Elliptic curve data - 104742.c1

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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': '104742p', 'Clabel': '104742p1', 'Cnumber': 1, 'abc_quality': 1.0140896439556915, 'absD': 324475078493158364756312064, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 2024, 'ainvs': [1, -1, 0, -858679776, 9646255952896], 'analytic_rank': 1, 'bad_primes': [2, 3, 11, 23], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 104742, 'degree': 77045760, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.9373799877195484676673902085', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 2, 'isogeny_degrees': [1], 'jinv': [648817971720191270353, 3006677182316544], 'lmfdb_iso': '104742.c', 'lmfdb_label': '104742.c1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -180357, 29287947], 'min_quad_twist_disc': 69, 'modell_images': [], 'modm_images': ['2024.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '9.2249550435518281042741515780', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 52371], [3, 8, 11638], [11, 12, 9522], [19, 2, 52371], [23, 288, 198]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.8203267354209187765663911741', 'prec': 100}, 'szpiro_ratio': 6.343516080372069, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, -3, 0, -1, -1, 0, 3, -1, 0, -1, 1, 0, 1, 7, 0, 6, -3], 'aplist': [-1, 0, -3, -1, -1, -1, 7, 6, 0, 9, -5, 9, -4, 6, 7, 2, -12, 14, 11, 7, 4, -1, 14, 0, -16], 'class_deg': 1, 'class_size': 1, 'conductor': 104742, 'isogeny_matrix': [[1]], 'lmfdb_iso': '104742.c', 'trace_hash': 2082329934914023265}
• 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': '0.00038022020910649376882952352819', 'prec': 113}, 'conductor': 104742, 'gens': [[17938035, 9163753481, 34]], 'heights': [{'__RealLiteral__': 0, 'data': '9.2249550435518281042741515780', 'prec': 100}], 'lmfdb_label': '104742.c1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.054517048107251463810280885517', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.0233385431723762820274395902949015440', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [7, 0], '3': 'a', '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [3, 0], '17': [1, 0], '19': [1, 0], '23': 'a', '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '104742.c1'}
• ec_torsion_growth •

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

  
  
  • id: 4845042
    {'degree': 3, 'field': [-6, -10, -1, 1], 'lmfdb_label': '104742.c1', 'torsion': [2]}
  • id: 4845043
    {'degree': 6, 'field': [16, -208, 162, 60, -51, -2, 1], 'lmfdb_label': '104742.c1', 'torsion': [2, 2]}
  • id: 4845044
    {'degree': 8, 'field': [35392, -22303, -4196, 2117, 1057, -235, -29, -4, 1], 'lmfdb_label': '104742.c1', 'torsion': [3]}
  • id: 4845045
    {'degree': 12, 'field': [401703786, 0, -16932969, 0, -6658119, 0, 160326, 0, 4140, 0, -141, 0, 1], 'lmfdb_label': '104742.c1', 'torsion': [4]}
• 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: 2573368
    {'conductor': 104742, 'conductor_valuation': 1, 'discriminant_valuation': 19, 'j_denominator_valuation': 19, 'kodaira_symbol': 23, 'lmfdb_label': '104742.c1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 2573369
    {'conductor': 104742, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '104742.c1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2573370
    {'conductor': 104742, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '104742.c1', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 2573371
    {'conductor': 104742, 'conductor_valuation': 2, 'discriminant_valuation': 11, 'j_denominator_valuation': 5, 'kodaira_symbol': -9, 'lmfdb_label': '104742.c1', 'prime': 23, '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

  
  {'adelic_gens': [[2023, 2, 2022, 3], [1013, 2, 1013, 3], [1, 1, 2023, 0], [1289, 2, 1289, 3], [1, 0, 2, 1], [1, 2, 0, 1], [1519, 2, 0, 1], [1937, 2, 1937, 3]], 'adelic_image': '2024.2.0.?', 'conductor': 104742, 'lmfdb_label': '104742.c1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 5455471
    {'lmfdb_iso': '104742.c', 'p': 5, 'prec': 20, 'unit': 2281352299563, 'val': 1}
  • id: 5455472
    {'lmfdb_iso': '104742.c', 'p': 7, 'prec': 20, 'unit': 2401273452713209, 'val': 1}
  • id: 5455477
    {'lmfdb_iso': '104742.c', 'p': 13, 'prec': 20, 'unit': 835421359467304793, 'val': 3}
  • id: 5455479
    {'lmfdb_iso': '104742.c', 'p': 17, 'prec': 20, 'unit': 168668455599400613763281, 'val': 1}
  • id: 5455480
    {'lmfdb_iso': '104742.c', 'p': 19, 'prec': 20, 'unit': 1125054462401686499465079, 'val': 1}
  • id: 5455476
    {'lmfdb_iso': '104742.c', 'p': 29, 'prec': 20, 'unit': 5244211061916096365845524979, 'val': 1}
  • id: 5455473
    {'lmfdb_iso': '104742.c', 'p': 31, 'prec': 20, 'unit': 5343271522279139136992407482, 'val': 1}
  • id: 5455487
    {'lmfdb_iso': '104742.c', 'p': 37, 'prec': 20, 'unit': 96941498543910255397382047318, 'val': 1}
  • id: 5455474
    {'lmfdb_iso': '104742.c', 'p': 41, 'prec': 20, 'unit': 2479351047337423476961209459495, 'val': 1}
  • id: 5455475
    {'lmfdb_iso': '104742.c', 'p': 43, 'prec': 20, 'unit': 200500469649943141008253524065, 'val': 1}
  • id: 5455485
    {'lmfdb_iso': '104742.c', 'p': 47, 'prec': 20, 'unit': 36223475560437681709770850182337, 'val': 1}
  • id: 5455481
    {'lmfdb_iso': '104742.c', 'p': 53, 'prec': 20, 'unit': 468140324092383702742370513482244, 'val': 1}
  • id: 5455482
    {'lmfdb_iso': '104742.c', 'p': 59, 'prec': 20, 'unit': 3662503402758122728562074507894847, 'val': 1}
  • id: 5455486
    {'lmfdb_iso': '104742.c', 'p': 61, 'prec': 20, 'unit': 1161954445829691352450423155909524, 'val': 1}
  • id: 5455470
    {'lmfdb_iso': '104742.c', 'p': 67, 'prec': 20, 'unit': 48324823280335198249205102506171338, 'val': 1}
  • id: 5455484
    {'lmfdb_iso': '104742.c', 'p': 71, 'prec': 20, 'unit': 50574732769291326482065605191188688, 'val': 1}
  • id: 5455483
    {'lmfdb_iso': '104742.c', 'p': 73, 'prec': 20, 'unit': 151274326481916646911409625474713374, 'val': 1}
  • id: 5455478
    {'lmfdb_iso': '104742.c', 'p': 79, 'prec': 20, 'unit': 965974407877925037516338145662134982, 'val': 1}
  • id: 5455469
    {'lmfdb_iso': '104742.c', 'p': 83, 'prec': 20, 'unit': 277705540929255220433180864296114285, 'val': 1}
  • id: 5455468
    {'lmfdb_iso': '104742.c', 'p': 97, 'prec': 20, 'unit': 4425334293101750838135251025465605195, 'val': 1}