Elliptic curve data - 178752.hx3

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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': '178752gp', 'Clabel': '178752gp1', 'Cnumber': 1, 'abc_quality': 1.047658380732593, 'absD': 1012571037499392, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 3192, 'ainvs': [0, 1, 0, -25153, -125665], 'analytic_rank': 2, 'bad_primes': [2, 3, 7, 19], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 178752, 'degree': 663552, 'elladic_images': ['8.6.0.4', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5688717469836225221062295047', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 205, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [57066625, 32832], 'lmfdb_iso': '178752.hx', 'lmfdb_label': '178752.hx3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -8, 0], 'min_quad_twist_disc': -56, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '8.6.0.d.1', '24.24.0.bx.1', '84.24.0.?', '114.24.0.?', '168.48.0.?', '456.48.1.?', '1596.48.0.?', '3192.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 13, 'optimality': 1, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '3.1427980998287811087947235404', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 2793], [3, 4, 59584], [7, 26, 3648], [19, 20, 9408]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.44380409838395209457229504921', 'prec': 107}, 'szpiro_ratio': 3.473845911839223, '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, 0, 0, 0, 0, 1, 0, 0, 0, -4, 0, 0, 0, -6, 0, 1, 0], 'aplist': [0, 1, 0, 0, 0, -4, -6, 1, -6, -6, -2, 4, -6, 4, -6, -6, -12, 14, -8, 0, -14, -10, -12, 6, 10], 'class_deg': 6, 'class_size': 4, 'conductor': 178752, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '178752.hx', 'trace_hash': 1599967208035888230}
• 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': '0.043380576073574190302112446325', 'prec': 107}, 'conductor': 178752, 'gens': [[-19, 588, 1], [251, 3072, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.7313265297733042355737503788', 'prec': 100}, {'__RealLiteral__': 0, 'data': '1.9207450356290332653005723803', 'prec': 100}], 'lmfdb_label': '178752.hx3', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.41237705246431064379425248917', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '15.552213802773948809338969524294914868', 'prec': 130}, 'tamagawa_product': 48, 'torsion_generators': [[-5, 0, 1]], 'xcoord_integral_points': [-103, -19, -5, 170, 251, 562, 1787]}
• lmfdb_label 178752.hx3 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7916077
    {'degree': 2, 'field': [-14, -1, 1], 'lmfdb_label': '178752.hx3', 'torsion': [2, 2]}
  • id: 7916078
    {'degree': 2, 'field': [14, 0, 1], 'lmfdb_label': '178752.hx3', 'torsion': [6]}
  • id: 7916079
    {'degree': 4, 'field': [674, -28, 50, 0, 1], 'lmfdb_label': '178752.hx3', 'torsion': [4]}
  • id: 7916080
    {'degree': 4, 'field': [798, 0, 1, -2, 1], 'lmfdb_label': '178752.hx3', 'torsion': [2, 6]}
  • id: 7916081
    {'degree': 6, 'field': [-32928, 0, 2548, 0, -14, 0, 1], 'lmfdb_label': '178752.hx3', 'torsion': [6]}
  • id: 7916084
    {'degree': 8, 'field': [834, -204, 278, -156, 99, -28, 14, -4, 1], 'lmfdb_label': '178752.hx3', 'torsion': [12]}
  • id: 7916083
    {'degree': 8, 'field': [41209, 0, 12894, 0, 1514, 0, 78, 0, 1], 'lmfdb_label': '178752.hx3', 'torsion': [2, 4]}
  • id: 7916082
    {'degree': 8, 'field': [312076, 32912, -30968, -3808, 1705, 236, -74, -4, 1], 'lmfdb_label': '178752.hx3', 'torsion': [2, 4]}
  • id: 7916085
    {'degree': 12, 'field': [7609284, -3696192, 4331796, -1330020, 815095, -188742, 77573, -13086, 3930, -450, 101, -6, 1], 'lmfdb_label': '178752.hx3', 'torsion': [3, 6]}
  • id: 7916086
    {'degree': 12, 'field': [2290232134, 83082956, -85281381, 4534114, -2611799, 418128, -146795, 6402, -1647, 20, 7, -6, 1], 'lmfdb_label': '178752.hx3', 'torsion': [2, 6]}
  • id: 7916087
    {'degree': 16, 'field': [498, 5016, 38364, -138792, 142234, -50120, -1496, 23816, -7133, -56, 3008, -584, -62, 8, 28, -8, 1], 'lmfdb_label': '178752.hx3', 'torsion': [8]}
  • id: 7916089
    {'degree': 16, 'field': [682276, 0, 2028040, 0, 912272, 0, 80700, 0, -3715, 0, 1464, 0, 146, 0, 4, 0, 1], 'lmfdb_label': '178752.hx3', 'torsion': [2, 12]}
  • id: 7916088
    {'degree': 16, 'field': [119489472, 91221984, 88461828, 5097960, 34999906, -693924, 3459456, -137984, 476775, -83916, 60144, -3528, 3222, -56, 84, 0, 1], 'lmfdb_label': '178752.hx3', 'torsion': [2, 12]}
  • id: 7916090
    {'degree': 18, 'field': [11679134688, -1609756416, 13943667888, -6068630016, 4677640488, -1908419184, 844234740, -273831120, 95909220, -22695556, 7093032, -1173456, 336407, -38190, 9723, -728, 153, -6, 1], 'lmfdb_label': '178752.hx3', 'torsion': [18]}
• 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: 4424296
    {'conductor': 178752, 'conductor_valuation': 6, 'discriminant_valuation': 24, 'j_denominator_valuation': 6, 'kodaira_symbol': -18, 'lmfdb_label': '178752.hx3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 4424297
    {'conductor': 178752, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '178752.hx3', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 4424298
    {'conductor': 178752, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '178752.hx3', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4424299
    {'conductor': 178752, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '178752.hx3', 'prime': 19, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 2815026
    {'adelic_gens': [[2794, 1827, 1029, 904], [1, 0, 12, 1], [1, 6, 6, 37], [3181, 12, 3180, 13], [2279, 0, 0, 3191], [1, 12, 0, 1], [386, 1379, 2877, 3172], [1695, 1162, 686, 2885], [1595, 2268, 2730, 839], [11, 2, 3142, 3183]], 'adelic_image': '3192.96.1.?', 'conductor': 178752, 'lmfdb_label': '178752.hx3', 'prime': 0}
  • id: 671532
    {'conductor': 178752, 'elladic_image': '8.6.0.4', 'lmfdb_label': '178752.hx3', 'modell_image': '2B', 'prime': 2}
  • id: 671533
    {'conductor': 178752, 'elladic_image': '3.4.0.1', 'lmfdb_label': '178752.hx3', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 178752.hx does not appear in ec_padic