Elliptic curve data - 117600.gj4

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '117600cn', 'Clabel': '117600cn2', 'Cnumber': 2, 'abc_quality': 1.0384110894370049, 'absD': 980368514637120000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 840, 'ainvs': [0, 1, 0, 409967, 1503188063], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 117600, 'degree': 3538944, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.7072194369860458610800407448', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 165, 'isogeny_degrees': [1, 2, 4], 'jinv': [1012048064, 130203045], 'lmfdb_iso': '117600.gj', 'lmfdb_label': '117600.gj4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 335, 34945], 'min_quad_twist_disc': 140, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '20.12.0.h.1', '24.12.0.y.1', '28.12.0-4.c.1.1', '120.24.0.?', '140.24.0.?', '168.24.0.?', '840.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 5, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.4183508684113066097670991624', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.23639822568139371180975258501', 'prec': 103}, 'szpiro_ratio': 4.77811221403606, '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, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, -2, 0, -4, 0], 'aplist': [0, 1, 0, 0, 0, 2, -2, -4, -8, -2, -4, 6, 6, 4, 0, -6, 0, -6, -4, 8, 10, 12, 4, 6, -6], 'class_deg': 4, 'class_size': 4, 'conductor': 117600, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '117600.gj', 'trace_hash': 1525471246861614704}
• 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': '0.0044518351526007541658215763528', 'prec': 110}, 'conductor': 117600, 'gens': [[-271, 37044, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.4183508684113066097670991624', 'prec': 100}], 'lmfdb_label': '117600.gj4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.12027205719415502332446929253', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.1882228848133174697470632787038022695', 'prec': 130}, 'tamagawa_product': 192, 'torsion_generators': [[-1027, 0, 1]], 'xcoord_integral_points': [-1027, -271, 3698]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': 'a', '7': 'a', '11': [1, 1, 0], '13': [1, 0], '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, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '117600.gj4'}
• ec_torsion_growth •

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

  
  
  • id: 5386505
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '117600.gj4', 'torsion': [4]}
  • id: 5386504
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '117600.gj4', 'torsion': [2, 2]}
  • id: 5386506
    {'degree': 2, 'field': [9, -1, 1], 'lmfdb_label': '117600.gj4', 'torsion': [4]}
  • id: 5386507
    {'degree': 4, 'field': [9, 0, -1, 0, 1], 'lmfdb_label': '117600.gj4', 'torsion': [2, 4]}
  • id: 5386511
    {'degree': 8, 'field': [-19494, -47844, -26316, -9816, -1980, -396, -26, -4, 1], 'lmfdb_label': '117600.gj4', 'torsion': [6]}
  • id: 5386508
    {'degree': 8, 'field': [46, 68, -34, -76, 59, -28, 14, -4, 1], 'lmfdb_label': '117600.gj4', 'torsion': [2, 4]}
  • id: 5386510
    {'degree': 8, 'field': [7569, 0, -48, 0, 58, 0, 16, 0, 1], 'lmfdb_label': '117600.gj4', 'torsion': [8]}
  • id: 5386509
    {'degree': 8, 'field': [12321, 0, -5892, 0, 934, 0, -68, 0, 1], 'lmfdb_label': '117600.gj4', 'torsion': [8]}
  • id: 5386516
    {'degree': 16, 'field': [-6373104, 3141504, 13048048, -551696, -7799504, -376800, 2265924, 441612, -21719, 11524, -10004, 60, 606, 108, -8, -8, 1], 'lmfdb_label': '117600.gj4', 'torsion': [12]}
  • id: 5386512
    {'degree': 16, 'field': [2116, 0, 7752, 0, 16920, 0, 4692, 0, -1091, 0, -192, 0, 90, 0, -12, 0, 1], 'lmfdb_label': '117600.gj4', 'torsion': [4, 4]}
  • id: 5386513
    {'degree': 16, 'field': [8289, 19548, 49680, -67716, -110124, 88632, 88012, -58364, -31875, 21224, 4784, -4020, -58, 308, -24, -8, 1], 'lmfdb_label': '117600.gj4', 'torsion': [2, 8]}
  • id: 5386517
    {'degree': 16, 'field': [33877125, -128385000, 161122800, -71085000, 50142270, -19176760, 9286556, -2752768, 1043615, -261640, 78068, -15392, 3718, -560, 100, -8, 1], 'lmfdb_label': '117600.gj4', 'torsion': [12]}
  • id: 5386515
    {'degree': 16, 'field': [43142841, -32337900, 1219554, 17250744, -2148342, -2650284, 1308358, 717624, -111641, -96292, -2498, 6368, 928, -172, -44, 0, 1], 'lmfdb_label': '117600.gj4', 'torsion': [2, 6]}
  • id: 5386514
    {'degree': 16, 'field': [44436681, -24910740, 33057288, -17629596, 12391812, -4979016, 2885076, -1217868, 526165, -167408, 53968, -12308, 3022, -476, 88, -8, 1], 'lmfdb_label': '117600.gj4', '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: 2893808
    {'conductor': 117600, 'conductor_valuation': 5, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '117600.gj4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2893809
    {'conductor': 117600, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '117600.gj4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
  • id: 2893810
    {'conductor': 117600, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '117600.gj4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2893811
    {'conductor': 117600, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '117600.gj4', 'prime': 7, '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

