Elliptic curve data - 76050.gb1

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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': '76050ew', 'Clabel': '76050ew4', 'Cnumber': 4, 'abc_quality': 1.0375259015845228, 'absD': 557500964633437500000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1560, 'ainvs': [1, -1, 1, -3290247005, -72641691675003], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 76050, 'degree': 41287680, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.8337632562527205076174449255', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 157, 'isogeny_degrees': [1, 2, 4], 'jinv': [71647584155243142409, 10140000], 'lmfdb_iso': '76050.gb', 'lmfdb_label': '76050.gb1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -86529, 9789652], 'min_quad_twist_disc': -195, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0.s.1', '40.12.0.bb.1', '104.12.0.?', '120.24.0.?', '260.12.0.?', '312.24.0.?', '520.24.0.?', '1560.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '15.665541293578642151286564412', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 38025], [3, 8, 8450], [5, 18, 1521], [13, 98, 450]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1972634769708471065926989196', 'prec': 100}, 'szpiro_ratio': 6.8827548296612955, '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, 1, 0, 1, 0, 0, 4, 1, 0, 0, 0, 0, 0, 4, 0, 1, -2, 0, -4, 0], 'aplist': [1, 0, 0, 4, 0, 0, -2, -4, 8, -2, 8, 2, -6, -12, 0, 10, 0, -10, -4, -16, -6, -8, 4, -14, -6], 'class_deg': 4, 'class_size': 4, 'conductor': 76050, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '76050.gb', 'trace_hash': 650805885185146413}
• 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': '0.00046777342564906952133511506791', 'prec': 113}, 'conductor': 76050, 'gens': [[285773139, 4105417923020, 49]], 'heights': [{'__RealLiteral__': 0, 'data': '15.665541293578642151286564412', 'prec': 100}], 'lmfdb_label': '76050.gb1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.019933907060097478563622273908', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '12.491017767692635276336331967569850330', 'prec': 130}, 'tamagawa_product': 160, 'torsion_generators': [[-132469, 132465, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 1], '3': 'a', '5': 'a', '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, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '76050.gb1'}
• ec_torsion_growth •

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

  
  
