Elliptic curve data - 187200.hx1

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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': '187200mk', 'Clabel': '187200mk3', 'Cnumber': 3, 'abc_quality': 0.9697774643830833, 'absD': 7675442012160000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1560, 'ainvs': [0, 0, 0, -6962700, 7070294000], 'analytic_rank': 2, 'bad_primes': [2, 3, 5, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 187200, 'degree': 4718592, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.6207784142397780511037157021', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 205, 'isogeny_degrees': [1, 2, 4], 'jinv': [12501706118329, 2570490], 'lmfdb_iso': '187200.hx', 'lmfdb_label': '187200.hx1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -483, -4293], 'min_quad_twist_disc': -120, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0-4.c.1.1', '40.12.0.v.1', '60.12.0-4.c.1.1', '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': 19, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '1.8314384686013673571399187347', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 225], [3, 8, 20800], [5, 18, 7488], [13, 14, 14400]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.22703254284875505397986523484', 'prec': 103}, 'szpiro_ratio': 4.850260496367497, '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, 0, 0, -1, 0, 0, 0, -6, 0, 0, 0], 'aplist': [0, 0, 0, 0, 0, -1, -6, 0, -4, -10, 0, -6, -2, -4, 0, 6, 0, -6, 4, -16, 2, 0, -4, 6, -14], '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.hx', 'trace_hash': 1839516722211228923}
• 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': '0.0052920116649031772053024130846', 'prec': 110}, 'conductor': 187200, 'gens': [[1630, 7200, 1], [1480, 2700, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.0305565357134011534646330280', 'prec': 100}, {'__RealLiteral__': 0, 'data': '1.7774993117573511386549698601', 'prec': 100}], 'lmfdb_label': '187200.hx1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.22775624385087621341547934468', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '13.347889486484746342144090706272360273', 'prec': 130}, 'tamagawa_product': 128, 'torsion_generators': [[1540, 0, 1]], 'xcoord_integral_points': [-2210, -995, 1246, 1480, 1540, 1630, 1640, 3061, 3230, 2276830]}
• lmfdb_label 187200.hx1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8254324
    {'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '187200.hx1', 'torsion': [4]}
  • id: 8254322
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '187200.hx1', 'torsion': [2, 2]}
  • id: 8254323
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '187200.hx1', 'torsion': [4]}
  • id: 8254325
    {'degree': 4, 'field': [1, 0, -8, 0, 1], 'lmfdb_label': '187200.hx1', 'torsion': [2, 4]}
  • id: 8254329
    {'degree': 8, 'field': [-86700, 0, -39090, 0, 4140, 0, 130, 0, 1], 'lmfdb_label': '187200.hx1', 'torsion': [6]}
  • id: 8254326
    {'degree': 8, 'field': [186, -696, 772, -168, 125, -52, 22, -4, 1], 'lmfdb_label': '187200.hx1', 'torsion': [2, 4]}
  • id: 8254328
    {'degree': 8, 'field': [2401, 0, -980, 0, 432, 0, -20, 0, 1], 'lmfdb_label': '187200.hx1', 'torsion': [8]}
  • id: 8254327
    {'degree': 8, 'field': [3760, 1760, -3040, -1120, 691, 142, -61, -2, 1], 'lmfdb_label': '187200.hx1', 'torsion': [8]}
  • id: 8254331
    {'degree': 16, 'field': [1296, 0, -15120, 0, 53676, 0, -72060, 0, 39721, 0, -9960, 0, 1166, 0, -60, 0, 1], 'lmfdb_label': '187200.hx1', 'torsion': [2, 8]}
  • id: 8254330
    {'degree': 16, 'field': [2116, 14720, 51200, 104000, 118436, 44560, 0, -9920, -459, 1160, 800, -80, -54, -40, 0, 0, 1], 'lmfdb_label': '187200.hx1', 'torsion': [4, 4]}
  • id: 8254334
    {'degree': 16, 'field': [34594785, 15946380, -149867400, 128957280, -31880420, -11749860, 4797216, 424264, -384894, -67284, -13080, 6360, 2472, -212, -72, 0, 1], 'lmfdb_label': '187200.hx1', 'torsion': [12]}
  • id: 8254332
    {'degree': 16, 'field': [134792100, 0, 11143440, 0, 2220724, 0, 22512, 0, 44805, 0, 2540, 0, -60, 0, 12, 0, 1], 'lmfdb_label': '187200.hx1', 'torsion': [2, 8]}
  • id: 8254333
    {'degree': 16, 'field': [183605400, 112464000, -105104100, -12884160, 2260050, 3928200, 361761, -1149288, -47360, 193810, -10547, -14012, 1213, 490, -50, -8, 1], 'lmfdb_label': '187200.hx1', 'torsion': [2, 6]}
  • id: 8254335
    {'degree': 16, 'field': [1778899329, 0, -680463288, 0, 388412380, 0, -67891656, 0, 4647750, 0, -192904, 0, 6108, 0, -120, 0, 1], 'lmfdb_label': '187200.hx1', '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: 4633224
    {'conductor': 187200, 'conductor_valuation': 6, 'discriminant_valuation': 19, 'j_denominator_valuation': 1, 'kodaira_symbol': -13, 'lmfdb_label': '187200.hx1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 4633225
    {'conductor': 187200, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '187200.hx1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4633226
    {'conductor': 187200, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '187200.hx1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 4633227
    {'conductor': 187200, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '187200.hx1', 'prime': 13, 'reduction_type': -1, '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: 2866516
    {'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [1232, 447, 333, 866], [1243, 1236, 762, 1501], [1553, 8, 1552, 9], [7, 6, 1554, 1555], [1081, 528, 684, 553], [824, 1557, 1035, 518], [1039, 0, 0, 1559]], 'adelic_image': '1560.48.0.?', 'conductor': 187200, 'lmfdb_label': '187200.hx1', 'prime': 0}
  • id: 699232
    {'conductor': 187200, 'elladic_image': '4.6.0.1', 'lmfdb_label': '187200.hx1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 187200.hx does not appear in ec_padic