Elliptic curve data - 2178.h1

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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': '2178g', 'Clabel': '2178g4', 'Cnumber': 4, 'abc_quality': 1.0492563620983195, 'absD': 270030454702272, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 132, 'ainvs': [1, -1, 1, -1115885, 453986965], 'analytic_rank': 1, 'bad_primes': [2, 3, 11], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 2178, 'degree': 23040, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0283128166215277329651274541', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 6, 'iso_nlabel': 7, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [4406910829875, 7744], 'lmfdb_iso': '2178.h', 'lmfdb_label': '2178.h1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -9222, -338572], 'min_quad_twist_disc': -11, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '12.48.0-12.h.1.2', '33.8.0-3.a.1.1', '44.6.0.e.1', '66.24.0-6.a.1.1', '132.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 8, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.74306636125745548094871559449', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 363], [3, 2, 121], [11, 72, 18]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.0054059637212601923877217374265', 'prec': 110}, 'szpiro_ratio': 6.946129315845605, '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, 1, 0, 1, 0, 0, -2, 1, 0, 0, 0, 0, -2, -2, 0, 1, -6, 0, -2, 0], 'aplist': [1, 0, 0, -2, 0, -2, -6, -2, 0, -6, -4, 2, 6, 10, -12, 12, -12, 10, 8, -12, -14, -2, -12, 0, 2], 'class_deg': 6, 'class_size': 4, 'conductor': 2178, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '2178.h', 'trace_hash': 2120433119350132398}
• 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': '0.017307321944281532980724463971', 'prec': 107}, 'conductor': 2178, 'gens': [[641, 1010, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.74306636125745548094871559449', 'prec': 103}], 'lmfdb_label': '2178.h1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.47129745298170517541372903637', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.2024634014842685203622706192172183630', 'prec': 130}, 'tamagawa_product': 48, 'torsion_generators': [[2443, -2447, 2]], 'xcoord_integral_points': [611, 641, 685, 9595]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': 'a', '5': [3, 1, 0], '7': [1, 0], '11': 'a', '13': [1, 0], '17': [1, 0], '19': [3, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '2178.h1'}
• ec_torsion_growth •

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

  
  
