Elliptic curve data - 104742.e1

Formats: - HTML - YAML - JSON - 2025-10-24T04:42:06.066113

• 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': '104742o', 'Clabel': '104742o2', 'Cnumber': 2, 'abc_quality': 0.969879037258856, 'absD': 125831277091071895464, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 6072, 'ainvs': [1, -1, 0, -22886226, -42132264372], 'analytic_rank': 1, 'bad_primes': [2, 3, 11, 23], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 104742, 'degree': 10948608, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.8937825724404747563219249871', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 4, 'isogeny_degrees': [1, 3], 'jinv': [12284337086925553, 1165987944], 'lmfdb_iso': '104742.e', 'lmfdb_label': '104742.e1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -4807, -128671], 'min_quad_twist_disc': 69, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '69.8.0-3.a.1.2', '264.8.0.?', '2024.2.0.?', '6072.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '7.2627433597438388817627822054', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 52371], [3, 8, 529], [11, 12, 9522], [23, 288, 198]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.77672932014184506522092595273', 'prec': 103}, 'szpiro_ratio': 5.402747665552577, '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, -7, -1, 0, 1, -3, 0, -8, -3], 'aplist': [-1, 0, -3, 1, -1, -7, -3, -8, 0, 9, -7, 7, 6, -2, -9, -6, 0, -8, -5, 15, 2, -11, 6, 0, -2], 'class_deg': 3, 'class_size': 2, 'conductor': 104742, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '104742.e', 'trace_hash': 1255423955632279642}
• 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': '0.0030654369919944632810107739603', 'prec': 110}, 'conductor': 104742, 'gens': [[-469221, 214761, 13]], 'heights': [{'__RealLiteral__': 0, 'data': '7.2627433597438388817627822054', 'prec': 100}], 'lmfdb_label': '104742.e1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.069025328421001737783910037609', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.0052529825750722012941548978890274341', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [5, 0], '3': 'a', '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [1, 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.e1'}
• ec_torsion_growth •

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

  
  
