Elliptic curve data - 193200.hp1

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '193200bu', 'Clabel': '193200bu4', 'Cnumber': 4, 'abc_quality': 1.0003496450255243, 'absD': 19400479646350118400000000, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 2760, 'ainvs': [0, 1, 0, -192944008, 1009495135988], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 23], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 193200, 'degree': 71663616, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.6363514070299659022137965556', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 6, 'iso_nlabel': 197, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [12411881707829361287041, 303132494474220600], 'lmfdb_iso': '193200.hp', 'lmfdb_label': '193200.hp1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -482360, -126235128], 'min_quad_twist_disc': -20, '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.1.2', '60.48.0-60.t.1.10', '184.6.0.?', '552.48.0.?', '2760.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.1384852702529704054961847675', 'prec': 100}, 'szpiro_ratio': 5.656446711347624, '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, 1, 0, 1, 0, 6, 0, 4, 0, 0, 0, 6, 0, 4, 0], 'aplist': [0, 1, 0, 1, 6, 4, 6, 4, -1, 0, 4, 10, 6, -10, 0, 6, 0, 2, 14, -6, -14, -8, -12, -12, -8], 'class_deg': 6, 'class_size': 4, 'conductor': 193200, 'isogeny_matrix': [[1, 3, 6, 2], [3, 1, 2, 6], [6, 2, 1, 3], [2, 6, 3, 1]], 'lmfdb_iso': '193200.hp', 'trace_hash': 801458099708203505}
• 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': '0.00069423307280669076113581371838', 'prec': 113}, 'conductor': 193200, 'gens': [], 'heights': [], 'lmfdb_label': '193200.hp1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.068450572707301607494124429897', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.5712549799009543194359452700839560518', 'prec': 130}, 'tamagawa_product': 384, 'torsion_generators': [[7043, 0, 1]], 'xcoord_integral_points': [7043]}
• lmfdb_label 193200.hp1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8499439
    {'degree': 2, 'field': [-46, 0, 1], 'lmfdb_label': '193200.hp1', 'torsion': [2, 2]}
  • id: 8499440
    {'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '193200.hp1', 'torsion': [6]}
  • id: 8499441
    {'degree': 4, 'field': [6, 6, 7, -1, 1], 'lmfdb_label': '193200.hp1', 'torsion': [4]}
  • id: 8499442
    {'degree': 4, 'field': [961, 0, -122, 0, 1], 'lmfdb_label': '193200.hp1', 'torsion': [2, 6]}
  • id: 8499443
    {'degree': 6, 'field': [405, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '193200.hp1', 'torsion': [6]}
  • id: 8499446
    {'degree': 8, 'field': [36, 0, -48, 0, 73, 0, -13, 0, 1], 'lmfdb_label': '193200.hp1', 'torsion': [12]}
  • id: 8499444
    {'degree': 8, 'field': [2025, 0, 1230, 0, 199, 0, 34, 0, 1], 'lmfdb_label': '193200.hp1', 'torsion': [2, 4]}
  • id: 8499445
    {'degree': 8, 'field': [13225, 0, -74060, 0, 3956, 0, -92, 0, 1], 'lmfdb_label': '193200.hp1', 'torsion': [2, 4]}
  • id: 8499447
    {'degree': 12, 'field': [196, 84, 246, -650, 315, -36, 111, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '193200.hp1', 'torsion': [3, 6]}
  • id: 8499448
    {'degree': 12, 'field': [9553303081, 0, -1210068456, 0, 67720740, 0, -1945910, 0, 31740, 0, -276, 0, 1], 'lmfdb_label': '193200.hp1', 'torsion': [2, 6]}
  • id: 8499450
    {'degree': 16, 'field': [239121, -803916, 1351368, 544992, 247786, -232164, 1248, -50276, -1333, 316, 3296, -356, 90, 72, 8, -4, 1], 'lmfdb_label': '193200.hp1', 'torsion': [2, 12]}
  • id: 8499451
    {'degree': 16, 'field': [5809640841, 0, -8830901772, 0, 321717366, 0, 14825448, 0, 5166775, 0, 4432, 0, -3414, 0, -68, 0, 1], 'lmfdb_label': '193200.hp1', 'torsion': [2, 12]}
  • id: 8499449
    {'degree': 16, 'field': [132263846412156, -9903394313136, -12989177761680, 548522072448, 610863319648, -17364229408, -16251513904, 541845792, 238983175, -7131404, -2159048, 15688, 23617, -468, -82, -4, 1], 'lmfdb_label': '193200.hp1', 'torsion': [8]}
  • id: 8499452
    {'degree': 18, 'field': [-1443366388681875, 492154591005000, -94652687193750, -13617039350250, 11948892795000, -73179429750, -262854267075, 25719310350, 10267676775, 556912740, 385621380, -45849510, -10624781, 401178, 137304, -814, -699, 0, 1], 'lmfdb_label': '193200.hp1', '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: 4783934
    {'conductor': 193200, 'conductor_valuation': 4, 'discriminant_valuation': 15, 'j_denominator_valuation': 3, 'kodaira_symbol': -11, 'lmfdb_label': '193200.hp1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4783935
    {'conductor': 193200, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '193200.hp1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4783936
    {'conductor': 193200, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '193200.hp1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 4783937
    {'conductor': 193200, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '193200.hp1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
  • id: 4783938
    {'conductor': 193200, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '193200.hp1', 'prime': 23, '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: 2904211
    {'adelic_gens': [[10, 3, 1353, 2752], [1841, 12, 466, 73], [2749, 12, 2748, 13], [1, 0, 12, 1], [1494, 1943, 115, 574], [1103, 2748, 1098, 2687], [1, 6, 6, 37], [1, 12, 0, 1], [11, 2, 2710, 2751], [970, 3, 693, 2752]], 'adelic_image': '2760.96.1.?', 'conductor': 193200, 'lmfdb_label': '193200.hp1', 'prime': 0}
  • id: 719642
    {'conductor': 193200, 'elladic_image': '2.3.0.1', 'lmfdb_label': '193200.hp1', 'modell_image': '2B', 'prime': 2}
  • id: 719643
    {'conductor': 193200, 'elladic_image': '3.4.0.1', 'lmfdb_label': '193200.hp1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 193200.hp does not appear in ec_padic