Elliptic curve data - 178752.hn2

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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': '178752gm', 'Clabel': '178752gm5', 'Cnumber': 5, 'abc_quality': 1.0385639997055625, 'absD': 5919417084886034298175488, 'adelic_genus': 21, 'adelic_index': 864, 'adelic_level': 9576, 'ainvs': [0, 1, 0, -1918198753, 32335314318719], 'analytic_rank': 2, 'bad_primes': [2, 3, 7, 19], 'class_deg': 18, 'class_size': 6, 'cm': 0, 'conductor': 178752, 'degree': 95551488, 'elladic_images': ['2.3.0.1', '9.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.9283354910875339680780018367', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 9, 'iso_nlabel': 195, 'isogeny_degrees': [1, 2, 3, 6, 9, 18], 'jinv': [25309080274342544331625, 191933498523648], 'lmfdb_iso': '178752.hn', 'lmfdb_label': '178752.hn2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -611671, -184179718], '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', '9.12.0.a.1', '18.36.0.a.1', '24.24.0-6.a.1.15', '28.6.0.b.1', '72.72.0.?', '84.24.0.?', '114.24.0.?', '168.48.0.?', '252.72.1.?', '342.72.1.?', '456.48.0.?', '504.144.1.?', '1197.36.0.?', '1368.144.1.?', '1596.48.1.?', '2394.216.7.?', '3192.96.1.?', '4788.432.21.?', '9576.864.21.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '55.736733209642157239418534040', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 2793], [3, 4, 59584], [7, 32, 3648], [19, 20, 9408]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.9156596457199593513994772828', 'prec': 100}, 'szpiro_ratio': 6.262534880935944, '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, -6, 0, -4, 0, 0, 0, 0, 0, 1, 0], 'aplist': [0, 1, 0, 0, -6, -4, 0, 1, 6, -6, 4, -2, 6, -8, -12, -6, -12, -10, -14, -12, -2, -10, 12, -18, -8], 'class_deg': 18, 'class_size': 6, 'conductor': 178752, 'isogeny_matrix': [[1, 2, 3, 6, 9, 18], [2, 1, 6, 3, 18, 9], [3, 6, 1, 2, 3, 6], [6, 3, 2, 1, 6, 3], [9, 18, 3, 6, 1, 2], [18, 9, 6, 3, 2, 1]], 'lmfdb_iso': '178752.hn', 'trace_hash': 343408202781376957}
• 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': '0.00038716059293921456952508987917', 'prec': 113}, 'conductor': 178752, 'gens': [[26602, 365295, 1], [2510701, 47044851, 10]], 'heights': [{'__RealLiteral__': 0, 'data': '5.8514509825626068807188477238', 'prec': 100}, {'__RealLiteral__': 0, 'data': '9.8251094379532300528409620201', 'prec': 100}], 'lmfdb_label': '178752.hn2', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.067885150701542807753389058161', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '15.134786134192974405661745956784548613', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-50573, 0, 1]], 'xcoord_integral_points': [-50573, 26602]}
• lmfdb_label 178752.hn2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7916018
    {'degree': 2, 'field': [-42, 0, 1], 'lmfdb_label': '178752.hn2', 'torsion': [6]}
  • id: 7916017
    {'degree': 2, 'field': [-14, -1, 1], 'lmfdb_label': '178752.hn2', 'torsion': [2, 2]}
  • id: 7916019
    {'degree': 4, 'field': [57, 0, 16, 0, 1], 'lmfdb_label': '178752.hn2', 'torsion': [4]}
  • id: 7916020
    {'degree': 4, 'field': [742, 112, -111, -2, 1], 'lmfdb_label': '178752.hn2', 'torsion': [2, 6]}
  • id: 7916021
    {'degree': 6, 'field': [181944, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '178752.hn2', 'torsion': [6]}
