Elliptic curve data - 7752.a4

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '7752g', 'Clabel': '7752g1', 'Cnumber': 1, 'abc_quality': 1.0788919745794874, 'absD': 33907248, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 2584, 'ainvs': [0, -1, 0, 81, 0], 'analytic_rank': 1, 'bad_primes': [2, 3, 17, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 7752, 'degree': 1792, 'elladic_images': ['8.12.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.13434729043504349719784455604', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [3628156928, 2119203], 'lmfdb_iso': '7752.a', 'lmfdb_label': '7752.a4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 81, 0], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.5', '68.12.0-4.c.1.2', '76.12.0.?', '136.24.0.?', '152.24.0.?', '646.6.0.?', '1292.24.0.?', '2584.48.0.?'], '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': '1.8997996867318776644172653907', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 323], [3, 4, 2584], [17, 18, 456], [19, 20, 408]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.096701769751604939274566151113', 'prec': 110}, 'szpiro_ratio': 2.767462321807856, '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, -2, 0, -4, 0, 1, 0, 0, 0, -2, 0, 2, 0, 1, 0, -1, 0], 'aplist': [0, -1, -2, -4, 0, -2, 1, -1, 4, -6, 8, 2, 6, 4, 0, 14, -4, -2, -12, 0, 2, 16, -12, 10, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 7752, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '7752.a', 'trace_hash': 948884941442157738}
• 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': '0.76437667526006081604329698302', 'prec': 103}, 'conductor': 7752, 'gens': [[1, 9, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.8997996867318776644172653907', 'prec': 100}], 'lmfdb_label': '7752.a4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.2522347484233205979073213228', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.3789951827693961099598630900224335919', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[0, 0, 1]], 'xcoord_integral_points': [0, 1, 81]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [1, 0], '7': [1, 0], '11': [1, 1, 0], '13': [1, 0], '17': [2, 0], '19': [1, 0], '23': [3, 0], '29': [1, 0], '31': [1, 0], '37': [3, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '7752.a4'}
• ec_torsion_growth •

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

  
  
