Elliptic curve data - 4275.k2

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '4275b', 'Clabel': '4275b1', 'Cnumber': 1, 'abc_quality': 1.005333352881482, 'absD': 888195375, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1140, 'ainvs': [1, -1, 0, -852, -9469], 'analytic_rank': 1, 'bad_primes': [3, 5, 19], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 4275, 'degree': 1536, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.52587314793047999153962498538', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2], 'jinv': [-27818127, 361], 'lmfdb_iso': '4275.k', 'lmfdb_label': '4275.k2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -95, 382], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '30.6.0.a.1', '76.6.0.?', '1140.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.8040462327921206178313349451', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 15], [3, 2, 475], [5, 10, 171], [19, 20, 225]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.70044554667912737065699877562', 'prec': 107}, 'szpiro_ratio': 3.8130553639767246, '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, 0, 0, -2, -3, 0, 0, 2, 0, 2, -2, 0, -1, 2, 0, 1, 0], 'aplist': [1, 0, 0, -2, 2, 2, 2, 1, 0, -6, -4, -2, 2, 10, 0, -10, 0, -10, 4, -8, -4, -8, -12, 10, 18], 'class_deg': 2, 'class_size': 2, 'conductor': 4275, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '4275.k', 'trace_hash': 2002546895910822902}
• 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': '0.34932718753402784849395147143', 'prec': 103}, 'conductor': 4275, 'gens': [[382, 4063, 3]], 'heights': [{'__RealLiteral__': 0, 'data': '4.8040462327921206178313349451', 'prec': 100}], 'lmfdb_label': '4275.k2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.44146914844410907294875918494', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.2416763989537353382310413813054547428', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[34, -17, 1]], 'xcoord_integral_points': [34]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '3': 'a', '5': 'a', '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [2, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '4275.k2'}
• ec_torsion_growth •

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

  
  
  • id: 222372
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '4275.k2', 'torsion': [2, 2]}
  • id: 222373
    {'degree': 4, 'field': [-164, 22, -21, -2, 1], 'lmfdb_label': '4275.k2', 'torsion': [4]}
  • id: 222376
    {'degree': 8, 'field': [-75, 0, 75, 0, -30, 0, 0, 0, 1], 'lmfdb_label': '4275.k2', 'torsion': [6]}
  • id: 222374
    {'degree': 8, 'field': [646, 418, -379, -86, 64, -28, 14, -4, 1], 'lmfdb_label': '4275.k2', 'torsion': [2, 4]}
  • id: 222375
    {'degree': 8, 'field': [3481, 0, 1591, 0, 336, 0, 31, 0, 1], 'lmfdb_label': '4275.k2', 'torsion': [2, 4]}
  • id: 222378
    {'degree': 16, 'field': [81, 0, 10125, 0, 11313, 0, 9180, 0, 3564, 0, 810, 0, 132, 0, 15, 0, 1], 'lmfdb_label': '4275.k2', 'torsion': [2, 6]}
  • id: 222377
    {'degree': 16, 'field': [839056, 0, -1935152, 0, 517100, 0, 627688, 0, 167029, 0, 21962, 0, 1595, 0, 62, 0, 1], 'lmfdb_label': '4275.k2', 'torsion': [8]}
• 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: 80460
    {'conductor': 4275, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '4275.k2', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 80461
    {'conductor': 4275, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '4275.k2', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 80462
    {'conductor': 4275, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '4275.k2', 'prime': 19, 'reduction_type': 1, '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: 1691772
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1137, 4, 1136, 5], [1, 2, 2, 5], [1, 4, 0, 1], [688, 1, 683, 0], [781, 4, 422, 9], [857, 286, 284, 855], [764, 1, 379, 0]], 'adelic_image': '1140.12.0.?', 'conductor': 4275, 'lmfdb_label': '4275.k2', 'prime': 0}
  • id: 21216
    {'conductor': 4275, 'elladic_image': '2.3.0.1', 'lmfdb_label': '4275.k2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 151702
    {'lmfdb_iso': '4275.k', 'p': 7, 'prec': 20, 'unit': 10953969172324686, 'val': 1}
  • id: 151700
    {'lmfdb_iso': '4275.k', 'p': 11, 'prec': 20, 'unit': 14051697636757308453, 'val': 1}
  • id: 151706
    {'lmfdb_iso': '4275.k', 'p': 13, 'prec': 20, 'unit': 1210173533351430641881, 'val': 1}
  • id: 151708
    {'lmfdb_iso': '4275.k', 'p': 17, 'prec': 20, 'unit': 86240707990837792973529, 'val': 1}
  • id: 151705
    {'lmfdb_iso': '4275.k', 'p': 29, 'prec': 20, 'unit': 4538034306876354922567523307, 'val': 1}
  • id: 151715
    {'lmfdb_iso': '4275.k', 'p': 31, 'prec': 20, 'unit': 4827395574840421190358907467, 'val': 1}
  • id: 151701
    {'lmfdb_iso': '4275.k', 'p': 37, 'prec': 20, 'unit': 244937044500411573433766066105, 'val': 1}
  • id: 151703
    {'lmfdb_iso': '4275.k', 'p': 41, 'prec': 20, 'unit': 223152898150348482765235586669, 'val': 1}
  • id: 151704
    {'lmfdb_iso': '4275.k', 'p': 43, 'prec': 20, 'unit': 6872206448862036554774512861935, 'val': 1}
  • id: 151710
    {'lmfdb_iso': '4275.k', 'p': 53, 'prec': 20, 'unit': 353088228108103005061235531570325, 'val': 1}
  • id: 151714
    {'lmfdb_iso': '4275.k', 'p': 61, 'prec': 20, 'unit': 2915900019044024619584468741400510, 'val': 1}
  • id: 151699
    {'lmfdb_iso': '4275.k', 'p': 67, 'prec': 20, 'unit': 10457494816998551916123582604900064, 'val': 1}
  • id: 151713
    {'lmfdb_iso': '4275.k', 'p': 71, 'prec': 20, 'unit': 17067225793067996410867297134826959, 'val': 1}
  • id: 151711
    {'lmfdb_iso': '4275.k', 'p': 73, 'prec': 20, 'unit': 65595504822447062477867150809546024, 'val': 1}
  • id: 151707
    {'lmfdb_iso': '4275.k', 'p': 79, 'prec': 20, 'unit': 300524978333820409158234418573322920, 'val': 1}
  • id: 151709
    {'lmfdb_iso': '4275.k', 'p': 83, 'prec': 20, 'unit': 2706345846398115821303005605999135594, 'val': 1}
  • id: 151712
    {'lmfdb_iso': '4275.k', 'p': 89, 'prec': 20, 'unit': 1979699346197140941693446481442561962, 'val': 1}
  • id: 151698
    {'lmfdb_iso': '4275.k', 'p': 97, 'prec': 20, 'unit': 26296851452268124565044471586532402965, 'val': 1}