  • id: 7916022
    {'degree': 6, 'field': [3208618, 1597596, 164493, -5852, -924, 0, 1], 'lmfdb_label': '178752.hn2', 'torsion': [18]}
  • id: 7916025
    {'degree': 8, 'field': [324, 0, 12, 0, 61, 0, -4, 0, 1], 'lmfdb_label': '178752.hn2', 'torsion': [12]}
  • id: 7916023
    {'degree': 8, 'field': [13456, 0, 8992, 0, 1305, 0, 64, 0, 1], 'lmfdb_label': '178752.hn2', 'torsion': [2, 4]}
  • id: 7916024
    {'degree': 8, 'field': [802816, 0, -36736, 0, -132, 0, -16, 0, 1], 'lmfdb_label': '178752.hn2', 'torsion': [2, 4]}
  • id: 7916027
    {'degree': 12, 'field': [28550977, 47441016, 25767336, 3908436, -159852, 239904, 70870, 0, 2940, -204, 84, 0, 1], 'lmfdb_label': '178752.hn2', 'torsion': [18]}
  • id: 7916028
    {'degree': 12, 'field': [30658369, 0, -13195896, 0, 1749300, 0, 49294, 0, 2940, 0, 84, 0, 1], 'lmfdb_label': '178752.hn2', 'torsion': [2, 6]}
  • id: 7916029
    {'degree': 12, 'field': [9343654768, 13641905760, -45303182064, 398423312, 2554208496, -43637832, -46694844, 435708, 353241, -532, -1050, 0, 1], 'lmfdb_label': '178752.hn2', 'torsion': [2, 18]}
  • id: 7916026
    {'degree': 12, 'field': [33103983025, -1091670, -2729139, 7277710, -2729070, -1091790, 364029, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '178752.hn2', 'torsion': [3, 6]}
  • id: 7916030
    {'degree': 16, 'field': [262248, -590352, 1475880, 576240, 401324, 249872, 151928, 31136, 2942, 1452, -910, -476, 147, 84, -14, -4, 1], 'lmfdb_label': '178752.hn2', 'torsion': [8]}
  • id: 7916031
    {'degree': 16, 'field': [19027044, 0, 8331108, 0, 2557717, 0, 164796, 0, 22719, 0, -1972, 0, 15, 0, -12, 0, 1], 'lmfdb_label': '178752.hn2', 'torsion': [2, 12]}
  • id: 7916032
    {'degree': 16, 'field': [683548432, 1719253200, -71389836, -1034885880, -406997198, 91474572, 101686920, 20190240, -3514689, -1987860, -165336, 48888, 9214, -336, -156, 0, 1], 'lmfdb_label': '178752.hn2', '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: 4424272
    {'conductor': 178752, 'conductor_valuation': 6, 'discriminant_valuation': 54, 'j_denominator_valuation': 36, 'kodaira_symbol': -48, 'lmfdb_label': '178752.hn2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 4424273
    {'conductor': 178752, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '178752.hn2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 4424274
    {'conductor': 178752, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '178752.hn2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4424275
    {'conductor': 178752, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '178752.hn2', '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: 2815001
    {'adelic_gens': [[4787, 0, 0, 9575], [1, 36, 0, 1], [9557, 9540, 6336, 8225], [2692, 27, 877, 3134], [2077, 36, 678, 265], [1, 18, 14, 253], [9541, 36, 9540, 37], [7181, 9540, 0, 9575], [4823, 9540, 4824, 9539], [4036, 9, 3103, 178], [19, 36, 3240, 6139], [1, 0, 36, 1]], 'adelic_image': '9576.864.21.?', 'conductor': 178752, 'lmfdb_label': '178752.hn2', 'prime': 0}
  • id: 671500
    {'conductor': 178752, 'elladic_image': '2.3.0.1', 'lmfdb_label': '178752.hn2', 'modell_image': '2B', 'prime': 2}
  • id: 671501
    {'conductor': 178752, 'elladic_image': '9.12.0.1', 'lmfdb_label': '178752.hn2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 178752.hn does not appear in ec_padic