Elliptic curve data - 63870.o2

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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': '63870p', 'Clabel': '63870p1', 'Cnumber': 1, 'abc_quality': 0.9932863758556641, 'absD': 97645976616960000000, 'adelic_genus': 2, 'adelic_index': 96, 'adelic_level': 894180, 'ainvs': [1, 0, 0, -35874060, 82698195600], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 2129], 'class_deg': 7, 'class_size': 2, 'cm': 0, 'conductor': 63870, 'degree': 4346496, 'elladic_images': ['7.48.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.9589217535955948931421486178', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 14, 'isogeny_degrees': [1, 7], 'jinv': [5105817686570071165887579841, 97645976616960000000], 'lmfdb_iso': '63870.o', 'lmfdb_label': '63870.o2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -35874060, 82698195600], 'min_quad_twist_disc': 1, 'modell_images': ['7B.1.1'], 'modm_images': ['7.48.0-7.a.1.2', '127740.2.0.?', '894180.96.2.?'], 'nonmax_primes': [7], 'nonmax_rad': 7, 'num_bad_primes': 4, 'num_int_pts': 16, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.7690315184735211907602513638', 'prec': 100}, 'semistable': True, 'serre_invariants': [[2, 4, 31935], [3, 4, 21290], [5, 6, 12774], [7, 2, 2129], [2129, 2130, 30]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.9589217535955948931421486178', 'prec': 100}, 'szpiro_ratio': 5.766150518238079, 'torsion': 7, 'torsion_primes': [7], 'torsion_structure': [7]}
• 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, 1, 1, 1, 1, 1, 1, 1, 1, -2, 1, 0, 1, 1, 1, -3, 1, 6, 1], 'aplist': [1, 1, 1, 1, -2, 0, -3, 6, -4, -5, 4, 3, -7, 2, 6, -2, -3, -8, -2, -12, -10, 3, -7, -15, -14], 'class_deg': 7, 'class_size': 2, 'conductor': 63870, 'isogeny_matrix': [[1, 7], [7, 1]], 'lmfdb_iso': '63870.o', 'trace_hash': 506916230268854358}
• 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': '0.0026909970400258942832063187428', 'prec': 110}, 'conductor': 63870, 'gens': [[3470, -1360, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.7690315184735211907602513638', 'prec': 100}], 'lmfdb_label': '63870.o2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.17448909532839870654139304699', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '13.528642528639472166187709657280432963', 'prec': 130}, 'tamagawa_product': 1372, 'torsion_generators': [[3480, 180, 1]], 'xcoord_integral_points': [3470, 3480, 3720, 4152, 4800, 7320, 16920, 45720]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': [2, 0], '5': [2, 0], '7': [3, 0], '11': [1, 0], '13': [1, 1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0], '2129': 'o?'}, 'iwp0': 0, 'lmfdb_label': '63870.o2'}
• ec_torsion_growth •

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

  
  
  • id: 3053685
    {'degree': 3, 'field': [60, -80, -1, 1], 'lmfdb_label': '63870.o2', 'torsion': [14]}
  • id: 3053686
    {'degree': 6, 'field': [29760, -56400, 3994, 3274, -393, -2, 1], 'lmfdb_label': '63870.o2', 'torsion': [2, 14]}
  • id: 3053687
    {'degree': 8, 'field': [-55488, 0, 12668, 0, -816, 0, 0, 0, 1], 'lmfdb_label': '63870.o2', 'torsion': [21]}
  • id: 3053688
    {'degree': 12, 'field': [1178289792, -928476576, 3227171280, -389193408, -208522504, 30085718, 3686149, -642248, -8429, 3998, -169, -4, 1], 'lmfdb_label': '63870.o2', 'torsion': [28]}
• 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: 1541948
    {'conductor': 63870, 'conductor_valuation': 1, 'discriminant_valuation': 28, 'j_denominator_valuation': 28, 'kodaira_symbol': 32, 'lmfdb_label': '63870.o2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 28}
  • id: 1541949
    {'conductor': 63870, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '63870.o2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 7}
  • id: 1541950
    {'conductor': 63870, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '63870.o2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 7}
  • id: 1541951
    {'conductor': 63870, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '63870.o2', 'prime': 2129, '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: 2087240
    {'adelic_gens': [[447091, 14, 0, 63871], [8, 5, 91, 57], [800528, 7, 864353, 894174], [1, 14, 0, 1], [1, 0, 14, 1], [536516, 7, 536501, 894174], [894167, 14, 894166, 15], [596128, 7, 596113, 894174], [8, 7, 447083, 894174]], 'adelic_image': '894180.96.2.?', 'conductor': 63870, 'lmfdb_label': '63870.o2', 'prime': 0}
  • id: 268329
    {'conductor': 63870, 'elladic_image': '7.48.0.1', 'lmfdb_label': '63870.o2', 'modell_image': '7B.1.1', 'prime': 7}
• ec_padic •

