Elliptic curve data - 388080.x3

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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': '388080x', 'Clabel': '388080x1', 'Cnumber': 1, 'abc_quality': 1.0082037341923265, 'absD': 11143782731005405034400000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 9240, 'ainvs': [0, 0, 0, -1737079743, -27865736983042], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 388080, 'degree': 188743680, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.9290547641079810801125302446', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 23, 'isogeny_degrees': [1, 2, 4], 'jinv': [26401417552259125806544, 507547744790625], 'lmfdb_iso': '388080.x', 'lmfdb_label': '388080.x3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -3938956, 3010246900], 'min_quad_twist_disc': -84, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '40.12.0.y.1', '132.12.0.?', '168.12.0.?', '420.12.0.?', '616.12.0.?', '770.6.0.?', '840.24.0.?', '1320.24.0.?', '1540.12.0.?', '1848.24.0.?', '3080.24.0.?', '4620.24.0.?', '9240.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '23.940408684699784544269044761', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 24255], [3, 8, 43120], [5, 6, 77616], [7, 32, 7920], [11, 12, 35280]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.9446954248729727089174098401', 'prec': 100}, 'szpiro_ratio': 5.862165782236551, '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, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, -6, 0, -4, 0], 'aplist': [0, 0, -1, 0, -1, -2, -6, -4, -8, 6, 4, 2, -6, -12, 0, -2, -4, 2, 8, -8, -2, -12, 8, 18, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 388080, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '388080.x', 'trace_hash': 80142290756803416}
• 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': '0.00038660404500694124188317311207', 'prec': 113}, 'conductor': 388080, 'gens': [[5066816363578, 10628397933559905024, 6439]], 'heights': [{'__RealLiteral__': 0, 'data': '23.940408684699784544269044761', 'prec': 100}], 'lmfdb_label': '388080.x3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.023385416902438880592642696908', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.4788515032517832882316567679827451109', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-24143, 0, 1]], 'xcoord_integral_points': [-24143]}
• lmfdb_label 388080.x3 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 16037856
    {'degree': 2, 'field': [-96, -1, 1], 'lmfdb_label': '388080.x3', 'torsion': [2, 2]}
  • id: 16037858
    {'degree': 2, 'field': [33, 0, 1], 'lmfdb_label': '388080.x3', 'torsion': [4]}
  • id: 16037857
    {'degree': 2, 'field': [105, 0, 1], 'lmfdb_label': '388080.x3', 'torsion': [4]}
  • id: 16037859
    {'degree': 4, 'field': [324, 0, 69, 0, 1], 'lmfdb_label': '388080.x3', 'torsion': [2, 4]}
  • id: 16037861
    {'degree': 8, 'field': [66586, -20524, 21790, -2476, 1099, 164, -50, -4, 1], 'lmfdb_label': '388080.x3', 'torsion': [8]}
  • id: 16037860
    {'degree': 8, 'field': [715716, 0, 88092, 0, 4549, 0, -227, 0, 1], 'lmfdb_label': '388080.x3', 'torsion': [2, 4]}
  • id: 16037863
    {'degree': 8, 'field': [777126, 1263192, 519054, 108624, 11058, -534, -196, -2, 1], 'lmfdb_label': '388080.x3', 'torsion': [6]}
  • id: 16037862
    {'degree': 8, 'field': [1030225, 0, 119168, 0, 5166, 0, -112, 0, 1], 'lmfdb_label': '388080.x3', 'torsion': [8]}
  • id: 16037867
    {'degree': 16, 'field': [-447442630290, -514112039820, -212377498506, -32369335884, 3084436044, 2358385038, 518061258, 129736134, 32727321, -1140216, -139722, 49938, -5492, 862, -52, -4, 1], 'lmfdb_label': '388080.x3', 'torsion': [2, 6]}
  • id: 16037864
    {'degree': 16, 'field': [43046721, 0, 0, 0, -43341966, 0, 0, 0, 15413571, 0, 0, 0, -6606, 0, 0, 0, 1], 'lmfdb_label': '388080.x3', 'torsion': [4, 4]}
  • id: 16037865
    {'degree': 16, 'field': [17555190016, 0, -1752127104, 0, 187305232, 0, -18954912, 0, 877560, 0, -12408, 0, -263, 0, -6, 0, 1], 'lmfdb_label': '388080.x3', 'torsion': [2, 8]}
  • id: 16037866
    {'degree': 16, 'field': [23404578129, 7997158404, 2660541396, -5977670724, 3574230292, -1607611644, 461317602, -108767340, 26099013, -4233708, 900358, -62100, 16368, -648, 162, 0, 1], 'lmfdb_label': '388080.x3', 'torsion': [2, 8]}
  • id: 16037869
    {'degree': 16, 'field': [281762397288, -149265646992, 68152242888, 199509278688, 33583488480, -8375781672, 1203364168, 367433056, -16360732, -1749380, -860748, 58720, 22574, -1752, -22, -4, 1], 'lmfdb_label': '388080.x3', 'torsion': [12]}
  • id: 16037868
    {'degree': 16, 'field': [7805887851505, 6304035660440, 2082801799016, -21948015736, -90483109452, -9486353932, 1037739484, 28403656, -14763786, 9364648, 617048, 55184, 18224, -84, 212, -8, 1], 'lmfdb_label': '388080.x3', '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: 9597285
    {'conductor': 388080, 'conductor_valuation': 4, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '388080.x3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 9597286
    {'conductor': 388080, 'conductor_valuation': 2, 'discriminant_valuation': 22, 'j_denominator_valuation': 16, 'kodaira_symbol': -20, 'lmfdb_label': '388080.x3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 9597287
    {'conductor': 388080, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '388080.x3', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 9597288
    {'conductor': 388080, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '388080.x3', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 9597289
    {'conductor': 388080, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '388080.x3', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 4074427
    {'adelic_gens': [[4768, 3, 285, 3082], [5548, 3081, 8031, 6166], [9233, 8, 9232, 9], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [2687, 5772, 8850, 7313], [4243, 1158, 5010, 6547], [3079, 0, 0, 9239], [7, 6, 9234, 9235], [872, 9237, 4395, 6158]], 'adelic_image': '9240.48.0.?', 'conductor': 388080, 'lmfdb_label': '388080.x3', 'prime': 0}
  • id: 1324478
    {'conductor': 388080, 'elladic_image': '4.6.0.1', 'lmfdb_label': '388080.x3', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 388080.x does not appear in ec_padic