Elliptic curve data - 51376.o2

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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': '51376t', 'Clabel': '51376t3', 'Cnumber': 3, 'abc_quality': 0.9721245466261954, 'absD': 66989666172575744, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1976, 'ainvs': [0, 0, 0, -395291, 94844490], 'analytic_rank': 1, 'bad_primes': [2, 13, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 51376, 'degree': 548352, 'elladic_images': ['4.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0478512922675703115636724295', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 14, 'isogeny_degrees': [1, 2, 4], 'jinv': [345505073913, 3388346], 'lmfdb_iso': '51376.o', 'lmfdb_label': '51376.o2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -146, -638], 'min_quad_twist_disc': -52, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '104.24.0.?', '152.24.0.?', '1976.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 7, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.6280420639474724123383704565', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.072229432976856634119696587258', 'prec': 107}, 'szpiro_ratio': 4.635021345914065, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
• 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, 0, 0, -2, 0, 4, 0, -3, 0, 4, 0, 0, 0, 0, 0, 2, 0, 1, 0], 'aplist': [0, 0, -2, 4, 4, 0, 2, 1, 8, 2, 0, -10, 2, -12, 4, -6, -12, 14, -12, 8, -2, 16, -12, -6, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 51376, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '51376.o', 'trace_hash': 818563686994712666}
• 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': '0.016644048323033112257537956484', 'prec': 107}, 'conductor': 51376, 'gens': [[101, 7480, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '4.6280420639474724123383704565', 'prec': 100}], 'lmfdb_label': '51376.o2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.34945518532146563833502693731', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.4691731885292091938573252257724840910', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[143, 6422, 1]], 'xcoord_integral_points': [101, 143, 390, 109317]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 3, 0], '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': 'a', '17': [1, 0], '19': [2, 0], '23': [1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '51376.o2'}
• ec_torsion_growth •

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

  
  
