Elliptic curve data - 103933.b3

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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': '103933b', 'Clabel': '103933b1', 'Cnumber': 1, 'abc_quality': 0.8826782160855301, 'absD': 820081361773, 'adelic_genus': 43, 'adelic_index': 1296, 'adelic_level': 105894, 'ainvs': [0, -1, 1, -9363, 349122], 'analytic_rank': 0, 'bad_primes': [37, 53], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 103933, 'degree': 100776, 'elladic_images': ['27.36.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1086152276316545806837743381', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 3, 9], 'jinv': [4096000, 37], 'lmfdb_iso': '103933.b', 'lmfdb_label': '103933.b3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -3, 1], 'min_quad_twist_disc': 53, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '9.12.0.a.1', '27.36.0.a.1', '74.2.0.?', '159.8.0.?', '222.8.0.?', '333.36.0.?', '477.24.0.?', '666.72.3.?', '999.324.16.?', '1431.72.0.?', '1998.648.43.?', '11766.16.0.?', '17649.72.0.?', '35298.144.3.?', '52947.648.16.?', '105894.1296.43.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[37, 38, 2809], [53, 1406, 37]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.87653072914440633638846023141', 'prec': 107}, 'szpiro_ratio': 3.3802767645918617, '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, 0, -1, -2, 0, 0, -1, 0, -2, 0, 3, 2, -4, 0, 0, 4, 6, 0, -2, 0], 'aplist': [0, -1, 0, -1, 3, -4, 6, -2, -6, -6, 4, 1, 9, 8, 3, 0, 12, -8, 4, 15, -11, 10, -9, 6, 8], 'class_deg': 9, 'class_size': 3, 'conductor': 103933, 'isogeny_matrix': [[1, 3, 9], [3, 1, 3], [9, 3, 1]], 'lmfdb_iso': '103933.b', 'trace_hash': 1001457860366761839}
• 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': '0.10891032353192811327747619241', 'prec': 103}, 'conductor': 103933, 'gens': [], 'heights': [], 'lmfdb_label': '103933.b3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.89711963922990127146165145159', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.89711963922990127146165145158679852124', 'prec': 133}, 'tamagawa_product': 1, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [0, 5, 0], '3': [0, 0], '5': [0, 0, 0], '7': [0, 0], '11': [0, 0], '13': [0, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [1, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0], '53': 'a'}, 'iwp0': 0, 'lmfdb_label': '103933.b3'}
• ec_torsion_growth •

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

  
  
  • id: 4809112
    {'degree': 2, 'field': [-13, -1, 1], 'lmfdb_label': '103933.b3', 'torsion': [3]}
  • id: 4809113
    {'degree': 3, 'field': [1, -3, -1, 1], 'lmfdb_label': '103933.b3', 'torsion': [2]}
  • id: 4809117
    {'degree': 6, 'field': [-1289, -173, 530, 31, -46, -1, 1], 'lmfdb_label': '103933.b3', 'torsion': [6]}
  • id: 4809114
    {'degree': 6, 'field': [1, -5, 0, 9, -2, -3, 1], 'lmfdb_label': '103933.b3', 'torsion': [2, 2]}
  • id: 4809116
    {'degree': 6, 'field': [97, 604, 653, 73, -64, -1, 1], 'lmfdb_label': '103933.b3', 'torsion': [9]}
  • id: 4809115
    {'degree': 6, 'field': [69772, -13569, 4809, -167, 123, -3, 1], 'lmfdb_label': '103933.b3', 'torsion': [3]}
  • id: 4809118
    {'degree': 12, 'field': [-6724214162, -8352865420, -1467785592, -12366524, -37073060, 1170824, 1262872, 16960, -6190, -498, 8, -6, 1], 'lmfdb_label': '103933.b3', 'torsion': [4]}
  • id: 4809121
    {'degree': 12, 'field': [2010724, 0, -1540148, 0, 417672, 0, -51589, 0, 3139, 0, -91, 0, 1], 'lmfdb_label': '103933.b3', 'torsion': [2, 6]}
  • id: 4809119
    {'degree': 12, 'field': [5098564, 0, -2459617, 0, 528507, 0, -47561, 0, 2589, 0, -79, 0, 1], 'lmfdb_label': '103933.b3', 'torsion': [3, 3]}
  • id: 4809120
    {'degree': 12, 'field': [5508517, 180751, -2522770, -38018, 471630, 2190, -46541, 0, 2610, -2, -79, 0, 1], 'lmfdb_label': '103933.b3', 'torsion': [9]}
  • id: 4809123
    {'degree': 18, 'field': [-592992737, 249541282, 1963481465, 728882483, -1024784639, -504875187, 230079665, 124689587, -29978395, -15687740, 2621364, 1107527, -157605, -43761, 5991, 886, -123, -7, 1], 'lmfdb_label': '103933.b3', 'torsion': [18]}
  • id: 4809122
    {'degree': 18, 'field': [232667301156826, -9365485963354, 57122396515450, -3137035747969, 5961141616593, -321465782508, 352148053524, -16877441103, 13178215427, -533199051, 327289637, -10681115, 5425417, -134165, 57999, -966, 362, -3, 1], 'lmfdb_label': '103933.b3', 'torsion': [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: 2551702
    {'conductor': 103933, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '103933.b3', 'prime': 37, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 2551703
    {'conductor': 103933, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '103933.b3', 'prime': 53, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 2346068
    {'adelic_gens': [[32225, 61215, 62911, 39274], [105841, 54, 105840, 55], [19979, 0, 0, 105893], [1, 54, 0, 1], [31, 36, 100072, 99133], [90472, 73935, 14999, 92698], [1, 0, 54, 1], [28, 27, 729, 703]], 'adelic_image': '105894.1296.43.?', 'conductor': 103933, 'lmfdb_label': '103933.b3', 'prime': 0}
  • id: 415610
    {'conductor': 103933, 'elladic_image': '27.36.0.1', 'lmfdb_label': '103933.b3', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 103933.b does not appear in ec_padic