Elliptic curve data - 5070.m2

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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': '5070o', 'Clabel': '5070o1', 'Cnumber': 1, 'abc_quality': 0.879641388243507, 'absD': 3181349811900, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1560, 'ainvs': [1, 1, 1, -7186, 246683], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 5070, 'degree': 12480, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1465771996417924157394779735', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 12, 'isogeny_degrees': [1, 2], 'jinv': [-3869893, 300], 'lmfdb_iso': '5070.m', 'lmfdb_label': '5070.m2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -42, 96], 'min_quad_twist_disc': 13, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '78.6.0.?', '120.6.0.?', '520.6.0.?', '1560.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.9891409438521738213996826428', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 39], [3, 4, 1690], [5, 6, 1014], [13, 62, 30]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.77713481845436013630063760767', 'prec': 107}, 'szpiro_ratio': 4.498717943604138, '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, -1, 1, -1, -1, 0, 1, 1, -1, 4, -1, 0, 0, 1, 1, -4, 1, -4, -1], 'aplist': [1, -1, -1, 0, 4, 0, -4, -4, -6, 4, -10, -4, 2, 12, 0, -2, 4, -10, 10, -12, 6, -8, 0, -10, 14], 'class_deg': 2, 'class_size': 2, 'conductor': 5070, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '5070.m', 'trace_hash': 1715504405491202163}
• 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': '0.10094753028237431073214147763', 'prec': 103}, 'conductor': 5070, 'gens': [[61, 169, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.9891409438521738213996826428', 'prec': 100}], 'lmfdb_label': '5070.m2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.78217852099400880120569795166', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.6760836850098576492770317776722181703', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-99, 49, 1]], 'xcoord_integral_points': [-99, 61]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': [1, 0], '5': [1, 0], '7': [3, 1, 0], '11': [1, 0], '13': 'a', '17': [3, 0], '19': [1, 0], '23': [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': '5070.m2'}
• ec_torsion_growth •

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

  
  
  • id: 265583
    {'degree': 2, 'field': [10, -1, 1], 'lmfdb_label': '5070.m2', 'torsion': [2, 2]}
  • id: 265584
    {'degree': 4, 'field': [-351, 0, 26, 0, 1], 'lmfdb_label': '5070.m2', 'torsion': [4]}
  • id: 265586
    {'degree': 8, 'field': [1056, -3504, 3970, -976, 599, -136, 50, -4, 1], 'lmfdb_label': '5070.m2', 'torsion': [2, 4]}
  • id: 265585
    {'degree': 8, 'field': [3136, -2240, 968, 400, -182, 38, 5, -4, 1], 'lmfdb_label': '5070.m2', 'torsion': [2, 4]}
  • id: 265587
    {'degree': 8, 'field': [7400, 14152, 3122, 604, -46, -107, 7, -1, 1], 'lmfdb_label': '5070.m2', 'torsion': [6]}
  • id: 265589
    {'degree': 16, 'field': [385641, 0, 6883947, 0, -1169802, 0, 222669, 0, 65070, 0, 11529, 0, 898, 0, 47, 0, 1], 'lmfdb_label': '5070.m2', 'torsion': [2, 6]}
  • id: 265588
    {'degree': 16, 'field': [12199788316, -22933815616, 15976634564, -4997761040, 600861373, 7149668, 8311598, -6304148, 559407, 171544, -43888, 9080, -2225, 436, -10, -4, 1], 'lmfdb_label': '5070.m2', '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: 98521
    {'conductor': 5070, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '5070.m2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 98522
    {'conductor': 5070, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '5070.m2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 98523
    {'conductor': 5070, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '5070.m2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 98524
    {'conductor': 5070, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '5070.m2', 'prime': 13, 'reduction_type': 0, '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: 1697115
    {'adelic_gens': [[1, 2, 2, 5], [1204, 1, 479, 0], [1, 4, 0, 1], [1042, 1, 1039, 0], [1557, 4, 1556, 5], [977, 586, 584, 975], [1, 0, 4, 1], [781, 4, 2, 9], [3, 4, 8, 11], [937, 4, 314, 9]], 'adelic_image': '1560.12.0.?', 'conductor': 5070, 'lmfdb_label': '5070.m2', 'prime': 0}
  • id: 25217
    {'conductor': 5070, 'elladic_image': '2.3.0.1', 'lmfdb_label': '5070.m2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 186920
    {'lmfdb_iso': '5070.m', 'p': 11, 'prec': 20, 'unit': 43335281059117759825, 'val': 1}
  • id: 186921
    {'lmfdb_iso': '5070.m', 'p': 17, 'prec': 20, 'unit': 507151311167583411298, 'val': 3}
  • id: 186922
    {'lmfdb_iso': '5070.m', 'p': 19, 'prec': 20, 'unit': 1220129368744021455492090, 'val': 1}
  • id: 186925
    {'lmfdb_iso': '5070.m', 'p': 23, 'prec': 20, 'unit': 72281562380856593653340336, 'val': 1}
  • id: 186918
    {'lmfdb_iso': '5070.m', 'p': 29, 'prec': 20, 'unit': 5116389384273456023867306959, 'val': 1}
  • id: 186929
    {'lmfdb_iso': '5070.m', 'p': 31, 'prec': 20, 'unit': 15091762763757638576155128943, 'val': 1}
  • id: 186914
    {'lmfdb_iso': '5070.m', 'p': 37, 'prec': 20, 'unit': 143084853816438723049532181104, 'val': 1}
  • id: 186916
    {'lmfdb_iso': '5070.m', 'p': 41, 'prec': 20, 'unit': 889811406575480781136758090307, 'val': 1}
  • id: 186917
    {'lmfdb_iso': '5070.m', 'p': 43, 'prec': 20, 'unit': 4358159148628943786691784959023, 'val': 1}
  • id: 186923
    {'lmfdb_iso': '5070.m', 'p': 53, 'prec': 20, 'unit': 445093829323281897008239011413074, 'val': 1}
  • id: 186927
    {'lmfdb_iso': '5070.m', 'p': 59, 'prec': 20, 'unit': 1735925117965619585642851648564318, 'val': 1}
  • id: 186928
    {'lmfdb_iso': '5070.m', 'p': 61, 'prec': 20, 'unit': 3651195984933814033839046828259612, 'val': 1}
  • id: 186913
    {'lmfdb_iso': '5070.m', 'p': 67, 'prec': 20, 'unit': 21679189315609961395922226628075015, 'val': 1}
  • id: 186915
    {'lmfdb_iso': '5070.m', 'p': 71, 'prec': 20, 'unit': 91691771662196740538174912439910277, 'val': 1}
  • id: 186924
    {'lmfdb_iso': '5070.m', 'p': 73, 'prec': 20, 'unit': 206046448087889629117071437639504635, 'val': 1}
  • id: 186919
    {'lmfdb_iso': '5070.m', 'p': 79, 'prec': 20, 'unit': 726194152097977573472631453846943050, 'val': 1}
  • id: 186926
    {'lmfdb_iso': '5070.m', 'p': 89, 'prec': 20, 'unit': 3930231888261633360008209507619384586, 'val': 1}
  • id: 186912
    {'lmfdb_iso': '5070.m', 'p': 97, 'prec': 20, 'unit': 26936666107976810037310544284889568175, 'val': 1}