Elliptic curve data - 87360.he4

Formats: - HTML - YAML - JSON - 2024-06-12T02:18:01.782959

• 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': '87360dn', 'Clabel': '87360dn1', 'Cnumber': 1, 'abc_quality': 0.9401756067094464, 'absD': 5009571840000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1560, 'ainvs': [0, 1, 0, 415, 107775], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 87360, 'degree': 147456, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1159137658411926134140217965', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 186, 'isogeny_degrees': [1, 2, 4], 'jinv': [30080231, 19110000], 'lmfdb_iso': '87360.he', 'lmfdb_label': '87360.he4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 7, 213], 'min_quad_twist_disc': 8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0-4.c.1.2', '40.12.0-4.c.1.5', '78.6.0.?', '104.12.0.?', '120.24.0.?', '156.12.0.?', '312.24.0.?', '520.24.0.?', '1560.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.076192995001274649288173614313', 'prec': 107}, 'szpiro_ratio': 3.225245956048179, '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, 1, 0, 1, 0, 4, 0, -1, 0, 1, 0, -2, 0, -4, 0], 'aplist': [0, 1, 1, 1, 4, -1, -2, -4, 4, 6, 4, 2, -2, 4, 8, -6, 12, 10, 0, -8, 14, 0, 4, 6, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 87360, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '87360.he', 'trace_hash': 455765538845050043}
• 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': '0.10733209797922652630998273704', 'prec': 103}, 'conductor': 87360, 'gens': [], 'heights': [], 'lmfdb_label': '87360.he4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.59841545366253468921842845756', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.7873236293002775137474276604706047496', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-45, 0, 1]], 'xcoord_integral_points': [-45]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [1, 0], '7': [1, 0], '13': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '87360.he4'}
• ec_torsion_growth •

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

  
  
  • id: 4093337
    {'degree': 2, 'field': [-26, 0, 1], 'lmfdb_label': '87360.he4', 'torsion': [4]}
  • id: 4093338
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '87360.he4', 'torsion': [4]}
  • id: 4093336
    {'degree': 2, 'field': [10, -1, 1], 'lmfdb_label': '87360.he4', 'torsion': [2, 2]}
  • id: 4093339
    {'degree': 4, 'field': [64, 0, -10, 0, 1], 'lmfdb_label': '87360.he4', 'torsion': [2, 4]}
  • id: 4093343
    {'degree': 8, 'field': [-480000, 0, 53600, 0, -2400, 0, 0, 0, 1], 'lmfdb_label': '87360.he4', 'torsion': [6]}
  • id: 4093341
    {'degree': 8, 'field': [57775, -9570, 5289, 1030, -474, 14, -19, -2, 1], 'lmfdb_label': '87360.he4', 'torsion': [8]}
  • id: 4093340
    {'degree': 8, 'field': [230400, 0, 8586, 0, 969, 0, -6, 0, 1], 'lmfdb_label': '87360.he4', 'torsion': [2, 4]}
  • id: 4093342
    {'degree': 8, 'field': [672784, 26432, 78520, -1768, 4054, -220, 106, -4, 1], 'lmfdb_label': '87360.he4', 'torsion': [8]}
  • id: 4093345
    {'degree': 16, 'field': [5494375, -2904500, 4276350, -3054900, 2369250, -1194660, 723706, -316244, 128547, -37596, 12258, -2772, 644, -112, 36, -8, 1], 'lmfdb_label': '87360.he4', 'torsion': [2, 8]}
  • id: 4093346
    {'degree': 16, 'field': [35872600, -28552800, 100985960, -62053400, 85975514, -30385068, 25418474, -5092176, 3313237, -347844, 220648, -12436, 7872, -304, 142, -4, 1], 'lmfdb_label': '87360.he4', 'torsion': [2, 8]}
  • id: 4093344
    {'degree': 16, 'field': [397204900, 0, 173904456, 0, 6424144, 0, -1306188, 0, 15813, 0, 6708, 0, 142, 0, 24, 0, 1], 'lmfdb_label': '87360.he4', 'torsion': [4, 4]}
  • id: 4093349
    {'degree': 16, 'field': [5170185216, 0, 8542660608, 0, 2728339456, 0, 30457056, 0, 2096736, 0, -102056, 0, -444, 0, 12, 0, 1], 'lmfdb_label': '87360.he4', 'torsion': [12]}
  • id: 4093348
    {'degree': 16, 'field': [123566310400, 0, -38020403200, 0, 2924646400, 0, 79513824, 0, -8225568, 0, -125736, 0, 676, 0, -52, 0, 1], 'lmfdb_label': '87360.he4', 'torsion': [12]}
  • id: 4093347
    {'degree': 16, 'field': [230400000000, 0, -101176320000, 0, 12140800000, 0, 547680000, 0, 5625552, 0, 133798, 0, 3624, 0, 0, 0, 1], 'lmfdb_label': '87360.he4', 'torsion': [2, 6]}
• 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: 2134147
    {'conductor': 87360, 'conductor_valuation': 6, 'discriminant_valuation': 22, 'j_denominator_valuation': 4, 'kodaira_symbol': -16, 'lmfdb_label': '87360.he4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 2134148
    {'conductor': 87360, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '87360.he4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 2134149
    {'conductor': 87360, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '87360.he4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 2134150
    {'conductor': 87360, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '87360.he4', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2134151
    {'conductor': 87360, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '87360.he4', 'prime': 13, '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: 2239920
    {'adelic_gens': [[1357, 1362, 190, 973], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [937, 8, 628, 33], [1553, 8, 1552, 9], [7, 6, 1554, 1555], [1369, 1368, 598, 1375], [1204, 1, 1463, 6], [1048, 3, 1045, 2]], 'adelic_image': '1560.48.0.?', 'conductor': 87360, 'lmfdb_label': '87360.he4', 'prime': 0}
  • id: 356324
    {'conductor': 87360, 'elladic_image': '4.6.0.1', 'lmfdb_label': '87360.he4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 87360.he does not appear in ec_padic