Elliptic curve data - 177870.hb4

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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': '177870bo', 'Clabel': '177870bo4', 'Cnumber': 4, 'abc_quality': 0.9949953764457301, 'absD': 290163032280154687500, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1848, 'ainvs': [1, 0, 0, 696534, 788480496], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 177870, 'degree': 8847360, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.6078961070419356927502635760', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 183, 'isogeny_degrees': [1, 2, 4], 'jinv': [179310732119, 1392187500], 'lmfdb_iso': '177870.hb', 'lmfdb_label': '177870.hb4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 118, 1776], 'min_quad_twist_disc': 77, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '22.6.0.a.1', '24.12.0.ba.1', '28.12.0-4.c.1.1', '44.12.0.g.1', '168.24.0.?', '264.24.0.?', '308.24.0.?', '1848.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '5.9086653737788186742059848647', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 5929], [3, 4, 59290], [5, 6, 35574], [7, 26, 3630], [11, 72, 1470]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.43599339611509376816661541530', 'prec': 103}, 'szpiro_ratio': 4.507825233219929, '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, 1, 1, 1, -1, 1, 0, 1, 1, -1, 0, 1, -2, 0, -1, 1, -2, 1, -8, -1], 'aplist': [1, 1, -1, 0, 0, -2, -2, -8, 0, -2, 8, -10, -10, 0, 0, 14, 4, 14, -4, 8, 10, -12, 4, 6, 14], 'class_deg': 4, 'class_size': 4, 'conductor': 177870, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '177870.hb', 'trace_hash': 1913354456458848396}
• 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': '0.0054301299466265163348631611212', 'prec': 110}, 'conductor': 177870, 'gens': [[-2216, 665824, 3]], 'heights': [{'__RealLiteral__': 0, 'data': '5.9086653737788186742059848647', 'prec': 100}], 'lmfdb_label': '177870.hb4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.12629515662054169939910851867', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '11.939773100796279458878958553396180389', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[-2721, 2721, 2]], 'xcoord_integral_points': []}
• lmfdb_label 177870.hb4 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7879055
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '177870.hb4', 'torsion': [4]}
  • id: 7879054
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '177870.hb4', 'torsion': [2, 2]}
  • id: 7879056
    {'degree': 2, 'field': [77, 0, 1], 'lmfdb_label': '177870.hb4', 'torsion': [4]}
  • id: 7879057
    {'degree': 4, 'field': [93, 8, -7, -2, 1], 'lmfdb_label': '177870.hb4', 'torsion': [2, 4]}
  • id: 7879061
    {'degree': 8, 'field': [-239769, -90270, 4632, 6108, 492, -94, -12, 0, 1], 'lmfdb_label': '177870.hb4', 'torsion': [6]}
  • id: 7879059
    {'degree': 8, 'field': [729, 0, -32832, 0, 118, 0, 16, 0, 1], 'lmfdb_label': '177870.hb4', 'torsion': [8]}
  • id: 7879060
    {'degree': 8, 'field': [1446, 1116, 388, 98, 71, -10, -4, -4, 1], 'lmfdb_label': '177870.hb4', 'torsion': [8]}
  • id: 7879058
    {'degree': 8, 'field': [1996, 848, -736, -232, 137, -28, 14, -4, 1], 'lmfdb_label': '177870.hb4', 'torsion': [2, 4]}
  • id: 7879063
    {'degree': 16, 'field': [3600, 0, -1392, 0, 4408, 0, -3084, 0, 2289, 0, -836, 0, 222, 0, -24, 0, 1], 'lmfdb_label': '177870.hb4', 'torsion': [2, 8]}
  • id: 7879062
    {'degree': 16, 'field': [15876, 0, -504, 0, 65272, 0, -2988, 0, 5405, 0, -384, 0, 26, 0, -12, 0, 1], 'lmfdb_label': '177870.hb4', 'torsion': [4, 4]}
  • id: 7879064
    {'degree': 16, 'field': [531441, 0, 519048, 0, -477206, 0, 856224, 0, 1770507, 0, 95776, 0, 3834, 0, 72, 0, 1], 'lmfdb_label': '177870.hb4', 'torsion': [2, 8]}
  • id: 7879066
    {'degree': 16, 'field': [1360281924, 0, 407752056, 0, 49370580, 0, 2675597, 0, 16790, 0, -16543, 0, -995, 0, -14, 0, 1], 'lmfdb_label': '177870.hb4', 'torsion': [12]}
  • id: 7879065
    {'degree': 16, 'field': [2680062540, -2988244152, 2178136536, -854696276, 159527412, 20177176, -11407009, 3214192, -291994, 14708, 54959, 296, -1463, -64, -2, 0, 1], 'lmfdb_label': '177870.hb4', 'torsion': [2, 6]}
  • id: 7879067
    {'degree': 16, 'field': [6377619600, 0, 16187558112, 0, 2052961020, 0, 144492029, 0, 9133322, 0, 407165, 0, 10285, 0, 154, 0, 1], 'lmfdb_label': '177870.hb4', 'torsion': [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: 4401895
    {'conductor': 177870, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '177870.hb4', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4401896
    {'conductor': 177870, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '177870.hb4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4401897
    {'conductor': 177870, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '177870.hb4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4401898
    {'conductor': 177870, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '177870.hb4', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4401899
    {'conductor': 177870, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '177870.hb4', 'prime': 11, 'reduction_type': 0, '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: 2809733
    {'adelic_gens': [[263, 0, 0, 1847], [1841, 8, 1840, 9], [1163, 364, 938, 1821], [1555, 1554, 1498, 43], [1, 0, 8, 1], [160, 525, 595, 790], [617, 1064, 1148, 561], [7, 6, 1842, 1843], [1, 8, 0, 1], [1, 4, 4, 17]], 'adelic_image': '1848.48.0.?', 'conductor': 177870, 'lmfdb_label': '177870.hb4', 'prime': 0}
  • id: 668724
    {'conductor': 177870, 'elladic_image': '4.6.0.1', 'lmfdb_label': '177870.hb4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 177870.hb does not appear in ec_padic