Elliptic curve data - 8112.g1

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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': '8112y', 'Clabel': '8112y4', 'Cnumber': 4, 'abc_quality': 1.0923393619522563, 'absD': 82933972992, 'adelic_genus': 5, 'adelic_index': 288, 'adelic_level': 780, 'ainvs': [0, -1, 0, -1135944, -465618960], 'analytic_rank': 1, 'bad_primes': [2, 3, 13], 'class_deg': 10, 'class_size': 4, 'cm': 0, 'conductor': 8112, 'degree': 57600, 'elladic_images': ['2.3.0.1', '5.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8631530339327146520457834595', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 10, 'iso_nlabel': 6, 'isogeny_degrees': [1, 2, 5, 10], 'jinv': [18013780041269221, 9216], 'lmfdb_iso': '8112.g', 'lmfdb_label': '8112.g1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -70997, 7275296], 'min_quad_twist_disc': -4, 'modell_images': ['2B', '5B'], 'modm_images': ['2.3.0.a.1', '5.6.0.a.1', '10.36.0.b.1', '12.6.0.f.1', '26.6.0.b.1', '60.72.1.dy.1', '65.12.0.a.1', '130.72.1.?', '156.12.0.?', '260.144.1.?', '780.288.5.?'], 'nonmax_primes': [2, 5], 'nonmax_rad': 10, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '5.6518925064331426323428295743', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 13], [3, 4, 2704], [13, 50, 48]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.52876851400738515861517947765', 'prec': 103}, 'szpiro_ratio': 5.937333135361462, '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, 2, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, -6, 0], 'aplist': [0, -1, -2, 2, 0, 0, 2, -6, 4, -10, 10, 8, -10, 4, 12, -6, -4, 2, -2, 0, -4, 0, -4, -6, 12], 'class_deg': 10, 'class_size': 4, 'conductor': 8112, 'isogeny_matrix': [[1, 2, 5, 10], [2, 1, 10, 5], [5, 10, 1, 2], [10, 5, 2, 1]], 'lmfdb_iso': '8112.g', 'trace_hash': 1880527236372348963}
• 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': '0.024081627638486159214045714152', 'prec': 107}, 'conductor': 8112, 'gens': [[10548, 1077504, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '5.6518925064331426323428295743', 'prec': 100}], 'lmfdb_label': '8112.g1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.14623801800377619526346018601', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.3060862324447107111099881822576284220', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-615, 0, 1]], 'xcoord_integral_points': [-615, 10548]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '5': [3, 1], '7': [1, 0], '11': [1, 1, 0], '13': 'a', '17': [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': '8112.g1'}
• ec_torsion_growth •

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

  
  
  • id: 424149
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '8112.g1', 'torsion': [2, 2]}
  • id: 424150
    {'degree': 4, 'field': [16, 4, 2, -1, 1], 'lmfdb_label': '8112.g1', 'torsion': [4]}
  • id: 424151
    {'degree': 4, 'field': [260, 0, 65, 0, 1], 'lmfdb_label': '8112.g1', 'torsion': [10]}
  • id: 424154
    {'degree': 8, 'field': [-507, 0, -1352, 0, -78, 0, 0, 0, 1], 'lmfdb_label': '8112.g1', 'torsion': [6]}
  • id: 424153
    {'degree': 8, 'field': [1, 0, -9, 0, 32, 0, -9, 0, 1], 'lmfdb_label': '8112.g1', 'torsion': [2, 4]}
  • id: 424152
    {'degree': 8, 'field': [81, 0, -136, 0, 50, 0, -8, 0, 1], 'lmfdb_label': '8112.g1', 'torsion': [2, 4]}
  • id: 424155
    {'degree': 8, 'field': [4225, 0, 4225, 0, 1040, 0, 65, 0, 1], 'lmfdb_label': '8112.g1', 'torsion': [2, 10]}
  • id: 424156
    {'degree': 16, 'field': [1062, -720, 4644, -10062, 12189, -13614, 14490, -12138, 8620, -5546, 3208, -1514, 586, -182, 46, -8, 1], 'lmfdb_label': '8112.g1', 'torsion': [8]}
  • id: 424157
    {'degree': 16, 'field': [598841, -1712224, 2675304, -1497276, -339234, 1353900, -546476, 112372, -70989, 35476, -14012, 3804, -634, -28, 24, -8, 1], 'lmfdb_label': '8112.g1', 'torsion': [2, 6]}
  • id: 424158
    {'degree': 16, 'field': [1000000, 0, -1000000, 0, 2006000, 0, 1137125, 0, 257950, 0, 30625, 0, 2045, 0, 70, 0, 1], 'lmfdb_label': '8112.g1', 'torsion': [20]}
  • id: 424159
    {'degree': 20, 'field': [-29031428, 27817140, 14623570, 43731090, 9985365, -16453992, -2145390, 1368900, 2851680, 147030, -1006848, -20280, 210405, -3900, -25350, -66, 1755, 0, -65, 0, 1], 'lmfdb_label': '8112.g1', 'torsion': [2, 10]}
• 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: 168222
    {'conductor': 8112, 'conductor_valuation': 4, 'discriminant_valuation': 22, 'j_denominator_valuation': 10, 'kodaira_symbol': -18, 'lmfdb_label': '8112.g1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 168223
    {'conductor': 8112, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '8112.g1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 168224
    {'conductor': 8112, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '8112.g1', 'prime': 13, '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: 1717557
    {'adelic_gens': [[389, 774, 0, 779], [761, 20, 760, 21], [157, 20, 0, 1], [602, 15, 385, 518], [11, 16, 540, 431], [521, 6, 0, 1], [1, 10, 10, 101], [1, 0, 20, 1], [1, 20, 0, 1]], 'adelic_image': '780.288.5.?', 'conductor': 8112, 'lmfdb_label': '8112.g1', 'prime': 0}
  • id: 39721
    {'conductor': 8112, 'elladic_image': '2.3.0.1', 'lmfdb_label': '8112.g1', 'modell_image': '2B', 'prime': 2}
  • id: 39722
    {'conductor': 8112, 'elladic_image': '5.6.0.1', 'lmfdb_label': '8112.g1', 'modell_image': '5B', 'prime': 5}
• ec_padic •

