Elliptic curve data - 51376.z2

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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': '51376w', 'Clabel': '51376w1', 'Cnumber': 1, 'abc_quality': 0.7955327471096909, 'absD': 6886273249648, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 2964, 'ainvs': [0, -1, 0, -3098, 143675], 'analytic_rank': 1, 'bad_primes': [2, 13, 19], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 51376, 'degree': 72576, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1524526621500331183315992731', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 25, 'isogeny_degrees': [1, 3], 'jinv': [-42592000, 89167], 'lmfdb_iso': '51376.z', 'lmfdb_label': '51376.z2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -18, -71], 'min_quad_twist_disc': -52, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '156.8.0.?', '228.8.0.?', '494.2.0.?', '1482.8.0.?', '2964.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.3589474252451721745411301460', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.36107107676738368616755515484', 'prec': 107}, 'szpiro_ratio': 3.4350132277213383, '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, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, -3, 0, 1, 0], 'aplist': [0, 2, 0, 2, 0, 0, -3, 1, -3, 6, -1, 7, -9, -11, 6, 6, 9, -1, 11, 12, -8, 10, -6, -6, -11], 'class_deg': 3, 'class_size': 2, 'conductor': 51376, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '51376.z', 'trace_hash': 1053354304615727360}
• 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': '0.099768245835002596099816488773', 'prec': 107}, 'conductor': 51376, 'gens': [[25, 285, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.3589474252451721745411301460', 'prec': 100}], 'lmfdb_label': '51376.z2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.66486616919574804315178792843', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '9.4103060277415851109335091464550569718', 'prec': 130}, 'tamagawa_product': 6, 'torsion_generators': [], 'xcoord_integral_points': [25]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '5': [1, 1, 0], '7': [1, 0], '11': [1, 1, 0], '13': 'a', '17': [1, 0], '19': [2, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '51376.z2'}
• ec_torsion_growth •

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

  
  
  • id: 2490685
    {'degree': 2, 'field': [13, 0, 1], 'lmfdb_label': '51376.z2', 'torsion': [3]}
  • id: 2490686
    {'degree': 3, 'field': [-3, 1, 0, 1], 'lmfdb_label': '51376.z2', 'torsion': [2]}
  • id: 2490688
    {'degree': 6, 'field': [-39, 0, 91, 0, -13, 0, 1], 'lmfdb_label': '51376.z2', 'torsion': [3]}
  • id: 2490687
    {'degree': 6, 'field': [9, 21, 80, 1, -6, -2, 1], 'lmfdb_label': '51376.z2', 'torsion': [2, 2]}
  • id: 2490689
    {'degree': 6, 'field': [13, 0, 10, 0, 1, 0, 1], 'lmfdb_label': '51376.z2', 'torsion': [6]}
  • id: 2490690
    {'degree': 12, 'field': [-247, 0, -13150, 0, -9375, 0, -2630, 0, -250, 0, 0, 0, 1], 'lmfdb_label': '51376.z2', 'torsion': [4]}
  • id: 2490692
    {'degree': 12, 'field': [64, 0, 208, 0, 520, 0, 413, 0, 130, 0, 13, 0, 1], 'lmfdb_label': '51376.z2', 'torsion': [2, 6]}
  • id: 2490691
    {'degree': 12, 'field': [2809, -2332, 293, -2000, 1596, -536, 271, 38, 30, 2, 11, -2, 1], 'lmfdb_label': '51376.z2', 'torsion': [3, 3]}
  • id: 2490694
    {'degree': 18, 'field': [-126711, 0, -73125, 0, -54015, 0, 21904, 0, 16800, 0, 11715, 0, 2591, 0, 375, 0, 30, 0, 1], 'lmfdb_label': '51376.z2', 'torsion': [6]}
  • id: 2490693
    {'degree': 18, 'field': [48387275053, 0, 200993296374, 0, 212250005955, 0, 23128694927, 0, 665669199, 0, 10634832, 0, 244504, 0, 4953, 0, 39, 0, 1], 'lmfdb_label': '51376.z2', '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: 1229808
    {'conductor': 51376, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '51376.z2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1229809
    {'conductor': 51376, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '51376.z2', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1229810
    {'conductor': 51376, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '51376.z2', 'prime': 19, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
• ec_galrep •

