Elliptic curve data - 187200.pq4

Formats: - HTML - YAML - JSON - 2025-09-27T17:56:28.264703

• 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': '187200qm', 'Clabel': '187200qm1', 'Cnumber': 1, 'abc_quality': 0.949724584751915, 'absD': 388752998400000000, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 1560, 'ainvs': [0, 0, 0, 155700, -18458000], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 13], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 187200, 'degree': 2654208, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0623674848537869913183698430', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 406, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [3774555693, 3515200], 'lmfdb_iso': '187200.pq', 'lmfdb_label': '187200.pq4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, 876, 7568], 'min_quad_twist_disc': -120, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '12.24.0-6.a.1.8', '78.24.0.?', '120.48.0.?', '156.48.0.?', '520.6.0.?', '1560.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 975], [3, 6, 1600], [5, 18, 7488], [13, 14, 14400]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.056725314370208582956669315031', 'prec': 110}, 'szpiro_ratio': 3.9111140662913555, '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, 4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 6, 0, 4, 0], 'aplist': [0, 0, 0, 4, 0, 1, 6, 4, -6, 6, -10, -10, -6, -4, -12, 12, 12, 10, 14, 0, 16, 8, 12, 6, -8], 'class_deg': 6, 'class_size': 4, 'conductor': 187200, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '187200.pq', 'trace_hash': 881271446071324015}
• 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': '0.016167778971583819816870604364', 'prec': 107}, 'conductor': 187200, 'gens': [], 'heights': [], 'lmfdb_label': '187200.pq4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.16441341459072015851794239500', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.9459219501772838044306174800980083141', 'prec': 130}, 'tamagawa_product': 96, 'torsion_generators': [[110, 0, 1]], 'xcoord_integral_points': [110]}
• lmfdb_label 187200.pq4 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8256085
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '187200.pq4', 'torsion': [6]}
  • id: 8256084
    {'degree': 2, 'field': [10, -1, 1], 'lmfdb_label': '187200.pq4', 'torsion': [2, 2]}
  • id: 8256086
    {'degree': 4, 'field': [-39, 0, 42, 0, 1], 'lmfdb_label': '187200.pq4', 'torsion': [4]}
  • id: 8256087
    {'degree': 4, 'field': [390, 0, 1, -2, 1], 'lmfdb_label': '187200.pq4', 'torsion': [2, 6]}
  • id: 8256088
    {'degree': 6, 'field': [1080, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '187200.pq4', 'torsion': [6]}
  • id: 8256091
    {'degree': 8, 'field': [36, 0, -252, 0, 93, 0, 18, 0, 1], 'lmfdb_label': '187200.pq4', 'torsion': [12]}
  • id: 8256089
    {'degree': 8, 'field': [105625, 0, 4030, 0, 66, 0, -2, 0, 1], 'lmfdb_label': '187200.pq4', 'torsion': [2, 4]}
  • id: 8256090
    {'degree': 8, 'field': [126850, -14200, 14725, -1060, 556, -34, 16, -4, 1], 'lmfdb_label': '187200.pq4', 'torsion': [2, 4]}
  • id: 8256092
    {'degree': 12, 'field': [1521, 234, 621, -1650, 690, 114, 61, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '187200.pq4', 'torsion': [3, 6]}
  • id: 8256093
    {'degree': 12, 'field': [6553600, 0, 0, 0, 0, 0, 4600, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '187200.pq4', 'torsion': [2, 6]}
  • id: 8256095
    {'degree': 16, 'field': [531856, 1564160, 2061552, 1348768, 257556, -348912, -303872, -24992, 84600, 11816, -2840, -3408, 501, 128, -6, -8, 1], 'lmfdb_label': '187200.pq4', 'torsion': [2, 12]}
  • id: 8256096
    {'degree': 16, 'field': [6051600, 4575600, 1024020, -3709980, -350301, 299022, 792075, -521574, 163495, -76764, 37882, -10704, 1941, -378, 67, -6, 1], 'lmfdb_label': '187200.pq4', 'torsion': [2, 12]}
  • id: 8256094
    {'degree': 16, 'field': [37442161, 0, -246889672, 0, -13103752, 0, -2226184, 0, -76190, 0, -35624, 0, -712, 0, 88, 0, 1], 'lmfdb_label': '187200.pq4', 'torsion': [8]}
  • id: 8256097
    {'degree': 18, 'field': [-67600000, 0, 60840000, 0, -39156000, 0, 24500100, 0, -10251000, 0, 2348400, 0, -284460, 0, 16200, 0, -240, 0, 1], 'lmfdb_label': '187200.pq4', '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: 4634036
    {'conductor': 187200, 'conductor_valuation': 6, 'discriminant_valuation': 24, 'j_denominator_valuation': 6, 'kodaira_symbol': -18, 'lmfdb_label': '187200.pq4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 4634037
    {'conductor': 187200, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '187200.pq4', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4634038
    {'conductor': 187200, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '187200.pq4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 4634039
    {'conductor': 187200, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '187200.pq4', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
• ec_galrep •

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

  
  
  • id: 2866921
    {'adelic_gens': [[1450, 3, 453, 1552], [779, 1548, 1554, 1487], [1239, 1498, 86, 341], [272, 11, 1005, 1528], [1, 0, 12, 1], [623, 1548, 618, 1487], [1, 6, 6, 37], [1, 12, 0, 1], [11, 2, 1510, 1551], [1549, 12, 1548, 13]], 'adelic_image': '1560.96.1.?', 'conductor': 187200, 'lmfdb_label': '187200.pq4', 'prime': 0}
  • id: 699582
    {'conductor': 187200, 'elladic_image': '2.3.0.1', 'lmfdb_label': '187200.pq4', 'modell_image': '2B', 'prime': 2}
  • id: 699583
    {'conductor': 187200, 'elladic_image': '3.4.0.1', 'lmfdb_label': '187200.pq4', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 187200.pq does not appear in ec_padic