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

  
  
  • id: 334002
    {'lmfdb_iso': '8112.g', 'p': 5, 'prec': 20, 'unit': 1923144364316, 'val': 2}
  • id: 334003
    {'lmfdb_iso': '8112.g', 'p': 7, 'prec': 20, 'unit': 2262232473011586, 'val': 1}
  • id: 334009
    {'lmfdb_iso': '8112.g', 'p': 17, 'prec': 20, 'unit': 74212755888974529259368, 'val': 1}
  • id: 333999
    {'lmfdb_iso': '8112.g', 'p': 19, 'prec': 20, 'unit': 518797308723066289562725, 'val': 1}
  • id: 334013
    {'lmfdb_iso': '8112.g', 'p': 23, 'prec': 20, 'unit': 33990479980406765010209526, 'val': 1}
  • id: 334007
    {'lmfdb_iso': '8112.g', 'p': 29, 'prec': 20, 'unit': 2898131057105410190189479409, 'val': 1}
  • id: 334004
    {'lmfdb_iso': '8112.g', 'p': 31, 'prec': 20, 'unit': 20038421019441636678339802400, 'val': 1}
  • id: 334017
    {'lmfdb_iso': '8112.g', 'p': 37, 'prec': 20, 'unit': 189700963739238506035632608544, 'val': 1}
  • id: 334005
    {'lmfdb_iso': '8112.g', 'p': 41, 'prec': 20, 'unit': 3912072210818377758243366513525, 'val': 1}
  • id: 334006
    {'lmfdb_iso': '8112.g', 'p': 43, 'prec': 20, 'unit': 7936699447437662248696883232972, 'val': 1}
  • id: 334008
    {'lmfdb_iso': '8112.g', 'p': 47, 'prec': 20, 'unit': 2579772057825626537917203933761, 'val': 1}
  • id: 334011
    {'lmfdb_iso': '8112.g', 'p': 53, 'prec': 20, 'unit': 294979595693702824609074487616432, 'val': 1}
  • id: 334015
    {'lmfdb_iso': '8112.g', 'p': 59, 'prec': 20, 'unit': 248793843276097510014743443670131, 'val': 1}
  • id: 334016
    {'lmfdb_iso': '8112.g', 'p': 61, 'prec': 20, 'unit': 6716838004917842631421345482203868, 'val': 1}
  • id: 334001
    {'lmfdb_iso': '8112.g', 'p': 67, 'prec': 20, 'unit': 43367642811656690782535238780744233, 'val': 1}
  • id: 334012
    {'lmfdb_iso': '8112.g', 'p': 73, 'prec': 20, 'unit': 217877050436731913830735394643066082, 'val': 1}
  • id: 334010
    {'lmfdb_iso': '8112.g', 'p': 83, 'prec': 20, 'unit': 2244215338179156540820819119991515854, 'val': 1}
  • id: 334014
    {'lmfdb_iso': '8112.g', 'p': 89, 'prec': 20, 'unit': 3989957587494792867186935049772240823, 'val': 1}
  • id: 334000
    {'lmfdb_iso': '8112.g', 'p': 97, 'prec': 20, 'unit': 9603015521447534530138252571427806446, 'val': 1}