Elliptic curve data - 48672.bu2

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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': '48672r', 'Clabel': '48672r3', 'Cnumber': 3, 'abc_quality': 1.027047455683347, 'absD': 43238323335168, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 312, 'ainvs': [0, 0, 0, -26364, 1616992], 'analytic_rank': 0, 'bad_primes': [2, 3, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 48672, 'degree': 147456, 'elladic_images': ['8.12.0.11'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4055604525616570653387515775', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 2, 'iso_nlabel': 46, 'isogeny_degrees': [1, 2, 4], 'jinv': [140608, 3], 'lmfdb_iso': '48672.bu', 'lmfdb_label': '48672.bu2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -17, 33], 'min_quad_twist_disc': 156, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.m.1', '12.12.0.h.1', '24.24.0.bk.1', '52.12.0-4.c.1.2', '104.24.0.?', '156.24.0.?', '312.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 1521], [3, 8, 5408], [13, 86, 288]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1193675510631114578028468832', 'prec': 103}, 'szpiro_ratio': 3.905625602763272, '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, 2, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 6, 0, 4, 0], 'aplist': [0, 0, 2, 4, 4, 0, 6, 4, 0, -2, -4, 2, 2, 4, 8, -10, -4, 6, -4, -16, 6, 4, 12, 10, 14], 'class_deg': 4, 'class_size': 4, 'conductor': 48672, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '48672.bu', 'trace_hash': 1637110442028526045}
• 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': '0.060137546115452303142833192161', 'prec': 107}, 'conductor': 48672, 'gens': [], 'heights': [], 'lmfdb_label': '48672.bu2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.64120269099387643112619588085', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.1296215279510114490095670467845994504', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[104, 0, 1]], 'xcoord_integral_points': [104]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '13': 'a'}, 'iwp0': 3, 'lmfdb_label': '48672.bu2'}
• ec_torsion_growth •

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

  
  
  • id: 2369802
    {'degree': 2, 'field': [-39, 0, 1], 'lmfdb_label': '48672.bu2', 'torsion': [4]}
  • id: 2369801
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '48672.bu2', 'torsion': [4]}
  • id: 2369800
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '48672.bu2', 'torsion': [2, 2]}
  • id: 2369803
    {'degree': 4, 'field': [-3, 12, -11, -2, 1], 'lmfdb_label': '48672.bu2', 'torsion': [2, 4]}
  • id: 2369807
    {'degree': 8, 'field': [-4239, 11984, -13586, 5856, -1336, 88, 30, -4, 1], 'lmfdb_label': '48672.bu2', 'torsion': [6]}
  • id: 2369805
    {'degree': 8, 'field': [3, 96, 30, -228, 55, 68, -18, -4, 1], 'lmfdb_label': '48672.bu2', 'torsion': [8]}
  • id: 2369804
    {'degree': 8, 'field': [286, 468, 322, 96, 51, -12, 10, 0, 1], 'lmfdb_label': '48672.bu2', 'torsion': [2, 4]}
  • id: 2369806
    {'degree': 8, 'field': [17956, 0, 2296, 0, 360, 0, 28, 0, 1], 'lmfdb_label': '48672.bu2', 'torsion': [8]}
  • id: 2369813
    {'degree': 16, 'field': [-7590896, 23271168, -15311696, -663472, -2010464, 845024, 238416, 36968, -33942, -29524, -7548, -2680, -56, -76, 10, 0, 1], 'lmfdb_label': '48672.bu2', 'torsion': [12]}
  • id: 2369809
    {'degree': 16, 'field': [433, 3132, -11028, -13500, 42976, 9648, -51336, 324, 26289, -1344, -6588, 252, 826, -12, -48, 0, 1], 'lmfdb_label': '48672.bu2', 'torsion': [2, 8]}
  • id: 2369812
    {'degree': 16, 'field': [5589, -14184, 5520, 79896, -180114, 124392, 26652, -49248, 2287, 4696, 724, -512, -218, 112, 4, -8, 1], 'lmfdb_label': '48672.bu2', 'torsion': [12]}
  • id: 2369810
    {'degree': 16, 'field': [16657, -50940, 74836, -57684, -7888, 46824, -18768, -11724, 10217, 864, -2556, 156, 410, -12, -32, 0, 1], 'lmfdb_label': '48672.bu2', 'torsion': [2, 8]}
  • id: 2369808
    {'degree': 16, 'field': [22932, 58968, 42156, 24840, 47982, 25704, 12018, 10008, 6697, 492, 2158, -96, 336, -12, 28, 0, 1], 'lmfdb_label': '48672.bu2', 'torsion': [4, 4]}
  • id: 2369811
    {'degree': 16, 'field': [26604964, 55025544, 9829768, -5451256, -8595008, -5298376, -1980984, -901552, -183954, -76756, -2364, -3688, 628, -76, 46, 0, 1], 'lmfdb_label': '48672.bu2', '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: 1163266
    {'conductor': 48672, 'conductor_valuation': 5, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '48672.bu2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1163267
    {'conductor': 48672, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '48672.bu2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1163268
    {'conductor': 48672, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '48672.bu2', 'prime': 13, 'reduction_type': 0, '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: 1988180
    {'adelic_gens': [[40, 299, 195, 196], [7, 6, 306, 307], [1, 0, 8, 1], [167, 0, 0, 311], [220, 143, 65, 90], [131, 78, 26, 131], [1, 8, 0, 1], [1, 4, 4, 17], [305, 8, 304, 9]], 'adelic_image': '312.48.0.?', 'conductor': 48672, 'lmfdb_label': '48672.bu2', 'prime': 0}
  • id: 209843
    {'conductor': 48672, 'elladic_image': '8.12.0.11', 'lmfdb_label': '48672.bu2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 48672.bu does not appear in ec_padic