Elliptic curve data - 277440.ex1

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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': '277440ex', 'Clabel': '277440ex3', 'Cnumber': 3, 'abc_quality': 1.0397263843855777, 'absD': 8341943846400000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 408, 'ainvs': [0, 1, 0, -573761, 92935935], 'analytic_rank': 2, 'bad_primes': [2, 3, 5, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 277440, 'degree': 7864320, 'elladic_images': ['8.12.0.11'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3288207025257446037103481173', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 127, 'isogeny_degrees': [1, 2, 4], 'jinv': [26410345352, 10546875], 'lmfdb_iso': '277440.ex', 'lmfdb_label': '277440.ex1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -496, -2204], 'min_quad_twist_disc': -136, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.m.1', '24.24.0.bi.1', '68.12.0-4.c.1.2', '136.24.0.?', '408.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 15, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '5.1482048476176990864249527620', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.045780054797704926814040656542', 'prec': 107}, 'szpiro_ratio': 4.100537248186312, '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, 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': 277440, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '277440.ex', 'trace_hash': 391403257109936724}
• 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': '0.0094888163036485213461765427592', 'prec': 110}, 'conductor': 277440, 'gens': [[79, 6936, 1], [946, 19941, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.4981101644877739333014134593', 'prec': 100}, {'__RealLiteral__': 0, 'data': '3.4869580361275073764969008954', 'prec': 100}], 'lmfdb_label': '277440.ex1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.21138505319411157391645690879', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '13.059042666814204691248739914240216316', 'prec': 130}, 'tamagawa_product': 48, 'torsion_generators': [[657, 0, 1]], 'xcoord_integral_points': [-801, -593, -65, 79, 657, 946, 1441, 3157]}
• lmfdb_label 277440.ex1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11826531
    {'degree': 2, 'field': [-102, 0, 1], 'lmfdb_label': '277440.ex1', 'torsion': [4]}
  • id: 11826530
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '277440.ex1', 'torsion': [2, 2]}
  • id: 11826532
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '277440.ex1', 'torsion': [4]}
  • id: 11826533
    {'degree': 4, 'field': [-2, 20, -19, -2, 1], 'lmfdb_label': '277440.ex1', 'torsion': [2, 4]}
  • id: 11826537
    {'degree': 8, 'field': [-1803, -7116, -103354, -63612, -11328, -720, -114, 0, 1], 'lmfdb_label': '277440.ex1', 'torsion': [6]}
  • id: 11826535
    {'degree': 8, 'field': [33, 2916, -1284, -1044, 388, 116, -36, -4, 1], 'lmfdb_label': '277440.ex1', 'torsion': [8]}
  • id: 11826536
    {'degree': 8, 'field': [1634, 184, -88, -184, 73, 20, -2, -4, 1], 'lmfdb_label': '277440.ex1', 'torsion': [8]}
  • id: 11826534
    {'degree': 8, 'field': [42849, 0, -4860, 0, 336, 0, -12, 0, 1], 'lmfdb_label': '277440.ex1', 'torsion': [2, 4]}
  • id: 11826538
    {'degree': 16, 'field': [4, 0, 320688, 0, 406780, 0, 108864, 0, 28965, 0, 4860, 0, 526, 0, 36, 0, 1], 'lmfdb_label': '277440.ex1', 'torsion': [4, 4]}
  • id: 11826540
    {'degree': 16, 'field': [4734, 14112, -36108, -70344, 135246, 46560, -131604, -5964, 54295, -1260, -11072, 276, 1146, -12, -56, 0, 1], 'lmfdb_label': '277440.ex1', 'torsion': [2, 8]}
  • id: 11826539
    {'degree': 16, 'field': [14764, -15968, 126984, -213792, 102318, -34416, 63772, -18368, -24177, 12792, 3276, -2496, -130, 224, -12, -8, 1], 'lmfdb_label': '277440.ex1', 'torsion': [2, 8]}
  • id: 11826543
    {'degree': 16, 'field': [127924, 1550624, -1138648, -620448, -166396, 486400, -32528, -86304, -6923, 15384, 100, -1192, -226, 168, -4, -8, 1], 'lmfdb_label': '277440.ex1', 'torsion': [12]}
  • id: 11826541
    {'degree': 16, 'field': [7842609, 70176132, -86228784, 36201564, -12508938, -110232, 835236, -628668, 251592, -71556, 17400, -3804, 774, -96, 16, -4, 1], 'lmfdb_label': '277440.ex1', 'torsion': [2, 6]}
  • id: 11826542
    {'degree': 16, 'field': [936747217, -2358371312, 2514891224, -1458049828, 488856802, -95204844, 13400800, -3136004, 377936, 183224, -57848, 5076, 82, 148, -4, -4, 1], 'lmfdb_label': '277440.ex1', '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: 6873330
    {'conductor': 277440, 'conductor_valuation': 6, 'discriminant_valuation': 15, 'j_denominator_valuation': 0, 'kodaira_symbol': -9, 'lmfdb_label': '277440.ex1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 6873331
    {'conductor': 277440, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '277440.ex1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 6873332
    {'conductor': 277440, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '277440.ex1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6873333
    {'conductor': 277440, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '277440.ex1', 'prime': 17, '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: 3415542
    {'adelic_gens': [[288, 391, 221, 186], [256, 51, 85, 290], [1, 0, 8, 1], [1, 8, 0, 1], [167, 0, 0, 407], [1, 4, 4, 17], [7, 6, 402, 403], [401, 8, 400, 9], [288, 391, 119, 84]], 'adelic_image': '408.48.0.?', 'conductor': 277440, 'lmfdb_label': '277440.ex1', 'prime': 0}
  • id: 988618
    {'conductor': 277440, 'elladic_image': '8.12.0.11', 'lmfdb_label': '277440.ex1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 277440.ex does not appear in ec_padic