  
  
  • id: 2432554
    {'adelic_gens': [[323, 798, 770, 827], [833, 8, 832, 9], [1, 0, 8, 1], [692, 119, 49, 594], [1, 8, 0, 1], [1, 4, 4, 17], [599, 0, 0, 839], [7, 6, 834, 835], [288, 833, 217, 204], [281, 728, 644, 393]], 'adelic_image': '840.48.0.?', 'conductor': 117600, 'lmfdb_label': '117600.gj4', 'prime': 0}
  • id: 463379
    {'conductor': 117600, 'elladic_image': '4.6.0.1', 'lmfdb_label': '117600.gj4', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 6143239
    {'lmfdb_iso': '117600.gj', 'p': 13, 'prec': 20, 'unit': 100149367039795165987, 'val': 1}
  • id: 6143241
    {'lmfdb_iso': '117600.gj', 'p': 17, 'prec': 20, 'unit': 196100722034102235859411, 'val': 1}
  • id: 6143231
    {'lmfdb_iso': '117600.gj', 'p': 19, 'prec': 20, 'unit': 1479084514128686961097542, 'val': 1}
  • id: 6143245
    {'lmfdb_iso': '117600.gj', 'p': 23, 'prec': 20, 'unit': 41770030301707052644188343, 'val': 1}
  • id: 6143238
    {'lmfdb_iso': '117600.gj', 'p': 29, 'prec': 20, 'unit': 5457113334424355671893821750, 'val': 1}
  • id: 6143248
    {'lmfdb_iso': '117600.gj', 'p': 31, 'prec': 20, 'unit': 53168314720552285162948149, 'val': 1}
  • id: 6143234
    {'lmfdb_iso': '117600.gj', 'p': 37, 'prec': 20, 'unit': 550675384357153416857168943846, 'val': 1}
  • id: 6143236
    {'lmfdb_iso': '117600.gj', 'p': 41, 'prec': 20, 'unit': 4209798544734091035224412939471, 'val': 1}
  • id: 6143237
    {'lmfdb_iso': '117600.gj', 'p': 43, 'prec': 20, 'unit': 1587973521563314603380125033698, 'val': 1}
  • id: 6143243
    {'lmfdb_iso': '117600.gj', 'p': 53, 'prec': 20, 'unit': 470949303047070287766108161345100, 'val': 1}
  • id: 6143247
    {'lmfdb_iso': '117600.gj', 'p': 61, 'prec': 20, 'unit': 4380342048251193255597497360811156, 'val': 1}
  • id: 6143233
    {'lmfdb_iso': '117600.gj', 'p': 67, 'prec': 20, 'unit': 19354154482347841759379378211284564, 'val': 1}
  • id: 6143235
    {'lmfdb_iso': '117600.gj', 'p': 71, 'prec': 20, 'unit': 51673665446548324825470367505397996, 'val': 1}
  • id: 6143244
    {'lmfdb_iso': '117600.gj', 'p': 73, 'prec': 20, 'unit': 166191332618089396157703225204499444, 'val': 1}
  • id: 6143240
    {'lmfdb_iso': '117600.gj', 'p': 79, 'prec': 20, 'unit': 336855252272271488188164617009515675, 'val': 1}
  • id: 6143242
    {'lmfdb_iso': '117600.gj', 'p': 83, 'prec': 20, 'unit': 1436465458684603512882859502545727942, 'val': 1}
  • id: 6143246
    {'lmfdb_iso': '117600.gj', 'p': 89, 'prec': 20, 'unit': 4063104035934246919706543159546550549, 'val': 1}
  • id: 6143232
    {'lmfdb_iso': '117600.gj', 'p': 97, 'prec': 20, 'unit': 3262331126505408496622783057522764113, 'val': 1}