Elliptic curve data - 138720.l3

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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': '138720bj', 'Clabel': '138720bj1', 'Cnumber': 1, 'abc_quality': 1.0301379038265235, 'absD': 703851512040000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 408, 'ainvs': [0, -1, 0, -65410, -6289400], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 138720, 'degree': 983040, 'elladic_images': ['8.12.0.4'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6356735219657992942931159959', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 11, 'isogeny_degrees': [1, 2], 'jinv': [20034997696, 455625], 'lmfdb_iso': '138720.l', 'lmfdb_label': '138720.l3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -226, 1360], 'min_quad_twist_disc': -68, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '8.12.0.b.1', '12.12.0.a.1', '24.24.0.f.1', '68.12.0-2.a.1.1', '136.24.0.?', '204.24.0.?', '408.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.12750674034228140054026737377', 'prec': 107}, 'szpiro_ratio': 3.7903803252591293, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, -1, 0, 1, 0, -4, 0, 1, 0, 4, 0, 6, 0, -1, 0, 0, 0, -4, 0], 'aplist': [0, -1, 1, -4, 4, 6, 0, -4, 0, -10, -4, 10, -2, 4, -8, 2, -12, 10, -12, 0, -10, -4, -4, -6, 14], 'class_deg': 4, 'class_size': 4, 'conductor': 138720, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '138720.l', 'trace_hash': 264224770032525986}
• 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': '0.037955265214594085384706171037', 'prec': 107}, 'conductor': 138720, 'gens': [], 'heights': [], 'lmfdb_label': '138720.l3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.29894360911007072311122343999', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.1957744364402828924448937599697257714', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[-130, 0, 1], [295, 0, 1]], 'xcoord_integral_points': [-164, -130, 295]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '5': [3, 0], '17': 'a'}, 'iwp0': 3, 'lmfdb_label': '138720.l3'}
• ec_torsion_growth •

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

  
  
  • id: 6271893
    {'degree': 4, 'field': [-2, 14, -13, -2, 1], 'lmfdb_label': '138720.l3', 'torsion': [2, 4]}
  • id: 6271892
    {'degree': 4, 'field': [81, 0, -16, 0, 1], 'lmfdb_label': '138720.l3', 'torsion': [2, 4]}
  • id: 6271894
    {'degree': 4, 'field': [100, 0, 14, 0, 1], 'lmfdb_label': '138720.l3', 'torsion': [2, 4]}
  • id: 6271895
    {'degree': 8, 'field': [-250563, 0, -78608, 0, 1734, 0, 0, 0, 1], 'lmfdb_label': '138720.l3', 'torsion': [2, 6]}
  • id: 6271896
    {'degree': 16, 'field': [65536, 0, 0, 0, -12544, 0, 0, 0, 2145, 0, 0, 0, -49, 0, 0, 0, 1], 'lmfdb_label': '138720.l3', 'torsion': [4, 4]}
  • id: 6271898
    {'degree': 16, 'field': [1266904, 2283296, -1377984, -1518704, 114708, 549000, 150988, -209672, -34551, 44816, 3304, -5568, 18, 392, -36, -8, 1], 'lmfdb_label': '138720.l3', 'torsion': [2, 8]}
  • id: 6271897
    {'degree': 16, 'field': [17627264, 46244352, 34162944, -10256384, 6063872, 2074368, -2740224, -220160, 436080, 1024, -36288, 480, 2200, -32, -72, 0, 1], 'lmfdb_label': '138720.l3', 'torsion': [2, 8]}
  • id: 6271899
    {'degree': 16, 'field': [214183225, 0, 85395024, 0, 19659628, 0, 2947632, 0, 317658, 0, 24336, 0, 1348, 0, 48, 0, 1], 'lmfdb_label': '138720.l3', 'torsion': [2, 8]}
• 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: 3423962
    {'conductor': 138720, 'conductor_valuation': 5, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '138720.l3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3423963
    {'conductor': 138720, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '138720.l3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3423964
    {'conductor': 138720, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '138720.l3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 3423965
    {'conductor': 138720, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '138720.l3', 'prime': 17, 'reduction_type': 0, '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: 2565516
    {'adelic_gens': [[1, 0, 4, 1], [1, 4, 0, 1], [205, 170, 0, 1], [167, 0, 0, 407], [137, 340, 34, 273], [405, 4, 404, 5], [305, 238, 34, 67]], 'adelic_image': '408.48.0.?', 'conductor': 138720, 'lmfdb_label': '138720.l3', 'prime': 0}
  • id: 536414
    {'conductor': 138720, 'elladic_image': '8.12.0.4', 'lmfdb_label': '138720.l3', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 138720.l does not appear in ec_padic