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

  
  
  • id: 3254278
    {'lmfdb_iso': '63870.o', 'p': 7, 'prec': 20, 'unit': 31187475128959437, 'val': 0}
  • id: 3254283
    {'lmfdb_iso': '63870.o', 'p': 11, 'prec': 20, 'unit': 38868255117230040663, 'val': 1}
  • id: 3254284
    {'lmfdb_iso': '63870.o', 'p': 17, 'prec': 20, 'unit': 197637988420034822428501, 'val': 1}
  • id: 3254285
    {'lmfdb_iso': '63870.o', 'p': 19, 'prec': 20, 'unit': 1017767028680990520770125, 'val': 1}
  • id: 3254289
    {'lmfdb_iso': '63870.o', 'p': 23, 'prec': 20, 'unit': 7858942488758612300216410, 'val': 1}
  • id: 3254281
    {'lmfdb_iso': '63870.o', 'p': 29, 'prec': 20, 'unit': 5848325586277766786760429592, 'val': 1}
  • id: 3254294
    {'lmfdb_iso': '63870.o', 'p': 31, 'prec': 20, 'unit': 15499276107625311848332728750, 'val': 1}
  • id: 3254277
    {'lmfdb_iso': '63870.o', 'p': 37, 'prec': 20, 'unit': 419810503759560404117545446233, 'val': 1}
  • id: 3254279
    {'lmfdb_iso': '63870.o', 'p': 41, 'prec': 20, 'unit': 2156536216328856642493182284697, 'val': 1}
  • id: 3254280
    {'lmfdb_iso': '63870.o', 'p': 43, 'prec': 20, 'unit': 8760615718679908696421157242390, 'val': 1}
  • id: 3254292
    {'lmfdb_iso': '63870.o', 'p': 47, 'prec': 20, 'unit': 7008072468669797503951807680922, 'val': 1}
  • id: 3254286
    {'lmfdb_iso': '63870.o', 'p': 53, 'prec': 20, 'unit': 224368185251334826863659423283211, 'val': 1}
  • id: 3254287
    {'lmfdb_iso': '63870.o', 'p': 59, 'prec': 20, 'unit': 1955822857626357043668059089643286, 'val': 1}
  • id: 3254293
    {'lmfdb_iso': '63870.o', 'p': 61, 'prec': 20, 'unit': 5608204606082931526014624597346835, 'val': 1}
  • id: 3254276
    {'lmfdb_iso': '63870.o', 'p': 67, 'prec': 20, 'unit': 29833100356181443008884847542083420, 'val': 1}
  • id: 3254291
    {'lmfdb_iso': '63870.o', 'p': 71, 'prec': 20, 'unit': 146129147440902541969401835450160418, 'val': 1}
  • id: 3254288
    {'lmfdb_iso': '63870.o', 'p': 73, 'prec': 20, 'unit': 168850749549184016382354088100518151, 'val': 1}
  • id: 3254282
    {'lmfdb_iso': '63870.o', 'p': 79, 'prec': 20, 'unit': 364583403545748473641890166535083188, 'val': 1}
  • id: 3254275
    {'lmfdb_iso': '63870.o', 'p': 83, 'prec': 20, 'unit': 2547525028386765156674381708860544570, 'val': 1}
  • id: 3254290
    {'lmfdb_iso': '63870.o', 'p': 89, 'prec': 20, 'unit': 3314539714991959050465799780701021305, 'val': 1}
  • id: 3254274
    {'lmfdb_iso': '63870.o', 'p': 97, 'prec': 20, 'unit': 48562076030410779851021874305452941672, 'val': 1}