010440, 18992784, -7138364, -1599552, 290974, 18528, -40156, -1488, 1352, -144, -52, 0, 1], 'lmfdb_label': '12240.t2', '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: 264376
    {'conductor': 12240, 'conductor_valuation': 4, 'discriminant_valuation': 22, 'j_denominator_valuation': 10, 'kodaira_symbol': -18, 'lmfdb_label': '12240.t2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 264377
    {'conductor': 12240, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '12240.t2', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 264378
    {'conductor': 12240, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '12240.t2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 264379
    {'conductor': 12240, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '12240.t2', '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: 1745257
    {'adelic_gens': [[1, 2, 2, 5], [49, 76, 104, 15], [117, 4, 116, 5], [3, 4, 8, 11], [44, 1, 79, 0], [61, 4, 2, 9], [74, 1, 23, 0], [1, 4, 0, 1], [1, 0, 4, 1]], 'adelic_image': '120.12.0.?', 'conductor': 12240, 'lmfdb_label': '12240.t2', 'prime': 0}
  • id: 58410
    {'conductor': 12240, 'elladic_image': '2.3.0.1', 'lmfdb_label': '12240.t2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 12240.t does not appear in ec_padic