Elliptic curve data - 867.a1

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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': '867b', 'Clabel': '867b1', 'Cnumber': 1, 'abc_quality': 0.9424416881856162, 'absD': 397953, 'adelic_genus': 5, 'adelic_index': 192, 'adelic_level': 816, 'ainvs': [1, 1, 1, -23, 20], 'analytic_rank': 1, 'bad_primes': [3, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 867, 'degree': 96, 'elladic_images': ['8.24.0.84'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.21973633927667040674962551742', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [274625, 81], 'lmfdb_iso': '867.a', 'lmfdb_label': '867.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -23, 20], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0.f.1', '8.24.0.bh.1', '34.6.0.a.1', '48.48.1.gv.1', '68.24.0.h.1', '136.48.1.?', '272.96.1.?', '408.96.1.?', '816.192.5.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 7, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.46550926222445360873762100508', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 17], [3, 4, 289], [17, 82, 3]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.92803967529072442681200917189', 'prec': 107}, 'szpiro_ratio': 3.107565516475448, '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, -1, -1, 0, 1, -4, 3, 1, 0, 4, 1, 2, 4, 0, -1, 0, -1, 4, 0], 'aplist': [-1, -1, 0, -4, 4, 2, 0, 4, -4, 0, 4, -8, -8, 4, -8, -6, 12, -8, 12, -12, 0, -4, -12, -10, -16], 'class_deg': 2, 'class_size': 2, 'conductor': 867, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '867.a', 'trace_hash': 253355349066901477}
• 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': '1.5518886585357156816935122331', 'prec': 100}, 'conductor': 867, 'gens': [[0, 4, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.46550926222445360873762100508', 'prec': 103}], 'lmfdb_label': '867.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '2.7849176519372060399688690864', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2964049615091464710222585939903896382', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[1, -1, 1]], 'xcoord_integral_points': [0, 1, 5, 18]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [5, 0], '3': [1, 0], '5': [1, 1, 0], '7': [3, 0], '11': [1, 0], '13': [1, 0], '17': 'a', '19': [1, 0], '23': [1, 0], '29': [1, 1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '867.a1'}
• ec_torsion_growth •

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

  
  
