Elliptic curve data - 672.b4

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '672e', 'Clabel': '672e4', 'Cnumber': 4, 'abc_quality': 0.9710857330134317, 'absD': 3687936, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 168, 'ainvs': [0, -1, 0, 16, 84], 'analytic_rank': 1, 'bad_primes': [2, 3, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 672, 'degree': 128, 'elladic_images': ['4.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.058633227986711720054648936230', 'prec': 110}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 4], 'jinv': [830584, 7203], 'lmfdb_iso': '672.b', 'lmfdb_label': '672.b4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 16, 84], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '24.24.0-24.v.1.2', '56.24.0-56.ba.1.4', '168.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 7, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.9862183229196049035877592752', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.57849361340667070211757302732', 'prec': 107}, 'szpiro_ratio': 3.457041899317363, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
• 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': '1.1244189979365211138236954722', 'prec': 100}, 'conductor': 672, 'gens': [[1, 10, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.9862183229196049035877592752', 'prec': 100}], 'lmfdb_label': '672.b4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.8229797468368977844328206205', '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': [[4, 14, 1]], 'xcoord_integral_points': [-3, 1, 4, 60]}
• 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.b4'}
• ec_torsion_growth •

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

  
  
  • id: 31065
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '672.b4', 'torsion': [2, 4]}
  • id: 31066
    {'degree': 4, 'field': [-6, 0, -2, 0, 1], 'lmfdb_label': '672.b4', 'torsion': [8]}
  • id: 31070
    {'degree': 8, 'field': [-3, 0, -104, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '672.b4', 'torsion': [12]}
  • id: 31067
    {'degree': 8, 'field': [49, 0, -68, 0, 18, 0, 4, 0, 1], 'lmfdb_label': '672.b4', 'torsion': [4, 4]}
  • id: 31068
    {'degree': 8, 'field': [694, -536, 752, -464, 313, -100, 38, -4, 1], 'lmfdb_label': '672.b4', 'torsion': [2, 8]}
  • id: 31069
    {'degree': 8, 'field': [1089, -1188, 732, -60, -80, 20, 12, -4, 1], 'lmfdb_label': '672.b4', 'torsion': [2, 8]}
  • id: 31071
    {'degree': 16, 'field': [1296, 0, 1728, 0, -4032, 0, 6048, 0, -1512, 0, -1008, 0, -112, 0, -8, 0, 1], 'lmfdb_label': '672.b4', 'torsion': [16]}
  • id: 31072
    {'degree': 16, 'field': [321489, 0, 428652, 0, 142884, 0, -26244, 0, -12150, 0, 972, 0, 36, 0, 12, 0, 1], 'lmfdb_label': '672.b4', 'torsion': [2, 12]}
• 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: 8233
    {'conductor': 672, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '672.b4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 8234
    {'conductor': 672, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '672.b4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 8235
    {'conductor': 672, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '672.b4', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 1668953
    {'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [64, 3, 61, 2], [7, 6, 162, 163], [64, 155, 25, 54], [161, 8, 160, 9], [113, 108, 110, 23], [73, 8, 124, 33], [1, 4, 4, 17]], 'adelic_image': '168.48.0.?', 'conductor': 672, 'lmfdb_label': '672.b4', 'prime': 0}
  • id: 3047
    {'conductor': 672, 'elladic_image': '4.12.0.7', 'lmfdb_label': '672.b4', 'modell_image': '2B', '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}