  • id: 405564
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '7752.a4', 'torsion': [4]}
  • id: 405565
    {'degree': 2, 'field': [5, -1, 1], 'lmfdb_label': '7752.a4', 'torsion': [4]}
  • id: 405563
    {'degree': 2, 'field': [81, -1, 1], 'lmfdb_label': '7752.a4', 'torsion': [2, 2]}
  • id: 405567
    {'degree': 4, 'field': [-323, 0, -34, 0, 1], 'lmfdb_label': '7752.a4', 'torsion': [8]}
  • id: 405566
    {'degree': 4, 'field': [81, 0, 1, 0, 1], 'lmfdb_label': '7752.a4', 'torsion': [2, 4]}
  • id: 405571
    {'degree': 8, 'field': [-19683, 0, 324, 0, -486, 0, 0, 0, 1], 'lmfdb_label': '7752.a4', 'torsion': [6]}
  • id: 405568
    {'degree': 8, 'field': [6561, 0, 1130, 0, 2747, 0, -2, 0, 1], 'lmfdb_label': '7752.a4', 'torsion': [2, 4]}
  • id: 405569
    {'degree': 8, 'field': [8100, -3240, 648, -936, 436, 28, 8, -4, 1], 'lmfdb_label': '7752.a4', 'torsion': [8]}
  • id: 405570
    {'degree': 8, 'field': [9929, -866, 1676, -1570, 661, 146, -44, -4, 1], 'lmfdb_label': '7752.a4', 'torsion': [2, 8]}
  • id: 405573
    {'degree': 16, 'field': [390625, 0, 0, 0, -365000, 0, 0, 0, 191166, 0, 0, 0, -584, 0, 0, 0, 1], 'lmfdb_label': '7752.a4', 'torsion': [2, 8]}
  • id: 405572
    {'degree': 16, 'field': [25331089, 0, -24530288, 0, 19723882, 0, 142032, 0, 191643, 0, -6576, 0, 142, 0, -32, 0, 1], 'lmfdb_label': '7752.a4', 'torsion': [4, 4]}
  • id: 405575
    {'degree': 16, 'field': [387420489, 0, 88967160, 0, 286256430, 0, -314928, 0, 197799, 0, 3232, 0, 966, 0, 0, 0, 1], 'lmfdb_label': '7752.a4', 'torsion': [2, 6]}
  • id: 405574
    {'degree': 16, 'field': [627134404, -527145824, -6950616, 521777880, 134281044, -28266072, 12669484, 6778300, -1833483, -330852, 95748, -5364, -4234, -172, -72, -8, 1], 'lmfdb_label': '7752.a4', 'torsion': [16]}
  • id: 405576
    {'degree': 16, 'field': [796554412, -321151864, 314107772, 24887424, -38903224, 30256024, -7631516, -2024616, 403945, 74424, -21608, 4208, -1126, 168, -4, -8, 1], 'lmfdb_label': '7752.a4', 'torsion': [12]}
  • id: 405577
    {'degree': 16, 'field': [923261857, 320142776, -313488364, -26139912, 45732506, -40848008, 16416916, -2491968, 735271, -72528, 12772, 176, 638, -336, 68, -8, 1], 'lmfdb_label': '7752.a4', '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: 160029
    {'conductor': 7752, 'conductor_valuation': 3, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '7752.a4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 160030
    {'conductor': 7752, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '7752.a4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 160031
    {'conductor': 7752, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '7752.a4', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 160032
    {'conductor': 7752, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '7752.a4', '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: 1715160
    {'adelic_gens': [[1619, 1618, 2274, 979], [977, 972, 974, 2263], [1, 0, 8, 1], [2577, 8, 2576, 9], [1, 8, 0, 1], [1, 4, 4, 17], [7, 6, 2578, 2579], [160, 3, 1069, 2], [1908, 1, 1927, 6]], 'adelic_image': '2584.48.0.?', 'conductor': 7752, 'lmfdb_label': '7752.a4', 'prime': 0}
  • id: 37987
    {'conductor': 7752, 'elladic_image': '8.12.0.6', 'lmfdb_label': '7752.a4', 'modell_image': '2B', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 316872
    {'lmfdb_iso': '7752.a', 'p': 5, 'prec': 20, 'unit': 491998013036, 'val': 1}
  • id: 316873
    {'lmfdb_iso': '7752.a', 'p': 7, 'prec': 20, 'unit': 6250520970710997, 'val': 1}
  • id: 316878
    {'lmfdb_iso': '7752.a', 'p': 13, 'prec': 20, 'unit': 298683307327629945312, 'val': 1}
  • id: 316883
    {'lmfdb_iso': '7752.a', 'p': 23, 'prec': 20, 'unit': 943120358360704185789991, 'val': 2}
  • id: 316877
    {'lmfdb_iso': '7752.a', 'p': 29, 'prec': 20, 'unit': 2867576195182519165754663076, 'val': 1}
  • id: 316874
    {'lmfdb_iso': '7752.a', 'p': 31, 'prec': 20, 'unit': 9359823196676648418744725823, 'val': 1}
  • id: 316887
    {'lmfdb_iso': '7752.a', 'p': 37, 'prec': 20, 'unit': 12188195402834186973082841249, 'val': 2}
  • id: 316875
    {'lmfdb_iso': '7752.a', 'p': 41, 'prec': 20, 'unit': 1939117570484147365600603813975, 'val': 1}
  • id: 316876
    {'lmfdb_iso': '7752.a', 'p': 43, 'prec': 20, 'unit': 6132982154630966478737426910699, 'val': 1}
  • id: 316881
    {'lmfdb_iso': '7752.a', 'p': 53, 'prec': 20, 'unit': 466886548524367915248156161876316, 'val': 1}
  • id: 316885
    {'lmfdb_iso': '7752.a', 'p': 59, 'prec': 20, 'unit': 591623231303582323922492480332999, 'val': 1}
  • id: 316886
    {'lmfdb_iso': '7752.a', 'p': 61, 'prec': 20, 'unit': 7310631573860206553998843100378450, 'val': 1}
  • id: 316871
    {'lmfdb_iso': '7752.a', 'p': 67, 'prec': 20, 'unit': 28801719697677688430605569584288724, 'val': 1}
  • id: 316882
    {'lmfdb_iso': '7752.a', 'p': 73, 'prec': 20, 'unit': 191484650007355783598362759395714, 'val': 1}
  • id: 316879
    {'lmfdb_iso': '7752.a', 'p': 79, 'prec': 20, 'unit': 406702229410311556718123135355458758, 'val': 1}
  • id: 316880
    {'lmfdb_iso': '7752.a', 'p': 83, 'prec': 20, 'unit': 1850376008255615522779716239900660868, 'val': 1}
  • id: 316884
    {'lmfdb_iso': '7752.a', 'p': 89, 'prec': 20, 'unit': 4064144099935019080902415542519299820, 'val': 1}
  • id: 316870
    {'lmfdb_iso': '7752.a', 'p': 97, 'prec': 20, 'unit': 10585459242612393789762245656393652579, 'val': 1}