Elliptic curve data - 672.b3

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• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '672e', 'Clabel': '672e1', 'Cnumber': 1, 'absD': 28224, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 168, 'ainvs': [0, -1, 0, -14, 24], 'analytic_rank': 1, 'bad_primes': [2, 3, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 672, 'degree': 64, 'elladic_images': ['4.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.40520681826668437476326499696', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [5088448, 441], 'lmfdb_iso': '672.b', 'lmfdb_label': '672.b3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -14, 24], 'min_quad_twist_disc': 1, 'modell_images': ['2Cs'], 'modm_images': ['1.1.0.1', '2.6.0.1', '4.12.0.1', '24.24.0.7', '28.24.0.3', '168.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 9, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.99310916145980245179387963762', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.75178040854665702947188105769', 'prec': 107}, '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, -2, 0, 1, 0, 1, 0, 4, 0, -6, 0, 2, 0, -2, 0, -4, 0], 'aplist': [0, -1, -2, 1, 4, -6, -2, -4, 4, -2, -8, -10, -2, -8, 0, -10, 12, 10, 8, -12, 2, 0, -12, 6, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 672, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '672.b', 'trace_hash': 735138132754319977}
• 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': '2.2488379958730422276473909445', 'prec': 100}, 'conductor': 672, 'gens': [[4, 4, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.99310916145980245179387963762', 'prec': 103}], 'lmfdb_label': '672.b3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '3.6459594936737955688656412411', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.8104178877393945197070289466384483461', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[2, 0, 1], [3, 0, 1]], 'xcoord_integral_points': [-4, -1, 2, 3, 4, 10]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [5, 0], '5': [1, 0], '7': [2, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [3, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '672.b3'}
• ec_torsion_growth •

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

  
  
  • id: 31026
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '672.b3', 'torsion': [2, 4]}
  • id: 31028
    {'degree': 4, 'field': [9, 0, 0, 0, 1], 'lmfdb_label': '672.b3', 'torsion': [2, 4]}
  • id: 31027
    {'degree': 4, 'field': [22, -16, 17, -2, 1], 'lmfdb_label': '672.b3', 'torsion': [2, 4]}
  • id: 31031
    {'degree': 8, 'field': [-3, 0, -104, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '672.b3', 'torsion': [2, 6]}
  • id: 31030
    {'degree': 8, 'field': [1, 0, -4, 0, -106, 0, -4, 0, 1], 'lmfdb_label': '672.b3', 'torsion': [2, 8]}
  • id: 31029
    {'degree': 8, 'field': [106, 148, -106, -92, 67, -28, 14, -4, 1], 'lmfdb_label': '672.b3', 'torsion': [4, 4]}
  • id: 31034
    {'degree': 16, 'field': [-20412, 27216, 127008, 63504, -18144, 7560, -1728, -6696, 3996, -216, 72, -96, -12, 36, -8, -4, 1], 'lmfdb_label': '672.b3', 'torsion': [2, 12]}
  • id: 31033
    {'degree': 16, 'field': [36, -288, 1152, -2880, 4848, -5472, 3840, -1008, -932, 1232, -640, 128, 88, -80, 32, -8, 1], 'lmfdb_label': '672.b3', 'torsion': [2, 8]}
  • id: 31032
    {'degree': 16, 'field': [747994, 37440, 920448, 20040, 228328, -50976, -20652, -46320, 11829, -11184, 3432, -480, 466, -24, 36, 0, 1], 'lmfdb_label': '672.b3', '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: 8224
    {'conductor': 672, 'conductor_valuation': 5, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '672.b3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 8225
    {'conductor': 672, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '672.b3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 8226
    {'conductor': 672, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '672.b3', 'prime': 7, '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: 1668952
    {'adelic_gens': [[45, 2, 160, 163], [165, 4, 164, 5], [85, 4, 2, 9], [113, 4, 58, 9], [51, 2, 22, 167], [1, 4, 0, 1], [1, 0, 4, 1]], 'adelic_image': '168.48.0.?', 'conductor': 672, 'lmfdb_label': '672.b3', 'prime': 0}
  • id: 3046
    {'conductor': 672, 'elladic_image': '4.12.0.1', 'lmfdb_label': '672.b3', 'modell_image': '2Cs', 'prime': 2}
• ec_padic •

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

  
  
  • id: 12251
    {'lmfdb_iso': '672.b', 'p': 5, 'prec': 20, 'unit': 15689306069009, 'val': 1}
  • id: 12258
    {'lmfdb_iso': '672.b', 'p': 11, 'prec': 20, 'unit': 18847325255832758961, 'val': 1}
  • id: 12256
    {'lmfdb_iso': '672.b', 'p': 13, 'prec': 20, 'unit': 1330379186091415125495, 'val': 1}
  • id: 12259
    {'lmfdb_iso': '672.b', 'p': 17, 'prec': 20, 'unit': 137526919216798856525512, 'val': 1}
  • id: 12260
    {'lmfdb_iso': '672.b', 'p': 19, 'prec': 20, 'unit': 38871583238752846582603, 'val': 1}
  • id: 12263
    {'lmfdb_iso': '672.b', 'p': 23, 'prec': 20, 'unit': 12699638595225366962008720, 'val': 1}
  • id: 12257
    {'lmfdb_iso': '672.b', 'p': 29, 'prec': 20, 'unit': 1824389182130584831931986414, 'val': 1}
  • id: 12253
    {'lmfdb_iso': '672.b', 'p': 31, 'prec': 20, 'unit': 591458354066578002023732326, 'val': 2}
  • id: 12267
    {'lmfdb_iso': '672.b', 'p': 37, 'prec': 20, 'unit': 418582881260016171341521795939, 'val': 1}
  • id: 12254
    {'lmfdb_iso': '672.b', 'p': 41, 'prec': 20, 'unit': 1587951329279253733427871837058, 'val': 1}
  • id: 12255
    {'lmfdb_iso': '672.b', 'p': 43, 'prec': 20, 'unit': 5713852197084352805384579835765, 'val': 1}
  • id: 12261
    {'lmfdb_iso': '672.b', 'p': 53, 'prec': 20, 'unit': 534181217529867814425026635428443, 'val': 1}
  • id: 12265
    {'lmfdb_iso': '672.b', 'p': 59, 'prec': 20, 'unit': 1196432309162965407189020471137519, 'val': 1}
  • id: 12266
    {'lmfdb_iso': '672.b', 'p': 61, 'prec': 20, 'unit': 51372485835248269848632291964095, 'val': 2}
  • id: 12250
    {'lmfdb_iso': '672.b', 'p': 67, 'prec': 20, 'unit': 31417975202487320741173062816750760, 'val': 1}
  • id: 12252
    {'lmfdb_iso': '672.b', 'p': 71, 'prec': 20, 'unit': 51603886653449102638824565716094975, 'val': 1}
  • id: 12262
    {'lmfdb_iso': '672.b', 'p': 73, 'prec': 20, 'unit': 116179835552818713000168426507373071, 'val': 1}
  • id: 12249
    {'lmfdb_iso': '672.b', 'p': 83, 'prec': 20, 'unit': 2088678762578840019564046828821944098, 'val': 1}
  • id: 12264
    {'lmfdb_iso': '672.b', 'p': 89, 'prec': 20, 'unit': 6508372931631010542032591764449420036, 'val': 1}
  • id: 12248
    {'lmfdb_iso': '672.b', 'p': 97, 'prec': 20, 'unit': 55255466205372153664545140697388023694, 'val': 1}