  • id: 4845032
    {'degree': 2, 'field': [6, -1, 1], 'lmfdb_label': '104742.e1', 'torsion': [3]}
  • id: 4845033
    {'degree': 3, 'field': [-6, -10, -1, 1], 'lmfdb_label': '104742.e1', 'torsion': [2]}
  • id: 4845035
    {'degree': 6, 'field': [-375, 0, 0, -54, 0, 0, 1], 'lmfdb_label': '104742.e1', 'torsion': [3]}
  • id: 4845036
    {'degree': 6, 'field': [8, -22, 34, -25, 15, -3, 1], 'lmfdb_label': '104742.e1', 'torsion': [6]}
  • id: 4845034
    {'degree': 6, 'field': [16, -208, 162, 60, -51, -2, 1], 'lmfdb_label': '104742.e1', 'torsion': [2, 2]}
  • id: 4845039
    {'degree': 12, 'field': [27152, 15792, 39908, -21656, 17668, -7324, 4013, -1066, 423, -88, 27, -2, 1], 'lmfdb_label': '104742.e1', 'torsion': [2, 6]}
  • id: 4845038
    {'degree': 12, 'field': [46236, -49374, 68301, -42180, 32445, -15174, 7747, -2526, 915, -200, 51, -6, 1], 'lmfdb_label': '104742.e1', 'torsion': [3, 3]}
  • id: 4845037
    {'degree': 12, 'field': [5447002, 10132280, 4625739, 944316, -241835, -85180, -10073, 848, 523, -132, -3, -4, 1], 'lmfdb_label': '104742.e1', 'torsion': [4]}
  • id: 4845041
    {'degree': 18, 'field': [729, 0, 0, 4536, 0, 0, -135585, 0, 0, 34452, 0, 0, -297, 0, 0, -108, 0, 0, 1], 'lmfdb_label': '104742.e1', 'torsion': [6]}
  • id: 4845040
    {'degree': 18, 'field': [27791737227, -21150952065, 28605432204, -2275688790, 4470363513, -38518902, 1050609789, -203109228, 171012708, -29919198, 13293648, -1763748, 663222, -54072, 15174, -433, 159, 0, 1], 'lmfdb_label': '104742.e1', 'torsion': [9]}
• 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: 2573364
    {'conductor': 104742, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '104742.e1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 2573365
    {'conductor': 104742, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '104742.e1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2573366
    {'conductor': 104742, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '104742.e1', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 2573367
    {'conductor': 104742, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '104742.e1', 'prime': 23, '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: 2351523
    {'adelic_gens': [[3286, 2781, 3785, 3029], [3313, 6, 3867, 19], [4, 3, 9, 7], [2111, 6066, 261, 6053], [1519, 6, 0, 1], [1, 6, 0, 1], [6067, 6, 6066, 7], [3, 4, 8, 11], [3037, 6, 3039, 19], [1, 0, 6, 1]], 'adelic_image': '6072.16.0.?', 'conductor': 104742, 'lmfdb_label': '104742.e1', 'prime': 0}
  • id: 418609
    {'conductor': 104742, 'elladic_image': '3.4.0.1', 'lmfdb_label': '104742.e1', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 5455452
    {'lmfdb_iso': '104742.e', 'p': 5, 'prec': 20, 'unit': 9693381700338, 'val': 1}
  • id: 5455453
    {'lmfdb_iso': '104742.e', 'p': 7, 'prec': 20, 'unit': 50512087952917573, 'val': -1}
  • id: 5455458
    {'lmfdb_iso': '104742.e', 'p': 13, 'prec': 20, 'unit': 992581195195810399600, 'val': 1}
  • id: 5455460
    {'lmfdb_iso': '104742.e', 'p': 17, 'prec': 20, 'unit': 49873733101611894785053, 'val': 1}
  • id: 5455461
    {'lmfdb_iso': '104742.e', 'p': 19, 'prec': 20, 'unit': 407311765968855078280780, 'val': 1}
  • id: 5455457
    {'lmfdb_iso': '104742.e', 'p': 29, 'prec': 20, 'unit': 973808291732061414324608756, 'val': 1}
  • id: 5455454
    {'lmfdb_iso': '104742.e', 'p': 31, 'prec': 20, 'unit': 11911170580701500667471961258, 'val': 1}
  • id: 5455467
    {'lmfdb_iso': '104742.e', 'p': 37, 'prec': 20, 'unit': 144861588278710446498725143030, 'val': 1}
  • id: 5455455
    {'lmfdb_iso': '104742.e', 'p': 41, 'prec': 20, 'unit': 183043502948099415251768205142, 'val': 1}
  • id: 5455456
    {'lmfdb_iso': '104742.e', 'p': 43, 'prec': 20, 'unit': 8360324507509731538345342291802, 'val': 1}
  • id: 5455459
    {'lmfdb_iso': '104742.e', 'p': 47, 'prec': 20, 'unit': 5148196996760023600337483728335, 'val': 1}
  • id: 5455462
    {'lmfdb_iso': '104742.e', 'p': 53, 'prec': 20, 'unit': 118640164660790636647303279622141, 'val': 1}
  • id: 5455466
    {'lmfdb_iso': '104742.e', 'p': 61, 'prec': 20, 'unit': 6167578136373170678657743992980127, 'val': 1}
  • id: 5455451
    {'lmfdb_iso': '104742.e', 'p': 67, 'prec': 20, 'unit': 28221597374301525975512815392775733, 'val': 1}
  • id: 5455464
    {'lmfdb_iso': '104742.e', 'p': 71, 'prec': 20, 'unit': 135219606568991142266319071401752070, 'val': 1}
  • id: 5455463
    {'lmfdb_iso': '104742.e', 'p': 73, 'prec': 20, 'unit': 124365814362056865349792326775427600, 'val': 1}
  • id: 5455465
    {'lmfdb_iso': '104742.e', 'p': 79, 'prec': 20, 'unit': 951831952670402400911570422887707423, 'val': 1}
  • id: 5455450
    {'lmfdb_iso': '104742.e', 'p': 83, 'prec': 20, 'unit': 2641019023066920475655323187136319965, 'val': 1}
  • id: 5455449
    {'lmfdb_iso': '104742.e', 'p': 97, 'prec': 20, 'unit': 53580348519363148555695422606448600117, 'val': 1}