Elliptic curve data - 5415.b1

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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': '5415b', 'Clabel': '5415b1', 'Cnumber': 1, 'abc_quality': 1.0621597525174942, 'absD': 77915162881125, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 10, 'ainvs': [0, -1, 1, -13116, 396722], 'analytic_rank': 1, 'bad_primes': [3, 5, 19], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 5415, 'degree': 21168, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3698516683534065176389311908', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1], 'jinv': [1914902401024, 597871125], 'lmfdb_iso': '5415.b', 'lmfdb_label': '5415.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 1, -13116, 396722], 'min_quad_twist_disc': 1, 'modell_images': [], 'modm_images': ['10.2.0.a.1'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 4, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.2524321056408782447935825036', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 1805], [3, 4, 361], [5, 6, 1083], [7, 2, 1805], [19, 128, 15]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.38837200863125969763592204684', 'prec': 103}, 'szpiro_ratio': 4.659622942695113, '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, -2, -1, 2, -1, 2, -2, 0, 1, 2, 1, -2, 2, 4, 1, -4, 2, -2, 0, -2], 'aplist': [-2, -1, -1, -2, 1, 2, 2, 0, -4, -5, 9, -6, 6, -10, 0, -2, 7, -7, 8, 3, -2, -11, 6, 15, 8], 'class_deg': 1, 'class_size': 1, 'conductor': 5415, 'isogeny_matrix': [[1]], 'lmfdb_iso': '5415.b', 'trace_hash': 688991263135545875}
• 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': '0.064589505386590406650491251819', 'prec': 107}, 'conductor': 5415, 'gens': [[138, 1093, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.2524321056408782447935825036', 'prec': 100}], 'lmfdb_label': '5415.b1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.56529207637652257445050651530', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4159798910367046684059453296441116018', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': [125, 138]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 10, 0], '3': [1, 0], '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': 'a', '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [3, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '5415.b1'}
• ec_torsion_growth •

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

  
  
  • id: 281646
    {'degree': 3, 'field': [45, -25, -1, 1], 'lmfdb_label': '5415.b1', 'torsion': [2]}
  • id: 281647
    {'degree': 6, 'field': [-369, -183, 158, 49, -22, -3, 1], 'lmfdb_label': '5415.b1', 'torsion': [2, 2]}
  • id: 281648
    {'degree': 8, 'field': [-13, 25, -34, 17, -5, -7, 7, -4, 1], 'lmfdb_label': '5415.b1', 'torsion': [3]}
  • id: 281649
    {'degree': 12, 'field': [-7797, 36950, 12702, -19828, 4945, -836, 1704, -764, -115, 134, -18, -4, 1], 'lmfdb_label': '5415.b1', '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: 105502
    {'conductor': 5415, 'conductor_valuation': 1, 'discriminant_valuation': 14, 'j_denominator_valuation': 14, 'kodaira_symbol': 18, 'lmfdb_label': '5415.b1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 105503
    {'conductor': 5415, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '5415.b1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 105504
    {'conductor': 5415, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '5415.b1', 'prime': 19, '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': [[1, 2, 0, 1], [9, 2, 8, 3], [1, 0, 2, 1], [7, 2, 7, 3], [1, 1, 9, 0]], 'adelic_image': '10.2.0.?', 'conductor': 5415, 'lmfdb_label': '5415.b1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 202714
    {'lmfdb_iso': '5415.b', 'p': 7, 'prec': 20, 'unit': 4594635846417286, 'val': 1}
  • id: 202712
    {'lmfdb_iso': '5415.b', 'p': 11, 'prec': 20, 'unit': 309780440398326818687, 'val': -1}
  • id: 202718
    {'lmfdb_iso': '5415.b', 'p': 13, 'prec': 20, 'unit': 294524051266421395920, 'val': 1}
  • id: 202720
    {'lmfdb_iso': '5415.b', 'p': 17, 'prec': 20, 'unit': 144724572663005256016013, 'val': 1}
  • id: 202724
    {'lmfdb_iso': '5415.b', 'p': 23, 'prec': 20, 'unit': 42943784444871250226845988, 'val': 1}
  • id: 202717
    {'lmfdb_iso': '5415.b', 'p': 29, 'prec': 20, 'unit': 383303496736774967581875470, 'val': 1}
  • id: 202729
    {'lmfdb_iso': '5415.b', 'p': 31, 'prec': 20, 'unit': 16654991226243971466982824045, 'val': 1}
  • id: 202713
    {'lmfdb_iso': '5415.b', 'p': 37, 'prec': 20, 'unit': 170284728904074690087630017491, 'val': 1}
  • id: 202715
    {'lmfdb_iso': '5415.b', 'p': 41, 'prec': 20, 'unit': 1172775451462710677326519849961, 'val': 1}
  • id: 202716
    {'lmfdb_iso': '5415.b', 'p': 43, 'prec': 20, 'unit': 231998822892431278309207401433, 'val': 2}
  • id: 202722
    {'lmfdb_iso': '5415.b', 'p': 53, 'prec': 20, 'unit': 215710836092740263876504378169288, 'val': 1}
  • id: 202727
    {'lmfdb_iso': '5415.b', 'p': 59, 'prec': 20, 'unit': 3375766283727865207796006144319938, 'val': 1}
  • id: 202728
    {'lmfdb_iso': '5415.b', 'p': 61, 'prec': 20, 'unit': 728446185940821342436241665752289, 'val': 1}
  • id: 202711
    {'lmfdb_iso': '5415.b', 'p': 67, 'prec': 20, 'unit': 37722429851789445991124971966740454, 'val': 1}
  • id: 202726
    {'lmfdb_iso': '5415.b', 'p': 71, 'prec': 20, 'unit': 73293802650833083450351816824201982, 'val': 1}
  • id: 202723
    {'lmfdb_iso': '5415.b', 'p': 73, 'prec': 20, 'unit': 9615243859959744405177055092973080, 'val': 1}
  • id: 202719
    {'lmfdb_iso': '5415.b', 'p': 79, 'prec': 20, 'unit': 286978942953959405008593278972001552, 'val': 1}
  • id: 202721
    {'lmfdb_iso': '5415.b', 'p': 83, 'prec': 20, 'unit': 2232910415098909616923635063697083232, 'val': 1}
  • id: 202725
    {'lmfdb_iso': '5415.b', 'p': 89, 'prec': 20, 'unit': 5059475051496864315552330355672849281, 'val': 1}
  • id: 202710
    {'lmfdb_iso': '5415.b', 'p': 97, 'prec': 20, 'unit': 5195522404697724337544092739001580698, 'val': 1}