  • id: 2490621
    {'degree': 2, 'field': [-26, 0, 1], 'lmfdb_label': '51376.o2', 'torsion': [2, 4]}
  • id: 2490622
    {'degree': 4, 'field': [104, 0, -13, 0, 1], 'lmfdb_label': '51376.o2', 'torsion': [8]}
  • id: 2490623
    {'degree': 8, 'field': [729, 0, -308, 0, 58, 0, 4, 0, 1], 'lmfdb_label': '51376.o2', 'torsion': [4, 4]}
  • id: 2490626
    {'degree': 8, 'field': [1257, -498, -654, 252, 108, -42, -12, 0, 1], 'lmfdb_label': '51376.o2', 'torsion': [12]}
  • id: 2490625
    {'degree': 8, 'field': [17993, 1976, -12800, 1040, 1886, -104, -96, 0, 1], 'lmfdb_label': '51376.o2', 'torsion': [2, 8]}
  • id: 2490624
    {'degree': 8, 'field': [123175, -71500, 25896, -4784, 261, 100, 6, -4, 1], 'lmfdb_label': '51376.o2', 'torsion': [2, 8]}
  • id: 2490628
    {'degree': 16, 'field': [5180176, 0, -5936128, 0, 4394464, 0, -1891840, 0, 433768, 0, -46576, 0, 2161, 0, -52, 0, 1], 'lmfdb_label': '51376.o2', 'torsion': [2, 12]}
  • id: 2490627
    {'degree': 16, 'field': [116985856, 0, -58492928, 0, 26153088, 0, -7225088, 0, 1010048, 0, -69472, 0, 2418, 0, -52, 0, 1], 'lmfdb_label': '51376.o2', 'torsion': [16]}
• 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: 1229790
    {'conductor': 51376, 'conductor_valuation': 4, 'discriminant_valuation': 13, 'j_denominator_valuation': 1, 'kodaira_symbol': -9, 'lmfdb_label': '51376.o2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1229791
    {'conductor': 51376, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '51376.o2', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 1229792
    {'conductor': 51376, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '51376.o2', 'prime': 19, 'reduction_type': 1, '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: 2005583
    {'adelic_gens': [[1725, 1728, 718, 1723], [1769, 8, 1148, 33], [248, 1243, 745, 774], [1, 0, 8, 1], [1969, 8, 1968, 9], [7, 6, 1970, 1971], [148, 1975, 1345, 1970], [1, 8, 0, 1], [1, 4, 4, 17]], 'adelic_image': '1976.48.0.?', 'conductor': 51376, 'lmfdb_label': '51376.o2', 'prime': 0}
  • id: 220177
    {'conductor': 51376, 'elladic_image': '4.12.0.7', 'lmfdb_label': '51376.o2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 2584562
    {'lmfdb_iso': '51376.o', 'p': 5, 'prec': 20, 'unit': 12955592787632, 'val': 1}
  • id: 2584563
    {'lmfdb_iso': '51376.o', 'p': 7, 'prec': 20, 'unit': 11024409056882331, 'val': 1}
  • id: 2584561
    {'lmfdb_iso': '51376.o', 'p': 11, 'prec': 20, 'unit': 43975008839682755533, 'val': 1}
  • id: 2584568
    {'lmfdb_iso': '51376.o', 'p': 17, 'prec': 20, 'unit': 212321949039848162159311, 'val': 1}
  • id: 2584573
    {'lmfdb_iso': '51376.o', 'p': 23, 'prec': 20, 'unit': 18376241979968643757238708, 'val': 1}
  • id: 2584566
    {'lmfdb_iso': '51376.o', 'p': 29, 'prec': 20, 'unit': 5108208955854472952437796861, 'val': 1}
  • id: 2584578
    {'lmfdb_iso': '51376.o', 'p': 37, 'prec': 20, 'unit': 175852813678652590869954287817, 'val': 1}
  • id: 2584564
    {'lmfdb_iso': '51376.o', 'p': 41, 'prec': 20, 'unit': 2932049425575974635860537197287, 'val': 1}
  • id: 2584565
    {'lmfdb_iso': '51376.o', 'p': 43, 'prec': 20, 'unit': 2774316885012170437736951893662, 'val': 1}
  • id: 2584576
    {'lmfdb_iso': '51376.o', 'p': 47, 'prec': 20, 'unit': 34884900140076690101530804020821, 'val': 1}
  • id: 2584570
    {'lmfdb_iso': '51376.o', 'p': 53, 'prec': 20, 'unit': 460802653439465899741821018379749, 'val': 1}
  • id: 2584571
    {'lmfdb_iso': '51376.o', 'p': 59, 'prec': 20, 'unit': 1162892166114589644058224604994714, 'val': 1}
  • id: 2584577
    {'lmfdb_iso': '51376.o', 'p': 61, 'prec': 20, 'unit': 4060371237361515417493529244679584, 'val': 1}
  • id: 2584560
    {'lmfdb_iso': '51376.o', 'p': 67, 'prec': 20, 'unit': 5152567211316814601511570042287952, 'val': 1}
  • id: 2584575
    {'lmfdb_iso': '51376.o', 'p': 71, 'prec': 20, 'unit': 79863617898346673855314923552461170, 'val': 1}
  • id: 2584572
    {'lmfdb_iso': '51376.o', 'p': 73, 'prec': 20, 'unit': 132428624665362934021444139966457410, 'val': 1}
  • id: 2584567
    {'lmfdb_iso': '51376.o', 'p': 79, 'prec': 20, 'unit': 132013006450178558240525766162461002, 'val': 1}
  • id: 2584569
    {'lmfdb_iso': '51376.o', 'p': 83, 'prec': 20, 'unit': 110676531346689033339963092884435069, 'val': 1}
  • id: 2584574
    {'lmfdb_iso': '51376.o', 'p': 89, 'prec': 20, 'unit': 9987611808676834952077288885373399573, 'val': 1}
  • id: 2584559
    {'lmfdb_iso': '51376.o', 'p': 97, 'prec': 20, 'unit': 19556604262761609490866233607241644911, 'val': 1}