Elliptic curve data - 71478.cc2

Formats: - HTML - YAML - JSON - 2024-05-18T21:34:26.432302

• 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': '71478bn', 'Clabel': '71478bn3', 'Cnumber': 3, 'abc_quality': 0.9924779712445644, 'absD': 41722039635775488, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 2508, 'ainvs': [1, -1, 1, -210170, 35812153], 'analytic_rank': 0, 'bad_primes': [2, 3, 11, 19], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 71478, 'degree': 684288, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.9550110795255900362300533204', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 54, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [1108717875, 45056], 'lmfdb_iso': '71478.cc', 'lmfdb_label': '71478.cc2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -582, -5068], 'min_quad_twist_disc': -19, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '12.24.0.i.1', '44.6.0.e.1', '57.8.0-3.a.1.2', '66.24.0.b.1', '114.24.0.?', '132.48.1.?', '228.48.0.?', '1254.48.0.?', '2508.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.34116762655871246232089432324', 'prec': 107}, 'szpiro_ratio': 4.328530643344539, '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, 2, 1, 0, 0, 1, 0, -2, 2, 0, 1, 6, 0, 0, 0], 'aplist': [1, 0, 0, 2, 1, -2, 6, 0, 0, -6, 4, -2, 6, -10, -12, -12, 12, -10, -8, 12, 14, -2, 12, 0, -2], 'class_deg': 6, 'class_size': 4, 'conductor': 71478, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '71478.cc', 'trace_hash': 1402258621064230549}
• 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': '0.020040056988115459240838853020', 'prec': 107}, 'conductor': 71478, 'gens': [], 'heights': [], 'lmfdb_label': '71478.cc2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.35860359151175539589902851375', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.3032430981410647507883421650264736077', 'prec': 130}, 'tamagawa_product': 48, 'torsion_generators': [[-527, 263, 1]], 'xcoord_integral_points': [-527]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '3': 'a', '11': [1, 0], '19': 'a'}, 'iwp0': 5, 'lmfdb_label': '71478.cc2'}
• ec_torsion_growth •

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

  
  
  • id: 3393578
    {'degree': 2, 'field': [-14, -1, 1], 'lmfdb_label': '71478.cc2', 'torsion': [6]}
  • id: 3393577
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '71478.cc2', 'torsion': [2, 2]}
  • id: 3393580
    {'degree': 4, 'field': [4, 97, -37, -1, 1], 'lmfdb_label': '71478.cc2', 'torsion': [2, 6]}
  • id: 3393579
    {'degree': 4, 'field': [766, -86, 87, -2, 1], 'lmfdb_label': '71478.cc2', 'torsion': [4]}
  • id: 3393581
    {'degree': 6, 'field': [400, -372, 57, -9, 18, -3, 1], 'lmfdb_label': '71478.cc2', 'torsion': [6]}
  • id: 3393584
    {'degree': 8, 'field': [2116, 0, -688, 0, 117, 0, -10, 0, 1], 'lmfdb_label': '71478.cc2', 'torsion': [12]}
  • id: 3393583
    {'degree': 8, 'field': [213376, 16960, 33016, 5032, 1906, 58, 67, -2, 1], 'lmfdb_label': '71478.cc2', 'torsion': [2, 4]}
  • id: 3393582
    {'degree': 8, 'field': [1211596, 164344, -157045, -14462, 6892, 404, -130, -4, 1], 'lmfdb_label': '71478.cc2', 'torsion': [2, 4]}
  • id: 3393586
    {'degree': 12, 'field': [119872, 161232, -109980, -104410, 57345, -7248, 4307, -1806, 690, -170, 45, -6, 1], 'lmfdb_label': '71478.cc2', 'torsion': [2, 6]}
  • id: 3393585
    {'degree': 12, 'field': [160000, -148800, 115584, -14004, -7299, 11679, -1261, -192, 240, -36, -9, -3, 1], 'lmfdb_label': '71478.cc2', 'torsion': [3, 6]}
  • id: 3393588
    {'degree': 16, 'field': [-235232, 5275584, -17247424, 21560184, -11309534, -692934, 4524005, -1889220, -251486, 326946, -30679, -20094, 3115, 564, -94, -6, 1], 'lmfdb_label': '71478.cc2', 'torsion': [2, 12]}
  • id: 3393589
    {'degree': 16, 'field': [861184, 0, -440112, 0, 175492, 0, -72612, 0, 25977, 0, -5352, 0, 610, 0, -36, 0, 1], 'lmfdb_label': '71478.cc2', 'torsion': [2, 12]}
  • id: 3393587
    {'degree': 16, 'field': [11843486041, -3064885996, 370452124, 136112236, -89820328, 23371292, 244508, -900764, 469174, -95444, 6020, 1268, -808, 100, 4, -4, 1], 'lmfdb_label': '71478.cc2', 'torsion': [8]}
  • id: 3393590
    {'degree': 18, 'field': [22962304, 208419648, 596084352, 470075244, -165241716, 10369272, -26545272, 2780592, 241260, -455515, 160827, 6576, 258, 462, 156, 12, 6, -3, 1], 'lmfdb_label': '71478.cc2', 'torsion': [18]}
• 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: 1733762
    {'conductor': 71478, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '71478.cc2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
  • id: 1733763
    {'conductor': 71478, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '71478.cc2', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1733764
    {'conductor': 71478, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '71478.cc2', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1733765
    {'conductor': 71478, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '71478.cc2', 'prime': 19, '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: 2136964
    {'adelic_gens': [[2497, 12, 2496, 13], [11, 2, 2458, 2499], [131, 0, 0, 2507], [1863, 190, 494, 533], [2110, 399, 969, 1312], [1, 0, 12, 1], [1, 6, 6, 37], [208, 1045, 1311, 1880], [1, 12, 0, 1]], 'adelic_image': '2508.96.1.?', 'conductor': 71478, 'lmfdb_label': '71478.cc2', 'prime': 0}
  • id: 297301
    {'conductor': 71478, 'elladic_image': '2.3.0.1', 'lmfdb_label': '71478.cc2', 'modell_image': '2B', 'prime': 2}
  • id: 297302
    {'conductor': 71478, 'elladic_image': '3.4.0.1', 'lmfdb_label': '71478.cc2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 71478.cc does not appear in ec_padic