Elliptic curve data - 68400.et2

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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': '68400fh', 'Clabel': '68400fh1', 'Cnumber': 1, 'abc_quality': 1.08504151838819, 'absD': 20840103108358963200, 'adelic_genus': 1, 'adelic_index': 48, 'adelic_level': 1140, 'ainvs': [0, 0, 0, 687165, 13053890], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 19], 'class_deg': 5, 'class_size': 2, 'cm': 0, 'conductor': 68400, 'degree': 1382400, 'elladic_images': ['5.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3963996288940815329465706314', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 123, 'isogeny_degrees': [1, 5], 'jinv': [480705753733655, 279172334592], 'lmfdb_iso': '68400.et', 'lmfdb_label': '68400.et2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 4772, 7952], 'min_quad_twist_disc': 12, 'modell_images': ['5B.4.1'], 'modm_images': ['5.12.0.a.1', '60.24.0-5.a.1.2', '190.24.0.?', '228.2.0.?', '1140.48.1.?'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 4275], [3, 6, 7600], [5, 10, 2736], [19, 20, 3600]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.88570665192773131539825600261', 'prec': 103}, 'szpiro_ratio': 4.664869720397762, '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, 0, 0, 0, 0, 2, 0, 0, 0, -3, 0, -6, 0, 0, 0, 2, 0, 1, 0], 'aplist': [0, 0, 0, 2, -3, -6, 2, 1, -1, 5, -7, -2, -2, 6, -12, -9, -10, -13, 7, 12, 9, -5, -1, -5, -12], 'class_deg': 5, 'class_size': 2, 'conductor': 68400, 'isogeny_matrix': [[1, 5], [5, 1]], 'lmfdb_iso': '68400.et', 'trace_hash': 749126771745771109}
• 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': '0.0082892212080512540507606609765', 'prec': 110}, 'conductor': 68400, 'gens': [], 'heights': [], 'lmfdb_label': '68400.et2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.12977149074199715484436220225', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0381719259359772387548976180395968559', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': 'a', '7': [0, 0], '11': [0, 0], '13': [0, 0], '17': [0, 0], '19': [1, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '68400.et2'}
• ec_torsion_growth •

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

  
  
  • id: 3254285
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '68400.et2', 'torsion': [5]}
  • id: 3254286
    {'degree': 3, 'field': [7, 17, -1, 1], 'lmfdb_label': '68400.et2', 'torsion': [2]}
  • id: 3254288
    {'degree': 6, 'field': [-300, 0, 25, 0, -10, 0, 1], 'lmfdb_label': '68400.et2', 'torsion': [10]}
  • id: 3254287
    {'degree': 6, 'field': [2052, 0, -108, 0, 9, 0, 1], 'lmfdb_label': '68400.et2', 'torsion': [2, 2]}
  • id: 3254289
    {'degree': 8, 'field': [-24300, 0, -2055, 0, -105, 0, 15, 0, 1], 'lmfdb_label': '68400.et2', 'torsion': [3]}
  • id: 3254290
    {'degree': 12, 'field': [459, -2205, -532, 4195, 4820, 1455, 1600, 55, 140, 75, 28, -5, 1], 'lmfdb_label': '68400.et2', 'torsion': [4]}
  • id: 3254291
    {'degree': 12, 'field': [4957, -1540, 147, 2866, -1454, -456, 895, -522, -6, 80, -5, -6, 1], 'lmfdb_label': '68400.et2', 'torsion': [2, 10]}
  • id: 3254292
    {'degree': 16, 'field': [-37224, 196632, -107244, -190032, 118566, -14154, -22331, 29584, -13938, 2264, 1349, -624, -169, 98, 6, -8, 1], 'lmfdb_label': '68400.et2', 'torsion': [15]}
  • id: 3254293
    {'degree': 20, 'field': [6372719308801, -2786089465350, -386305989750, 264542947950, 357370234875, -1534377794, -48637856700, -1001504250, 1677789300, -56045250, 277211, 3411450, 577125, 379050, 47250, -1444, 2475, 0, 75, 0, 1], 'lmfdb_label': '68400.et2', 'torsion': [5]}
• 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: 1654969
    {'conductor': 68400, 'conductor_valuation': 4, 'discriminant_valuation': 22, 'j_denominator_valuation': 10, 'kodaira_symbol': -18, 'lmfdb_label': '68400.et2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1654970
    {'conductor': 68400, 'conductor_valuation': 2, 'discriminant_valuation': 21, 'j_denominator_valuation': 15, 'kodaira_symbol': -19, 'lmfdb_label': '68400.et2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1654971
    {'conductor': 68400, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '68400.et2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1654972
    {'conductor': 68400, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '68400.et2', 'prime': 19, '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: 2116481
    {'adelic_gens': [[781, 10, 485, 51], [1131, 10, 1130, 11], [571, 10, 0, 1027], [569, 1130, 565, 1089], [1, 0, 10, 1], [379, 1130, 755, 1089], [6, 13, 1085, 1021], [1, 10, 0, 1]], 'adelic_image': '1140.48.1.?', 'conductor': 68400, 'lmfdb_label': '68400.et2', 'prime': 0}
  • id: 285521
    {'conductor': 68400, 'elladic_image': '5.12.0.1', 'lmfdb_label': '68400.et2', 'modell_image': '5B.4.1', 'prime': 5}
• lmfdb_iso 68400.et does not appear in ec_padic