Elliptic curve data - 13872.h1

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '13872a', 'Clabel': '13872a1', 'Cnumber': 1, 'abc_quality': 0.8121640630444127, 'absD': 1997568, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 6, 'ainvs': [0, -1, 0, -28, -80], 'analytic_rank': 1, 'bad_primes': [2, 3, 17], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 13872, 'degree': 1728, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.092595886542074552720683358262', 'prec': 110}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 7, 'isogeny_degrees': [1], 'jinv': [-34000, 27], 'lmfdb_iso': '13872.h', 'lmfdb_label': '13872.h1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -28, 80], 'min_quad_twist_disc': -4, 'modell_images': [], 'modm_images': ['6.2.0.a.1'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.7109138263166412260477498799', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0268962309247407723737605422', 'prec': 103}, 'szpiro_ratio': 2.3600787658367626, '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, 0, 0, -3, 0, 1, 0, 2, 0, -3, 0, 0, 0, 0, 0, -1, 0], 'aplist': [0, -1, 0, -3, 2, -3, 0, -1, 4, 6, 7, -11, -6, 1, 8, 4, 6, -3, -5, 0, -2, -4, 8, -2, 3], 'class_deg': 1, 'class_size': 1, 'conductor': 13872, 'isogeny_matrix': [[1]], 'lmfdb_iso': '13872.h', 'trace_hash': 1064378206654617280}
• 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': '1.2034492071656097883855721539', 'prec': 100}, 'conductor': 13872, 'gens': [[8, 12, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.7109138263166412260477498799', 'prec': 100}], 'lmfdb_label': '13872.h1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.0005868461619264949964128312', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.4238357390580042416420924698572474462', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': [8]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '5': [1, 3, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': 'a', '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '13872.h1'}
• ec_torsion_growth •

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

  
  
  • id: 713673
    {'degree': 3, 'field': [-12, 6, -1, 1], 'lmfdb_label': '13872.h1', 'torsion': [2]}
  • id: 713674
    {'degree': 6, 'field': [12, 0, -11, 0, 1, 0, 1], 'lmfdb_label': '13872.h1', 'torsion': [2, 2]}
  • id: 713675
    {'degree': 8, 'field': [-570, -1104, -914, -540, -222, -58, -6, 0, 1], 'lmfdb_label': '13872.h1', 'torsion': [3]}
  • id: 713676
    {'degree': 12, 'field': [-4, -112, -320, -524, -210, -240, 180, -84, 75, -28, 14, -5, 1], 'lmfdb_label': '13872.h1', 'torsion': [4]}
• 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: 303606
    {'conductor': 13872, 'conductor_valuation': 4, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '13872.h1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 303607
    {'conductor': 13872, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '13872.h1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 303608
    {'conductor': 13872, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '13872.h1', 'prime': 17, 'reduction_type': 0, '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

  
  {'adelic_gens': [[5, 2, 5, 3], [1, 1, 5, 0], [1, 2, 0, 1], [5, 2, 4, 3], [1, 0, 2, 1]], 'adelic_image': '6.2.0.?', 'conductor': 13872, 'lmfdb_label': '13872.h1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 615271
    {'lmfdb_iso': '13872.h', 'p': 7, 'prec': 20, 'unit': 11120715623852698, 'val': 1}
  • id: 615269
    {'lmfdb_iso': '13872.h', 'p': 11, 'prec': 20, 'unit': 48144824566733670574, 'val': 1}
  • id: 615275
    {'lmfdb_iso': '13872.h', 'p': 13, 'prec': 20, 'unit': 294502014153673853558, 'val': 1}
  • id: 615278
    {'lmfdb_iso': '13872.h', 'p': 19, 'prec': 20, 'unit': 797962433336035765177239, 'val': 1}
  • id: 615281
    {'lmfdb_iso': '13872.h', 'p': 23, 'prec': 20, 'unit': 36715160082323429602178936, 'val': 1}
  • id: 615274
    {'lmfdb_iso': '13872.h', 'p': 29, 'prec': 20, 'unit': 2968621139613101912896575010, 'val': 1}
  • id: 615286
    {'lmfdb_iso': '13872.h', 'p': 31, 'prec': 20, 'unit': 10931059807893903376328373947, 'val': 1}
  • id: 615270
    {'lmfdb_iso': '13872.h', 'p': 37, 'prec': 20, 'unit': 185513793285351256519187600160, 'val': 1}
  • id: 615272
    {'lmfdb_iso': '13872.h', 'p': 41, 'prec': 20, 'unit': 849064933701719804703189683125, 'val': 1}
  • id: 615273
    {'lmfdb_iso': '13872.h', 'p': 43, 'prec': 20, 'unit': 119179069094897043549459197388665, 'val': -1}
  • id: 615283
    {'lmfdb_iso': '13872.h', 'p': 47, 'prec': 20, 'unit': 8151897277170549427070599871489, 'val': 1}
  • id: 615279
    {'lmfdb_iso': '13872.h', 'p': 53, 'prec': 20, 'unit': 398483332195476386846449575964265, 'val': 1}
  • id: 615277
    {'lmfdb_iso': '13872.h', 'p': 59, 'prec': 20, 'unit': 1122229643238008000864017411379013, 'val': 1}
  • id: 615284
    {'lmfdb_iso': '13872.h', 'p': 61, 'prec': 20, 'unit': 112198326717804865395345207895890, 'val': 1}
  • id: 615268
    {'lmfdb_iso': '13872.h', 'p': 67, 'prec': 20, 'unit': 46838370000242474939576730811837237, 'val': 1}
  • id: 615280
    {'lmfdb_iso': '13872.h', 'p': 73, 'prec': 20, 'unit': 181469672301524901435469015898622474, 'val': 1}
  • id: 615276
    {'lmfdb_iso': '13872.h', 'p': 79, 'prec': 20, 'unit': 93937446328227420000584379008796963, 'val': 1}
  • id: 615285
    {'lmfdb_iso': '13872.h', 'p': 83, 'prec': 20, 'unit': 1837086697236869432826231896437695504, 'val': 1}
  • id: 615282
    {'lmfdb_iso': '13872.h', 'p': 89, 'prec': 20, 'unit': 461986730353655354218155925503523866, 'val': 1}
  • id: 615267
    {'lmfdb_iso': '13872.h', 'p': 97, 'prec': 20, 'unit': 21093345342430213826334189935286683432, 'val': 1}