  • id: 40955
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '867.a1', 'torsion': [2, 2]}
  • id: 40957
    {'degree': 4, 'field': [-17, 0, 0, 0, 1], 'lmfdb_label': '867.a1', 'torsion': [2, 4]}
  • id: 40956
    {'degree': 4, 'field': [16, 8, 10, -2, 1], 'lmfdb_label': '867.a1', 'torsion': [4]}
  • id: 40959
    {'degree': 8, 'field': [-1169, 1040, -518, 54, -51, 9, 13, -4, 1], 'lmfdb_label': '867.a1', 'torsion': [6]}
  • id: 40958
    {'degree': 8, 'field': [16, 8, 2, -22, 17, -10, 8, -4, 1], 'lmfdb_label': '867.a1', 'torsion': [4, 4]}
  • id: 40963
    {'degree': 16, 'field': [-625, 1125, -650, 1445, -862, -2360, 1728, 740, -420, -133, 81, -167, 124, -31, 11, -6, 1], 'lmfdb_label': '867.a1', 'torsion': [2, 6]}
  • id: 40962
    {'degree': 16, 'field': [72, -432, 1518, -108, 1234, -436, 49, -252, 318, -44, -15, -34, 21, 0, -2, -2, 1], 'lmfdb_label': '867.a1', 'torsion': [2, 8]}
  • id: 40960
    {'degree': 16, 'field': [132, 248, -92, -1376, 4438, -8088, 10426, -10588, 8693, -5864, 3254, -1468, 548, -168, 44, -8, 1], 'lmfdb_label': '867.a1', 'torsion': [8]}
  • id: 40961
    {'degree': 16, 'field': [9604, 0, -41552, 0, 59492, 0, -34452, 0, 10829, 0, -2130, 0, 287, 0, -26, 0, 1], 'lmfdb_label': '867.a1', 'torsion': [2, 8]}
• 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: 11393
    {'conductor': 867, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '867.a1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 11394
    {'conductor': 867, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '867.a1', 'prime': 17, '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: 1670040
    {'adelic_gens': [[613, 16, 620, 435], [1, 16, 0, 1], [801, 16, 800, 17], [613, 16, 8, 129], [11, 12, 716, 707], [1, 0, 16, 1], [444, 5, 115, 68], [15, 8, 176, 239], [5, 16, 64, 205]], 'adelic_image': '816.192.5.?', 'conductor': 867, 'lmfdb_label': '867.a1', 'prime': 0}
  • id: 3990
    {'conductor': 867, 'elladic_image': '8.24.0.84', 'lmfdb_label': '867.a1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 18049
    {'lmfdb_iso': '867.a', 'p': 7, 'prec': 20, 'unit': 94345345650949, 'val': 2}
  • id: 18054
    {'lmfdb_iso': '867.a', 'p': 11, 'prec': 20, 'unit': 31205770952799451652, 'val': 1}
  • id: 18052
    {'lmfdb_iso': '867.a', 'p': 13, 'prec': 20, 'unit': 70320912026185953520, 'val': 1}
  • id: 18056
    {'lmfdb_iso': '867.a', 'p': 19, 'prec': 20, 'unit': 1089398114905297907913919, 'val': 1}
  • id: 18058
    {'lmfdb_iso': '867.a', 'p': 23, 'prec': 20, 'unit': 58912580180101412167866039, 'val': 1}
  • id: 18063
    {'lmfdb_iso': '867.a', 'p': 31, 'prec': 20, 'unit': 7128611116688196377632516769, 'val': 1}
  • id: 18048
    {'lmfdb_iso': '867.a', 'p': 37, 'prec': 20, 'unit': 77386565267930277031433390398, 'val': 1}
  • id: 18050
    {'lmfdb_iso': '867.a', 'p': 41, 'prec': 20, 'unit': 2301623940921618556872226470345, 'val': 1}
  • id: 18051
    {'lmfdb_iso': '867.a', 'p': 43, 'prec': 20, 'unit': 2245359986472357593103482771099, 'val': 1}
  • id: 18061
    {'lmfdb_iso': '867.a', 'p': 47, 'prec': 20, 'unit': 32962108757035559855595442857424, 'val': 1}
  • id: 18057
    {'lmfdb_iso': '867.a', 'p': 53, 'prec': 20, 'unit': 472142016465457388337110179516341, 'val': 1}
  • id: 18055
    {'lmfdb_iso': '867.a', 'p': 59, 'prec': 20, 'unit': 1935609261886983252689370254082807, 'val': 1}
  • id: 18062
    {'lmfdb_iso': '867.a', 'p': 61, 'prec': 20, 'unit': 4354821252976378145230648740951769, 'val': 1}
  • id: 18047
    {'lmfdb_iso': '867.a', 'p': 67, 'prec': 20, 'unit': 15899135699680181697046582075865214, 'val': 1}
  • id: 18060
    {'lmfdb_iso': '867.a', 'p': 71, 'prec': 20, 'unit': 72934623647769964727617270458274694, 'val': 1}
  • id: 18053
    {'lmfdb_iso': '867.a', 'p': 79, 'prec': 20, 'unit': 136660933573053703299973491324915239, 'val': 1}
  • id: 18046
    {'lmfdb_iso': '867.a', 'p': 83, 'prec': 20, 'unit': 140181201068610857539316174203810273, 'val': 1}
  • id: 18059
    {'lmfdb_iso': '867.a', 'p': 89, 'prec': 20, 'unit': 3241607462097988151085607654868771286, 'val': 1}
  • id: 18045
    {'lmfdb_iso': '867.a', 'p': 97, 'prec': 20, 'unit': 42282419816333880210975869568382144125, 'val': 1}