  • id: 110741
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '2178.h1', 'torsion': [6]}
  • id: 110740
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '2178.h1', 'torsion': [2, 2]}
  • id: 110742
    {'degree': 4, 'field': [1, -1, -6, -1, 1], 'lmfdb_label': '2178.h1', 'torsion': [12]}
  • id: 110743
    {'degree': 4, 'field': [4, 0, -7, 0, 1], 'lmfdb_label': '2178.h1', 'torsion': [2, 6]}
  • id: 110744
    {'degree': 6, 'field': [11, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '2178.h1', 'torsion': [6]}
  • id: 110746
    {'degree': 8, 'field': [1, 0, -11, 0, 24, 0, -11, 0, 1], 'lmfdb_label': '2178.h1', 'torsion': [2, 12]}
  • id: 110745
    {'degree': 8, 'field': [64, -64, 224, -88, 46, -32, 8, -2, 1], 'lmfdb_label': '2178.h1', 'torsion': [2, 4]}
  • id: 110747
    {'degree': 12, 'field': [144, -72, -144, 390, -75, -192, 163, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '2178.h1', 'torsion': [3, 6]}
  • id: 110748
    {'degree': 12, 'field': [1444, 0, 1512, 0, 2205, 0, -518, 0, 135, 0, -18, 0, 1], 'lmfdb_label': '2178.h1', 'torsion': [2, 6]}
  • id: 110750
    {'degree': 16, 'field': [256, 0, 0, 0, -236, 0, 0, 0, 321, 0, 0, 0, 10, 0, 0, 0, 1], 'lmfdb_label': '2178.h1', 'torsion': [2, 12]}
  • id: 110749
    {'degree': 16, 'field': [4096, 0, -16384, 0, 7568, 0, 7448, 0, -344, 0, -854, 0, -55, 0, 10, 0, 1], 'lmfdb_label': '2178.h1', 'torsion': [24]}
  • id: 110751
    {'degree': 18, 'field': [4096, 3072, -5376, 5184, 20160, 3360, -35916, -11028, 8316, 15367, -1155, -2076, -1392, 522, -138, 72, 12, -9, 1], 'lmfdb_label': '2178.h1', '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: 36413
    {'conductor': 2178, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '2178.h1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 36414
    {'conductor': 2178, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '2178.h1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 36415
    {'conductor': 2178, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '2178.h1', 'prime': 11, 'reduction_type': 0, '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: 1678156
    {'adelic_gens': [[1, 12, 0, 1], [121, 12, 120, 13], [76, 121, 123, 32], [119, 120, 54, 59], [78, 1, 77, 122], [1, 6, 6, 37], [1, 0, 12, 1], [11, 2, 82, 123]], 'adelic_image': '132.96.1.?', 'conductor': 2178, 'lmfdb_label': '2178.h1', 'prime': 0}
  • id: 10730
    {'conductor': 2178, 'elladic_image': '2.3.0.1', 'lmfdb_label': '2178.h1', 'modell_image': '2B', 'prime': 2}
  • id: 10731
    {'conductor': 2178, 'elladic_image': '3.4.0.1', 'lmfdb_label': '2178.h1', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 64897
    {'lmfdb_iso': '2178.h', 'p': 7, 'prec': 20, 'unit': 11080966201125868, 'val': 1}
  • id: 64901
    {'lmfdb_iso': '2178.h', 'p': 13, 'prec': 20, 'unit': 637319495218704983584, 'val': 1}
  • id: 64903
    {'lmfdb_iso': '2178.h', 'p': 17, 'prec': 20, 'unit': 131463837503946601391844, 'val': 1}
  • id: 64904
    {'lmfdb_iso': '2178.h', 'p': 19, 'prec': 20, 'unit': 33898548231855436359355, 'val': 2}
  • id: 64900
    {'lmfdb_iso': '2178.h', 'p': 29, 'prec': 20, 'unit': 5796664497706488052998716725, 'val': 1}
  • id: 64911
    {'lmfdb_iso': '2178.h', 'p': 31, 'prec': 20, 'unit': 18661267989834368841875545051, 'val': 1}
  • id: 64896
    {'lmfdb_iso': '2178.h', 'p': 37, 'prec': 20, 'unit': 509487959531890804664103253661, 'val': 1}
  • id: 64898
    {'lmfdb_iso': '2178.h', 'p': 41, 'prec': 20, 'unit': 266401118352652433871100644669, 'val': 1}
  • id: 64899
    {'lmfdb_iso': '2178.h', 'p': 43, 'prec': 20, 'unit': 10738443130656707709773973937352, 'val': 1}
  • id: 64909
    {'lmfdb_iso': '2178.h', 'p': 47, 'prec': 20, 'unit': 7362263759332732355306949300022, 'val': 1}
  • id: 64905
    {'lmfdb_iso': '2178.h', 'p': 53, 'prec': 20, 'unit': 2759791159506175726512792837974, 'val': 2}
  • id: 64906
    {'lmfdb_iso': '2178.h', 'p': 59, 'prec': 20, 'unit': 3310977528140873957300352817679092, 'val': 1}
  • id: 64910
    {'lmfdb_iso': '2178.h', 'p': 61, 'prec': 20, 'unit': 5809467790514561791461331095888083, 'val': 1}
  • id: 64895
    {'lmfdb_iso': '2178.h', 'p': 67, 'prec': 20, 'unit': 40285853522613619106229099089560260, 'val': 1}
  • id: 64908
    {'lmfdb_iso': '2178.h', 'p': 71, 'prec': 20, 'unit': 97879913595699670723108566159624743, 'val': 1}
  • id: 64907
    {'lmfdb_iso': '2178.h', 'p': 73, 'prec': 20, 'unit': 196050897646009246255822378497664489, 'val': 1}
  • id: 64902
    {'lmfdb_iso': '2178.h', 'p': 79, 'prec': 20, 'unit': 622700983789176106627854071807043063, 'val': 1}
  • id: 64894
    {'lmfdb_iso': '2178.h', 'p': 83, 'prec': 20, 'unit': 2795715214977507099525318797529623082, 'val': 1}
  • id: 64893
    {'lmfdb_iso': '2178.h', 'p': 97, 'prec': 20, 'unit': 16037633559548392392113714859303016398, 'val': 1}