Elliptic curve data - 57330.du1

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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': '57330eh', 'Clabel': '57330eh4', 'Cnumber': 4, 'abc_quality': 0.9697774643830833, 'absD': 220460956369290, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 10920, 'ainvs': [1, -1, 1, -213233, -37839049], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 57330, 'degree': 393216, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7492937617104665522301642251', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 98, 'isogeny_degrees': [1, 2, 4], 'jinv': [12501706118329, 2570490], 'lmfdb_iso': '57330.du', 'lmfdb_label': '57330.du1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -483, -4293], 'min_quad_twist_disc': 21, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '40.12.0.v.1', '104.12.0.?', '168.12.0.?', '420.12.0.?', '520.24.0.?', '840.24.0.?', '2184.24.0.?', '10920.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '5.0479439072760914730414332048', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 2205], [3, 8, 6370], [5, 6, 11466], [7, 26, 1170], [13, 14, 4410]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.22703254284875505397986523492', 'prec': 103}, 'szpiro_ratio': 4.419629468866317, '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, 1, 0, 1, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, 0, 1, -6, 0, 0, -1], 'aplist': [1, 0, -1, 0, 0, 1, -6, 0, 4, 10, 0, -6, 2, -4, 0, 6, 0, -6, 4, -16, 2, 0, 4, -6, -14], 'class_deg': 4, 'class_size': 4, 'conductor': 57330, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '57330.du', 'trace_hash': 580464211349152649}
• 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': '0.030240066656589584030299503341', 'prec': 107}, 'conductor': 57330, 'gens': [[5007, 320483, 2]], 'heights': [{'__RealLiteral__': 0, 'data': '5.0479439072760914730414332048', 'prec': 100}], 'lmfdb_label': '57330.du1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.22217309649574394395054051421', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.9721386305308303262317354013016859246', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-1077, 1073, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [6, 2], '3': 'a', '5': [1, 0], '7': 'a', '11': [1, 1, 0], '13': [2, 0], '17': [1, 0], '19': [1, 1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '57330.du1'}
• ec_torsion_growth •

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

  
  
