Elliptic curve data - 672.e2

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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': '672b', 'Clabel': '672b1', 'Cnumber': 1, 'abc_quality': 1.048044296462054, 'absD': 1829677248, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 84, 'ainvs': [0, 1, 0, 210, 1764], 'analytic_rank': 1, 'bad_primes': [2, 3, 7], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 672, 'degree': 480, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.46208130557250834950841531734', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2], 'jinv': [15926924096, 28588707], 'lmfdb_iso': '672.e', 'lmfdb_label': '672.e2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 210, -1764], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '6.6.0.a.1', '28.6.0.b.1', '84.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 13, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.13994926536143167654467707730', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 3], [3, 4, 32], [5, 2, 224], [7, 8, 96]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.11550771529253569479979925661', 'prec': 103}, 'szpiro_ratio': 4.361259915604426, '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, -4, 0, 1, 0, 1, 0, -2, 0, -2, 0, -4, 0, 0, 0, -4, 0], 'aplist': [0, 1, -4, 1, -2, -2, 0, -4, -6, -10, -8, 10, -4, -8, -4, 10, 8, -6, 4, 14, 6, 4, -12, 4, -2], 'class_deg': 2, 'class_size': 2, 'conductor': 672, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '672.e', 'trace_hash': 521933558131321449}
• 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': '0.39686360913269147596039916549', 'prec': 103}, 'conductor': 672, 'gens': [[0, 42, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.13994926536143167654467707730', 'prec': 103}], 'lmfdb_label': '672.e2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.0195945289440949912736142333', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.1403725793839162016645238534054505288', 'prec': 130}, 'tamagawa_product': 60, 'torsion_generators': [[-7, 0, 1]], 'xcoord_integral_points': [-7, -6, 0, 21, 42, 105, 336]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [6, 0], '5': [5, 0], '7': [2, 0], '11': [1, 0], '13': [1, 0], '17': [1, 1, 0], '19': [1, 0], '23': [3, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '672.e2'}
• ec_torsion_growth •

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

  
  
  • id: 30951
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '672.e2', 'torsion': [2, 2]}
  • id: 30952
    {'degree': 4, 'field': [1, -2, -4, -2, 1], 'lmfdb_label': '672.e2', 'torsion': [4]}
  • id: 30955
    {'degree': 8, 'field': [-3, 0, -40, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '672.e2', 'torsion': [6]}
  • id: 30954
    {'degree': 8, 'field': [1, -2, 8, 12, 11, 12, 8, -2, 1], 'lmfdb_label': '672.e2', 'torsion': [2, 4]}
  • id: 30953
    {'degree': 8, 'field': [81, 0, 54, 0, 3, 0, 0, 0, 1], 'lmfdb_label': '672.e2', 'torsion': [2, 4]}
  • id: 30956
    {'degree': 16, 'field': [-63, 1512, -8428, 24864, -43928, 42872, -14052, -11368, 10610, -824, -1708, 576, -40, -40, 28, -8, 1], 'lmfdb_label': '672.e2', 'torsion': [8]}
  • id: 30957
    {'degree': 16, 'field': [9, 0, -120, 0, 1582, 0, -240, 0, 39, 0, -80, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '672.e2', 'torsion': [2, 6]}
• 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: 8200
    {'conductor': 672, 'conductor_valuation': 5, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '672.e2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 8201
    {'conductor': 672, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '672.e2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 5}
  • id: 8202
    {'conductor': 672, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '672.e2', 'prime': 7, '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: 1668961
    {'adelic_gens': [[73, 4, 62, 9], [1, 4, 0, 1], [25, 64, 20, 63], [1, 0, 4, 1], [3, 4, 8, 11], [81, 4, 80, 5], [58, 1, 55, 0], [1, 2, 2, 5]], 'adelic_image': '84.12.0.?', 'conductor': 672, 'lmfdb_label': '672.e2', 'prime': 0}
  • id: 3055
    {'conductor': 672, 'elladic_image': '2.3.0.1', 'lmfdb_label': '672.e2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 12271
    {'lmfdb_iso': '672.e', 'p': 5, 'prec': 20, 'unit': 17584973018797, 'val': -1}
  • id: 12270
    {'lmfdb_iso': '672.e', 'p': 11, 'prec': 20, 'unit': 45931914151340158731, 'val': 1}
  • id: 12277
    {'lmfdb_iso': '672.e', 'p': 13, 'prec': 20, 'unit': 567886705031276975236, 'val': 1}
  • id: 12280
    {'lmfdb_iso': '672.e', 'p': 19, 'prec': 20, 'unit': 1599206764656097211320049, 'val': 1}
  • id: 12283
    {'lmfdb_iso': '672.e', 'p': 23, 'prec': 20, 'unit': 1566174960101190133414707, 'val': 2}
  • id: 12276
    {'lmfdb_iso': '672.e', 'p': 29, 'prec': 20, 'unit': 4725670057506716499011358208, 'val': 1}
  • id: 12273
    {'lmfdb_iso': '672.e', 'p': 31, 'prec': 20, 'unit': 3528824451586395464116037600, 'val': 1}
  • id: 12288
    {'lmfdb_iso': '672.e', 'p': 37, 'prec': 20, 'unit': 214114715603833369184774335279, 'val': 1}
  • id: 12274
    {'lmfdb_iso': '672.e', 'p': 41, 'prec': 20, 'unit': 365992108119204291864744617109, 'val': 1}
  • id: 12275
    {'lmfdb_iso': '672.e', 'p': 43, 'prec': 20, 'unit': 8320427233534577782095483245191, 'val': 1}
  • id: 12285
    {'lmfdb_iso': '672.e', 'p': 47, 'prec': 20, 'unit': 30337695951155838559747711411066, 'val': 1}
  • id: 12281
    {'lmfdb_iso': '672.e', 'p': 53, 'prec': 20, 'unit': 35867124580995577948214109512714, 'val': 1}
  • id: 12279
    {'lmfdb_iso': '672.e', 'p': 59, 'prec': 20, 'unit': 4041797209984995550800525001287809, 'val': 1}
  • id: 12286
    {'lmfdb_iso': '672.e', 'p': 61, 'prec': 20, 'unit': 237430363753690632138334533859091, 'val': 1}
  • id: 12269
    {'lmfdb_iso': '672.e', 'p': 67, 'prec': 20, 'unit': 18638497728111155492002288189191075, 'val': 1}
  • id: 12272
    {'lmfdb_iso': '672.e', 'p': 71, 'prec': 20, 'unit': 47771200427597763818344744682881423, 'val': 1}
  • id: 12282
    {'lmfdb_iso': '672.e', 'p': 73, 'prec': 20, 'unit': 110162917701949865503711097923035793, 'val': 1}
  • id: 12278
    {'lmfdb_iso': '672.e', 'p': 79, 'prec': 20, 'unit': 410085259303814468891834331697524713, 'val': 1}
  • id: 12287
    {'lmfdb_iso': '672.e', 'p': 83, 'prec': 20, 'unit': 814248040871752634838245698064608460, 'val': 1}
  • id: 12284
    {'lmfdb_iso': '672.e', 'p': 89, 'prec': 20, 'unit': 9318114897748988381380117265189383497, 'val': 1}
  • id: 12268
    {'lmfdb_iso': '672.e', 'p': 97, 'prec': 20, 'unit': 45075840189281604578986827538969428274, 'val': 1}