Elliptic curve data - 8624.s3

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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': '8624bb', 'Clabel': '8624bb3', 'Cnumber': 3, 'abc_quality': 1.0659265883154396, 'absD': 55677334351972315136, 'adelic_genus': 3, 'adelic_index': 144, 'adelic_level': 2772, 'ainvs': [0, 1, 0, 345483, -350275549], 'analytic_rank': 0, 'bad_primes': [2, 7, 11], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 8624, 'degree': 207360, 'elladic_images': ['9.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4697148743703075168900726769', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 9, 'iso_nlabel': 18, 'isogeny_degrees': [1, 3, 9], 'jinv': [9463555063808, 115539436859], 'lmfdb_iso': '8624.s', 'lmfdb_label': '8624.s3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, 441, -15815], 'min_quad_twist_disc': 28, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '9.12.0.a.1', '22.2.0.a.1', '63.36.0.e.2', '66.8.0.a.1', '84.8.0.?', '198.24.1.?', '252.72.0.?', '924.16.0.?', '1386.72.3.?', '2772.144.3.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 539], [3, 2, 784], [7, 32, 176], [11, 12, 784]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.80361261928270555492016418372', 'prec': 103}, 'szpiro_ratio': 5.834306886538049, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, -3, 0, 0, 0, -2, 0, 1, 0, 4, 0, -3, 0, 6, 0, 2, 0], 'aplist': [0, 1, -3, 0, 1, 4, 6, 2, -3, -6, 5, 11, -6, -8, 0, -6, -9, 10, -5, -9, -2, 10, 12, 3, 1], 'class_deg': 9, 'class_size': 3, 'conductor': 8624, 'isogeny_matrix': [[1, 3, 9], [3, 1, 3], [9, 3, 1]], 'lmfdb_iso': '8624.s', 'trace_hash': 1839584907010449930}
• 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': '0.0071586794545573393468697935782', 'prec': 110}, 'conductor': 8624, 'gens': [], 'heights': [], 'lmfdb_label': '8624.s3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.097572162782727689350148337067', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.7562989300890984083026700672073192410', 'prec': 130}, 'tamagawa_product': 18, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 2], '5': [0, 0], '7': 'a', '11': [1, 0], '13': [0, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0, 0]}, 'iwp0': 0, 'lmfdb_label': '8624.s3'}
• ec_torsion_growth •

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

  
  
  • id: 450828
    {'degree': 2, 'field': [21, 0, 1], 'lmfdb_label': '8624.s3', 'torsion': [3]}
  • id: 450829
    {'degree': 3, 'field': [1, 1, -1, 1], 'lmfdb_label': '8624.s3', 'torsion': [2]}
  • id: 450831
    {'degree': 6, 'field': [-7, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '8624.s3', 'torsion': [3]}
  • id: 450830
    {'degree': 6, 'field': [1, -1, 2, -3, 2, -1, 1], 'lmfdb_label': '8624.s3', 'torsion': [2, 2]}
  • id: 450832
    {'degree': 6, 'field': [525, 0, 441, 0, 42, 0, 1], 'lmfdb_label': '8624.s3', 'torsion': [9]}
  • id: 450833
    {'degree': 6, 'field': [2662, -484, 44, 18, -18, -2, 1], 'lmfdb_label': '8624.s3', 'torsion': [6]}
  • id: 450835
    {'degree': 12, 'field': [36, 36, 126, -330, 195, -84, 127, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '8624.s3', 'torsion': [3, 3]}
  • id: 450834
    {'degree': 12, 'field': [1037, -3306, 3248, -1040, 633, -932, 632, -424, 223, -74, 28, -4, 1], 'lmfdb_label': '8624.s3', 'torsion': [4]}
  • id: 450836
    {'degree': 12, 'field': [2401, 0, 0, 0, 0, 0, -77, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '8624.s3', 'torsion': [9]}
  • id: 450837
    {'degree': 12, 'field': [4932841, -235426, 126295, 211320, -88030, -21886, 8393, -706, -110, 180, -25, -6, 1], 'lmfdb_label': '8624.s3', 'torsion': [2, 6]}
  • id: 450838
    {'degree': 18, 'field': [-343, 0, 0, 0, 0, 0, 1911, 0, 0, 0, 0, 0, -77, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '8624.s3', 'torsion': [6]}
  • id: 450839
    {'degree': 18, 'field': [301849381, -742341552, 669053772, -646998580, 645847923, -368800326, 258348695, -96181632, 48000963, -12470976, 4769790, -882672, 270036, -34770, 8691, -716, 147, -6, 1], 'lmfdb_label': '8624.s3', '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: 180108
    {'conductor': 8624, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '8624.s3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 180109
    {'conductor': 8624, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '8624.s3', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 180110
    {'conductor': 8624, 'conductor_valuation': 1, 'discriminant_valuation': 9, 'j_denominator_valuation': 9, 'kodaira_symbol': 13, 'lmfdb_label': '8624.s3', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 9}
• ec_galrep •

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

  
  
  • id: 1721022
    {'adelic_gens': [[1, 18, 0, 1], [2771, 2754, 0, 2617], [1, 18, 10, 181], [1403, 2754, 1404, 2753], [10, 9, 81, 73], [2765, 2754, 1602, 2309], [2510, 2763, 1899, 1394], [1385, 0, 0, 2771], [1, 0, 18, 1], [2755, 18, 2754, 19]], 'adelic_image': '2772.144.3.?', 'conductor': 8624, 'lmfdb_label': '8624.s3', 'prime': 0}
  • id: 42238
    {'conductor': 8624, 'elladic_image': '9.12.0.1', 'lmfdb_label': '8624.s3', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 8624.s does not appear in ec_padic