  • id: 2762634
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '57330.du1', 'torsion': [2, 2]}
  • id: 2762635
    {'degree': 2, 'field': [42, 0, 1], 'lmfdb_label': '57330.du1', 'torsion': [4]}
  • id: 2762636
    {'degree': 2, 'field': [105, 0, 1], 'lmfdb_label': '57330.du1', 'torsion': [4]}
  • id: 2762637
    {'degree': 4, 'field': [169, 0, 16, 0, 1], 'lmfdb_label': '57330.du1', 'torsion': [2, 4]}
  • id: 2762638
    {'degree': 8, 'field': [1600, 0, 0, 0, -1130, 0, 0, 0, 1], 'lmfdb_label': '57330.du1', 'torsion': [2, 4]}
  • id: 2762641
    {'degree': 8, 'field': [26364, 29744, -19760, 1656, 182, -86, 51, -1, 1], 'lmfdb_label': '57330.du1', 'torsion': [6]}
  • id: 2762639
    {'degree': 8, 'field': [272428, -40560, 13416, 0, 2024, -312, 84, 0, 1], 'lmfdb_label': '57330.du1', 'torsion': [8]}
  • id: 2762640
    {'degree': 8, 'field': [970225, 0, 138750, 0, 6290, 0, 30, 0, 1], 'lmfdb_label': '57330.du1', 'torsion': [8]}
  • id: 2762645
    {'degree': 16, 'field': [-5001210864, -10084883328, -12939305184, -3851916192, 3947733744, 287445408, -57795144, 5354024, -4913968, 913696, -134632, -464, 767, -134, 23, -2, 1], 'lmfdb_label': '57330.du1', 'torsion': [2, 6]}
  • id: 2762642
    {'degree': 16, 'field': [442050625, 0, 0, 0, -26870000, 0, 0, 0, 434850, 0, 0, 0, 400, 0, 0, 0, 1], 'lmfdb_label': '57330.du1', 'torsion': [4, 4]}
  • id: 2762644
    {'degree': 16, 'field': [605488900, -1404264000, 1731810080, -693578400, 241785464, 16043280, -12776496, 9421440, -676456, 186000, 97248, -7440, 4916, -120, 104, 0, 1], 'lmfdb_label': '57330.du1', 'torsion': [2, 8]}
  • id: 2762646
    {'degree': 16, 'field': [6255544464, 0, 5552943864, 0, 421800340, 0, -30221832, 0, -2705580, 0, 77468, 0, 3480, 0, 84, 0, 1], 'lmfdb_label': '57330.du1', 'torsion': [12]}
  • id: 2762643
    {'degree': 16, 'field': [21906003001, -7795011596, 5694300204, -1625805676, 695423631, -137425968, 43510666, -6770428, 1856652, -221852, 65176, -7572, 951, 136, -6, -4, 1], 'lmfdb_label': '57330.du1', 'torsion': [2, 8]}
  • id: 2762647
    {'degree': 16, 'field': [42397964170, 14782966200, -20887871174, -1209775318, 3562590622, -763639564, 30383919, 25836284, -5627517, 421358, 96114, -31624, 64, 638, -47, -6, 1], 'lmfdb_label': '57330.du1', '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: 1379444
    {'conductor': 57330, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '57330.du1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1379445
    {'conductor': 57330, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '57330.du1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1379446
    {'conductor': 57330, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '57330.du1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1379447
    {'conductor': 57330, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '57330.du1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1379448
    {'conductor': 57330, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '57330.du1', 'prime': 13, 'reduction_type': 1, '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: 2044662
    {'adelic_gens': [[736, 4683, 525, 8842], [1, 0, 8, 1], [10913, 8, 10912, 9], [7279, 0, 0, 10919], [1, 8, 0, 1], [1, 4, 4, 17], [4201, 5208, 8484, 9913], [3119, 0, 0, 10919], [7, 6, 10914, 10915], [5923, 7476, 10122, 4621], [8128, 1113, 4347, 694]], 'adelic_image': '10920.48.0.?', 'conductor': 57330, 'lmfdb_label': '57330.du1', 'prime': 0}
  • id: 243303
    {'conductor': 57330, 'elladic_image': '4.6.0.1', 'lmfdb_label': '57330.du1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 2905973
    {'lmfdb_iso': '57330.du', 'p': 17, 'prec': 20, 'unit': 120323831281257706438116, 'val': 1}
  • id: 2905977
    {'lmfdb_iso': '57330.du', 'p': 23, 'prec': 20, 'unit': 9957374710291783804992478, 'val': 1}
  • id: 2905972
    {'lmfdb_iso': '57330.du', 'p': 29, 'prec': 20, 'unit': 4219160305996276279618124625, 'val': 1}
  • id: 2905968
    {'lmfdb_iso': '57330.du', 'p': 37, 'prec': 20, 'unit': 131750563726901230707148186914, 'val': 1}
  • id: 2905970
    {'lmfdb_iso': '57330.du', 'p': 41, 'prec': 20, 'unit': 1322599112450873577038062946686, 'val': 1}
  • id: 2905971
    {'lmfdb_iso': '57330.du', 'p': 43, 'prec': 20, 'unit': 1705229400023811796209645151895, 'val': 1}
  • id: 2905975
    {'lmfdb_iso': '57330.du', 'p': 53, 'prec': 20, 'unit': 337840276489546146896977447954198, 'val': 1}
  • id: 2905979
    {'lmfdb_iso': '57330.du', 'p': 61, 'prec': 20, 'unit': 1666784731757962431651215289939166, 'val': 1}
  • id: 2905967
    {'lmfdb_iso': '57330.du', 'p': 67, 'prec': 20, 'unit': 10051102557715954522910635985100395, 'val': 1}
  • id: 2905969
    {'lmfdb_iso': '57330.du', 'p': 71, 'prec': 20, 'unit': 950762552052788989681746575582427, 'val': 1}
  • id: 2905976
    {'lmfdb_iso': '57330.du', 'p': 73, 'prec': 20, 'unit': 181279987710310584494993148181679373, 'val': 1}
  • id: 2905974
    {'lmfdb_iso': '57330.du', 'p': 83, 'prec': 20, 'unit': 2308061192911255327400703342794319848, 'val': 1}
  • id: 2905978
    {'lmfdb_iso': '57330.du', 'p': 89, 'prec': 20, 'unit': 8267699614110775417302152180578793603, 'val': 1}
  • id: 2905966
    {'lmfdb_iso': '57330.du', 'p': 97, 'prec': 20, 'unit': 26478805219677232111290237947883239217, 'val': 1}