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

  
  
  • id: 2005601
    {'adelic_gens': [[4, 3, 9, 7], [1481, 0, 0, 2963], [1236, 253, 247, 495], [2507, 2958, 1593, 2945], [2959, 6, 2958, 7], [1487, 2958, 1488, 2957], [1, 6, 0, 1], [3, 4, 8, 11], [781, 6, 861, 19], [1, 0, 6, 1]], 'adelic_image': '2964.16.0.?', 'conductor': 51376, 'lmfdb_label': '51376.z2', 'prime': 0}
  • id: 220190
    {'conductor': 51376, 'elladic_image': '3.4.0.1', 'lmfdb_label': '51376.z2', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 2584602
    {'lmfdb_iso': '51376.z', 'p': 7, 'prec': 20, 'unit': 4377098336125189, 'val': 1}
  • id: 2584607
    {'lmfdb_iso': '51376.z', 'p': 17, 'prec': 20, 'unit': 174151867536832749299594, 'val': 1}
  • id: 2584612
    {'lmfdb_iso': '51376.z', 'p': 23, 'prec': 20, 'unit': 6121509059080455225456045, 'val': 1}
  • id: 2584605
    {'lmfdb_iso': '51376.z', 'p': 29, 'prec': 20, 'unit': 1210899279246701627071599158, 'val': 1}
  • id: 2584617
    {'lmfdb_iso': '51376.z', 'p': 31, 'prec': 20, 'unit': 4125472811291948342061472796, 'val': 1}
  • id: 2584601
    {'lmfdb_iso': '51376.z', 'p': 37, 'prec': 20, 'unit': 477591832865487518300154330749, 'val': 1}
  • id: 2584603
    {'lmfdb_iso': '51376.z', 'p': 41, 'prec': 20, 'unit': 2944052479206612615495883662507, 'val': 1}
  • id: 2584604
    {'lmfdb_iso': '51376.z', 'p': 43, 'prec': 20, 'unit': 9998077370151809188524197991869, 'val': 1}
  • id: 2584615
    {'lmfdb_iso': '51376.z', 'p': 47, 'prec': 20, 'unit': 30838867570538933350185854936531, 'val': 1}
  • id: 2584609
    {'lmfdb_iso': '51376.z', 'p': 53, 'prec': 20, 'unit': 57134728517012659876727435364849, 'val': 1}
  • id: 2584610
    {'lmfdb_iso': '51376.z', 'p': 59, 'prec': 20, 'unit': 1982516232131675355081439060757851, 'val': 1}
  • id: 2584616
    {'lmfdb_iso': '51376.z', 'p': 61, 'prec': 20, 'unit': 5817679676898194023047092954648870, 'val': 1}
  • id: 2584600
    {'lmfdb_iso': '51376.z', 'p': 67, 'prec': 20, 'unit': 38167125343387067677971349406265312, 'val': 1}
  • id: 2584614
    {'lmfdb_iso': '51376.z', 'p': 71, 'prec': 20, 'unit': 147754501085776813937946977852638895, 'val': 1}
  • id: 2584611
    {'lmfdb_iso': '51376.z', 'p': 73, 'prec': 20, 'unit': 62955307487609828757149196706271963, 'val': 1}
  • id: 2584606
    {'lmfdb_iso': '51376.z', 'p': 79, 'prec': 20, 'unit': 654372460363234619873170981660663389, 'val': 1}
  • id: 2584608
    {'lmfdb_iso': '51376.z', 'p': 83, 'prec': 20, 'unit': 777734423720831158795769267681116667, 'val': 1}
  • id: 2584613
    {'lmfdb_iso': '51376.z', 'p': 89, 'prec': 20, 'unit': 5797756158435362093398620894935020159, 'val': 1}
  • id: 2584599
    {'lmfdb_iso': '51376.z', 'p': 97, 'prec': 20, 'unit': 14504499711814315772060149689687273176, 'val': 1}