Elliptic curve data - 78400.co2

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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': '78400is', 'Clabel': '78400is1', 'Cnumber': 1, 'abc_quality': 0.8042613164744115, 'absD': 8780800000000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 56, 'ainvs': [0, 1, 0, 3967, -103937], 'analytic_rank': 1, 'bad_primes': [2, 5, 7], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 78400, 'degree': 147456, 'elladic_images': ['8.6.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1696142031284135664771054065', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 66, 'isogeny_degrees': [1, 2], 'jinv': [19652, 25], 'lmfdb_iso': '78400.co', 'lmfdb_label': '78400.co2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 40, 92], 'min_quad_twist_disc': -40, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.e.1', '14.6.0.b.1', '56.12.0.bc.1'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.7818160546377388482516109327', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0457785310990586929892552746', 'prec': 103}, 'szpiro_ratio': 3.252251775315925, '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, -2, 0, 0, 0, 0, 0, 1, 0, 4, 0, 2, 0, 0, 0, 0, 0, 2, 0], 'aplist': [0, -2, 0, 0, 4, 2, 0, 2, -4, -10, -4, -2, -12, 4, 4, 2, 10, -6, -4, 12, 4, 4, -14, 8, 8], 'class_deg': 2, 'class_size': 2, 'conductor': 78400, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '78400.co', 'trace_hash': 626112024670507661}
• 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': '0.096401992715485031274759077981', 'prec': 107}, 'conductor': 78400, 'gens': [[37, 308, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.7818160546377388482516109327', 'prec': 100}], 'lmfdb_label': '78400.co2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.39178799525805446340213287725', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.3595285408927608158123518195876113335', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[23, 0, 1]], 'xcoord_integral_points': [23, 37, 423]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': 'a', '7': 'a', '11': [1, 0], '13': [1, 0], '17': [1, 1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '78400.co2'}
• ec_torsion_growth •

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

  
  
  • id: 3702544
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '78400.co2', 'torsion': [2, 2]}
  • id: 3702545
    {'degree': 4, 'field': [-31, -46, -23, -2, 1], 'lmfdb_label': '78400.co2', 'torsion': [4]}
  • id: 3702548
    {'degree': 8, 'field': [-529200, 0, -70560, 0, -2520, 0, 0, 0, 1], 'lmfdb_label': '78400.co2', 'torsion': [6]}
  • id: 3702547
    {'degree': 8, 'field': [44, 96, 10, -88, 90, -16, -1, -2, 1], 'lmfdb_label': '78400.co2', 'torsion': [2, 4]}
  • id: 3702546
    {'degree': 8, 'field': [569, -362, -187, -30, 106, 22, -17, -2, 1], 'lmfdb_label': '78400.co2', 'torsion': [2, 4]}
  • id: 3702549
    {'degree': 16, 'field': [4, -48, 56, 448, -228, -2624, -5448, -6288, -4446, -2520, -1424, -568, -90, -8, -8, 0, 1], 'lmfdb_label': '78400.co2', 'torsion': [8]}
  • id: 3702550
    {'degree': 16, 'field': [13829760000, 0, -4148928000, 0, 608070400, 0, -46099200, 0, 1587600, 0, -7840, 0, -840, 0, 0, 0, 1], 'lmfdb_label': '78400.co2', 'torsion': [2, 6]}
• 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: 1908891
    {'conductor': 78400, 'conductor_valuation': 6, 'discriminant_valuation': 16, 'j_denominator_valuation': 0, 'kodaira_symbol': -10, 'lmfdb_label': '78400.co2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1908892
    {'conductor': 78400, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '78400.co2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1908893
    {'conductor': 78400, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '78400.co2', 'prime': 7, 'reduction_type': 0, '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: 2181590
    {'adelic_gens': [[12, 1, 39, 0], [29, 4, 2, 9], [1, 4, 0, 1], [1, 0, 4, 1], [3, 4, 8, 11], [53, 4, 52, 5], [1, 2, 2, 5], [25, 36, 48, 7]], 'adelic_image': '56.12.0.?', 'conductor': 78400, 'lmfdb_label': '78400.co2', 'prime': 0}
  • id: 323130
    {'conductor': 78400, 'elladic_image': '8.6.0.3', 'lmfdb_label': '78400.co2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 4038918
    {'lmfdb_iso': '78400.co', 'p': 11, 'prec': 20, 'unit': 47266022751594680031, 'val': 1}
  • id: 4038924
    {'lmfdb_iso': '78400.co', 'p': 13, 'prec': 20, 'unit': 1182539435659742599713, 'val': 1}
  • id: 4038927
    {'lmfdb_iso': '78400.co', 'p': 19, 'prec': 20, 'unit': 138952304323140219709626, 'val': 1}
  • id: 4038930
    {'lmfdb_iso': '78400.co', 'p': 23, 'prec': 20, 'unit': 1717059160582043947987708, 'val': 1}
  • id: 4038923
    {'lmfdb_iso': '78400.co', 'p': 29, 'prec': 20, 'unit': 6088062683163796261739902882, 'val': 1}
  • id: 4038935
    {'lmfdb_iso': '78400.co', 'p': 31, 'prec': 20, 'unit': 7007008088840418869597688615, 'val': 1}
  • id: 4038919
    {'lmfdb_iso': '78400.co', 'p': 37, 'prec': 20, 'unit': 433457242224535636682290718191, 'val': 1}
  • id: 4038921
    {'lmfdb_iso': '78400.co', 'p': 41, 'prec': 20, 'unit': 2227767835744700672583147485662, 'val': 1}
  • id: 4038922
    {'lmfdb_iso': '78400.co', 'p': 43, 'prec': 20, 'unit': 1556106728243703522237245843132, 'val': 1}
  • id: 4038932
    {'lmfdb_iso': '78400.co', 'p': 47, 'prec': 20, 'unit': 12003254133502276935203789938140, 'val': 1}
  • id: 4038928
    {'lmfdb_iso': '78400.co', 'p': 53, 'prec': 20, 'unit': 572476814905949612697207680855770, 'val': 1}
  • id: 4038926
    {'lmfdb_iso': '78400.co', 'p': 59, 'prec': 20, 'unit': 2555759455168349333686091238064282, 'val': 1}
  • id: 4038933
    {'lmfdb_iso': '78400.co', 'p': 61, 'prec': 20, 'unit': 2008023927813906234161760038393452, 'val': 1}
  • id: 4038917
    {'lmfdb_iso': '78400.co', 'p': 67, 'prec': 20, 'unit': 216830607826800910671558625753328, 'val': 2}
  • id: 4038920
    {'lmfdb_iso': '78400.co', 'p': 71, 'prec': 20, 'unit': 51123464857199864759034215504257126, 'val': 1}
  • id: 4038929
    {'lmfdb_iso': '78400.co', 'p': 73, 'prec': 20, 'unit': 73099539402724875629104573429471209, 'val': 1}
  • id: 4038925
    {'lmfdb_iso': '78400.co', 'p': 79, 'prec': 20, 'unit': 419236084874267827605364158902674304, 'val': 1}
  • id: 4038934
    {'lmfdb_iso': '78400.co', 'p': 83, 'prec': 20, 'unit': 1550639345229904386632463327392665140, 'val': 1}
  • id: 4038931
    {'lmfdb_iso': '78400.co', 'p': 89, 'prec': 20, 'unit': 4138144557499452307745999986329533045, 'val': 1}
  • id: 4038916
    {'lmfdb_iso': '78400.co', 'p': 97, 'prec': 20, 'unit': 36702398289040736554446202595241516931, 'val': 1}