  • id: 3596520
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '76050.gb1', 'torsion': [2, 2]}
  • id: 3596521
    {'degree': 2, 'field': [65, 0, 1], 'lmfdb_label': '76050.gb1', 'torsion': [4]}
  • id: 3596522
    {'degree': 2, 'field': [390, 0, 1], 'lmfdb_label': '76050.gb1', 'torsion': [4]}
  • id: 3596523
    {'degree': 4, 'field': [5041, 0, 118, 0, 1], 'lmfdb_label': '76050.gb1', 'torsion': [2, 4]}
  • id: 3596524
    {'degree': 8, 'field': [9216, 0, 0, 0, -1752, 0, 0, 0, 1], 'lmfdb_label': '76050.gb1', 'torsion': [2, 4]}
  • id: 3596526
    {'degree': 8, 'field': [33514, -5928, 6436, -1040, 581, -76, 30, -4, 1], 'lmfdb_label': '76050.gb1', 'torsion': [8]}
  • id: 3596525
    {'degree': 8, 'field': [68149, 31324, -4091, -2450, 646, 148, -35, -2, 1], 'lmfdb_label': '76050.gb1', 'torsion': [8]}
  • id: 3596527
    {'degree': 8, 'field': [172540, 234600, 37270, 4225, 105, -110, 76, -3, 1], 'lmfdb_label': '76050.gb1', 'torsion': [6]}
  • id: 3596531
    {'degree': 16, 'field': [-216764028680, -52555727760, 89549876924, 5570905184, 2476488202, 2320710856, 42895749, 61608290, 11359425, 1563680, -100050, 5620, 2716, -424, 113, -6, 1], 'lmfdb_label': '76050.gb1', 'torsion': [2, 6]}
  • id: 3596528
    {'degree': 16, 'field': [1030225, 0, -2294080, 0, 1721416, 0, 710648, 0, 178174, 0, -1696, 0, 904, 0, 8, 0, 1], 'lmfdb_label': '76050.gb1', 'torsion': [4, 4]}
  • id: 3596532
    {'degree': 16, 'field': [1459264, 0, 3182400, 0, -1008608, 0, -126956, 0, 169920, 0, 25516, 0, -815, 0, 63, 0, 1], 'lmfdb_label': '76050.gb1', 'torsion': [12]}
  • id: 3596529
    {'degree': 16, 'field': [6358465, 10336500, -356236, -5773604, 167303, 1548648, -187486, -271356, 57940, 33204, -9080, -2716, 831, 128, -38, -4, 1], 'lmfdb_label': '76050.gb1', 'torsion': [2, 8]}
  • id: 3596530
    {'degree': 16, 'field': [186595600, 0, 76009280, 0, 14586176, 0, 1832928, 0, 157304, 0, 9264, 0, 464, 0, 8, 0, 1], 'lmfdb_label': '76050.gb1', 'torsion': [2, 8]}
  • id: 3596533
    {'degree': 16, 'field': [438519435264, 0, -69485698560, 0, -2404908608, 0, 413147544, 0, 13380840, 0, 137726, 0, 5280, 0, 138, 0, 1], 'lmfdb_label': '76050.gb1', 'torsion': [12]}
• 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: 1849380
    {'conductor': 76050, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '76050.gb1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 5}
  • id: 1849381
    {'conductor': 76050, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '76050.gb1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1849382
    {'conductor': 76050, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '76050.gb1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 1849383
    {'conductor': 76050, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '76050.gb1', '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: 2166578
    {'adelic_gens': [[272, 117, 1235, 1078], [1, 0, 8, 1], [1, 8, 0, 1], [479, 0, 0, 1559], [1, 4, 4, 17], [976, 923, 1339, 768], [7, 6, 1554, 1555], [1553, 8, 1552, 9], [623, 832, 572, 207], [768, 1313, 1027, 534]], 'adelic_image': '1560.48.0.?', 'conductor': 76050, 'lmfdb_label': '76050.gb1', 'prime': 0}
  • id: 314210
    {'conductor': 76050, 'elladic_image': '4.6.0.1', 'lmfdb_label': '76050.gb1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 3915504
    {'lmfdb_iso': '76050.gb', 'p': 7, 'prec': 20, 'unit': 5557966398060912, 'val': 1}
  • id: 3915509
    {'lmfdb_iso': '76050.gb', 'p': 17, 'prec': 20, 'unit': 92503153590938053660520, 'val': 1}
  • id: 3915500
    {'lmfdb_iso': '76050.gb', 'p': 19, 'prec': 20, 'unit': 1702181375820707718030050, 'val': 1}
  • id: 3915513
    {'lmfdb_iso': '76050.gb', 'p': 23, 'prec': 20, 'unit': 51687850029260517268599040, 'val': 1}
  • id: 3915507
    {'lmfdb_iso': '76050.gb', 'p': 29, 'prec': 20, 'unit': 5634820327683163174563184111, 'val': 1}
  • id: 3915517
    {'lmfdb_iso': '76050.gb', 'p': 31, 'prec': 20, 'unit': 16401332971495639476198634687, 'val': 1}
  • id: 3915503
    {'lmfdb_iso': '76050.gb', 'p': 37, 'prec': 20, 'unit': 327463531938977189110607241878, 'val': 1}
  • id: 3915505
    {'lmfdb_iso': '76050.gb', 'p': 41, 'prec': 20, 'unit': 1514162098055522421807383863579, 'val': 1}
  • id: 3915506
    {'lmfdb_iso': '76050.gb', 'p': 43, 'prec': 20, 'unit': 6466627951819991716979127812504, 'val': 1}
  • id: 3915511
    {'lmfdb_iso': '76050.gb', 'p': 53, 'prec': 20, 'unit': 550108319985311292909051872250008, 'val': 1}
  • id: 3915516
    {'lmfdb_iso': '76050.gb', 'p': 61, 'prec': 20, 'unit': 104387080967741520457124284294190, 'val': 1}
  • id: 3915502
    {'lmfdb_iso': '76050.gb', 'p': 67, 'prec': 20, 'unit': 45881313513101220905959033852454013, 'val': 1}
  • id: 3915515
    {'lmfdb_iso': '76050.gb', 'p': 71, 'prec': 20, 'unit': 42415647703491003739373723998032162, 'val': 1}
  • id: 3915512
    {'lmfdb_iso': '76050.gb', 'p': 73, 'prec': 20, 'unit': 174946990952425351873247827585970381, 'val': 1}
  • id: 3915508
    {'lmfdb_iso': '76050.gb', 'p': 79, 'prec': 20, 'unit': 570751210989465672784652552051307945, 'val': 1}
  • id: 3915510
    {'lmfdb_iso': '76050.gb', 'p': 83, 'prec': 20, 'unit': 13349684547452534871893655606813294, 'val': 2}
  • id: 3915514
    {'lmfdb_iso': '76050.gb', 'p': 89, 'prec': 20, 'unit': 1054833752772997516175891649244794429, 'val': 1}
  • id: 3915501
    {'lmfdb_iso': '76050.gb', 'p': 97, 'prec': 20, 'unit': 10850175250423529573028592234915630104, 'val': 1}