Elliptic curve data - 187200.hg4

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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': '187200ma', 'Clabel': '187200ma1', 'Cnumber': 1, 'abc_quality': 1.069422794221752, 'absD': 562166163000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1560, 'ainvs': [0, 0, 0, -20775, 164500], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 187200, 'degree': 786432, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5201678526205137486849691732', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 188, 'isogeny_degrees': [1, 2, 4], 'jinv': [1360251712, 771147], 'lmfdb_iso': '187200.hg', 'lmfdb_label': '187200.hg4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -369, 513], 'min_quad_twist_disc': 120, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '12.12.0.h.1', '40.12.0-4.c.1.2', '104.12.0.?', '120.24.0.?', '312.24.0.?', '520.24.0.?', '1560.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.1968631073775867959549582633', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 225], [3, 6, 20800], [5, 14, 7488], [13, 14, 14400]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.18043083821056393902164917260', 'prec': 107}, 'szpiro_ratio': 3.4133730744400905, '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, 0, 0, 0, 0, 0, 0, -4, 0, 1, 0, 0, 0, -6, 0, -8, 0], 'aplist': [0, 0, 0, 0, -4, 1, -6, -8, -8, 2, -8, -10, -6, 4, 0, 14, 12, 10, 8, 0, 14, 4, 4, 10, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 187200, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '187200.hg', 'trace_hash': 862578469184150237}
• 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': '0.047818833766237995665750303617', 'prec': 107}, 'conductor': 187200, 'gens': [[-16, 702, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.1968631073775867959549582633', 'prec': 100}], 'lmfdb_label': '187200.hg4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.44571299197651064903472625346', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.2676594926045435758255815248900974619', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[140, 0, 1]], 'xcoord_integral_points': [-16, 140, 540]}
• lmfdb_label 187200.hg4 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8253937
    {'degree': 2, 'field': [-30, 0, 1], 'lmfdb_label': '187200.hg4', 'torsion': [4]}
  • id: 8253936
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '187200.hg4', 'torsion': [4]}
  • id: 8253935
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '187200.hg4', 'torsion': [2, 2]}
  • id: 8253938
    {'degree': 4, 'field': [25, 0, -20, 0, 1], 'lmfdb_label': '187200.hg4', 'torsion': [2, 4]}
  • id: 8253942
    {'degree': 8, 'field': [-1875, 0, 0, 0, -150, 0, 80, 0, 1], 'lmfdb_label': '187200.hg4', 'torsion': [6]}
  • id: 8253939
    {'degree': 8, 'field': [4, 0, 88, 0, 60, 0, 16, 0, 1], 'lmfdb_label': '187200.hg4', 'torsion': [2, 4]}
  • id: 8253940
    {'degree': 8, 'field': [5929, 0, -6628, 0, 1290, 0, -76, 0, 1], 'lmfdb_label': '187200.hg4', 'torsion': [8]}
  • id: 8253941
    {'degree': 8, 'field': [11449, 0, 4678, 0, 633, 0, 34, 0, 1], 'lmfdb_label': '187200.hg4', 'torsion': [8]}
  • id: 8253948
    {'degree': 16, 'field': [-11885774, 18820928, -1900644, -10801840, 3644608, 3064488, -1248220, -631832, 252840, 82756, -30172, -6096, 2038, 236, -72, -4, 1], 'lmfdb_label': '187200.hg4', 'torsion': [12]}
  • id: 8253944
    {'degree': 16, 'field': [-177674, 393176, 1555188, -3075680, -1664502, 4164384, 283840, -1776452, 145815, 283100, -34112, -20412, 2598, 668, -84, -8, 1], 'lmfdb_label': '187200.hg4', 'torsion': [2, 8]}
  • id: 8253947
    {'degree': 16, 'field': [-14391, 123132, -281496, 69732, 89994, -99960, -4092, 50812, -18952, 956, -112, -700, 338, 32, -16, -4, 1], 'lmfdb_label': '187200.hg4', 'torsion': [12]}
  • id: 8253943
    {'degree': 16, 'field': [16, 0, -352, 0, 7504, 0, -5152, 0, 2188, 0, -784, 0, 196, 0, -16, 0, 1], 'lmfdb_label': '187200.hg4', 'torsion': [4, 4]}
  • id: 8253946
    {'degree': 16, 'field': [390625, 0, 625000, 0, -1156250, 0, 650000, 0, -180625, 0, 26000, 0, -1850, 0, 40, 0, 1], 'lmfdb_label': '187200.hg4', 'torsion': [2, 6]}
  • id: 8253945
    {'degree': 16, 'field': [12680721, 0, -14716164, 0, 10881304, 0, -2528316, 0, 284334, 0, -12124, 0, 504, 0, -36, 0, 1], 'lmfdb_label': '187200.hg4', 'torsion': [2, 8]}
• 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: 4633092
    {'conductor': 187200, 'conductor_valuation': 6, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '187200.hg4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 4633093
    {'conductor': 187200, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '187200.hg4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4633094
    {'conductor': 187200, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '187200.hg4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4633095
    {'conductor': 187200, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '187200.hg4', 'prime': 13, '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: 2866469
    {'adelic_gens': [[504, 655, 1295, 684], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [109, 1050, 190, 349], [724, 935, 185, 1554], [623, 0, 0, 1559], [1553, 8, 1552, 9], [7, 6, 1554, 1555], [1081, 320, 580, 1281]], 'adelic_image': '1560.48.0.?', 'conductor': 187200, 'lmfdb_label': '187200.hg4', 'prime': 0}
  • id: 699189
    {'conductor': 187200, 'elladic_image': '4.6.0.1', 'lmfdb_label': '187200.hg4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 187200.hg does not appear in ec_padic