Elliptic curve data - 66139.a1

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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': '66139a', 'Clabel': '66139a3', 'Cnumber': 3, 'abc_quality': 1.104947099482495, 'absD': 801430139179, 'adelic_genus': 43, 'adelic_index': 1296, 'adelic_level': 60534, 'ainvs': [0, 1, 1, -2678049, 1685955405], 'analytic_rank': 1, 'bad_primes': [19, 59], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 66139, 'degree': 620136, 'elladic_images': ['27.36.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0722078789441775288281200704', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 9, 'iso_nlabel': 0, 'isogeny_degrees': [1, 3, 9], 'jinv': [-50357871050752, 19], 'lmfdb_iso': '66139.a', 'lmfdb_label': '66139.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -769, -8470], 'min_quad_twist_disc': -59, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '9.12.0.a.1', '27.36.0.a.1', '38.2.0.a.1', '114.8.0.?', '171.36.0.?', '177.8.0.?', '342.72.3.?', '513.324.16.?', '531.24.0.?', '1026.648.43.?', '1593.72.0.?', '6726.16.0.?', '10089.72.0.?', '20178.144.3.?', '30267.648.16.?', '60534.1296.43.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.6152310549732122407420087763', 'prec': 100}, 'semistable': False, 'serre_invariants': [[19, 20, 3481], [59, 1742, 19]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.033439156991317803520094883539', 'prec': 107}, 'szpiro_ratio': 5.046653518794261, '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, -2, -2, 3, 0, -1, 0, 1, 0, -3, 4, 4, 0, -6, 4, -3, 0, 1, -6], 'aplist': [0, -2, 3, -1, -3, 4, -3, 1, 0, 6, 4, -2, -6, 1, 3, 12, 0, 1, 4, 6, 7, 8, -12, -12, -8], 'class_deg': 9, 'class_size': 3, 'conductor': 66139, 'isogeny_matrix': [[1, 3, 9], [3, 1, 3], [9, 3, 1]], 'lmfdb_iso': '66139.a', 'trace_hash': 368092452407590682}
• 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': '0.015852695058313757450645094146', 'prec': 107}, 'conductor': 66139, 'gens': [[23041, 151361, 5]], 'heights': [{'__RealLiteral__': 0, 'data': '3.6152310549732122407420087763', 'prec': 100}], 'lmfdb_label': '66139.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.53730166399491128500717851282', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.8849393231263710638077877659016704870', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 5, 0], '3': [5, 0], '5': [3, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [4, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0], '59': 'a'}, 'iwp0': 0, 'lmfdb_label': '66139.a1'}
• ec_torsion_growth •

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

  
  
  • id: 3152626
    {'degree': 2, 'field': [-44, -1, 1], 'lmfdb_label': '66139.a1', 'torsion': [3]}
  • id: 3152627
    {'degree': 3, 'field': [-2, -2, 0, 1], 'lmfdb_label': '66139.a1', 'torsion': [2]}
  • id: 3152631
    {'degree': 6, 'field': [-97242, -1938, 5860, 85, -127, -1, 1], 'lmfdb_label': '66139.a1', 'torsion': [6]}
  • id: 3152630
    {'degree': 6, 'field': [-3123, -11907, 8811, 453, -243, -3, 1], 'lmfdb_label': '66139.a1', 'torsion': [9]}
  • id: 3152628
    {'degree': 6, 'field': [1, -3, 4, -3, 4, -3, 1], 'lmfdb_label': '66139.a1', 'torsion': [2, 2]}
  • id: 3152629
    {'degree': 6, 'field': [7011, -1653, 684, 7, 32, -1, 1], 'lmfdb_label': '66139.a1', 'torsion': [3]}
  • id: 3152632
    {'degree': 12, 'field': [-13180601699, 2245230534, 477505932, -32200334, -6169781, -1850540, 578408, 19660, -13361, 526, 12, -6, 1], 'lmfdb_label': '66139.a1', 'torsion': [4]}
  • id: 3152633
    {'degree': 12, 'field': [9290304, 0, 4370379, 0, 728347, 0, 65171, 0, 3273, 0, 89, 0, 1], 'lmfdb_label': '66139.a1', 'torsion': [3, 3]}
  • id: 3152634
    {'degree': 12, 'field': [11452231, -5001717, 5508003, -1627452, 963552, -218802, 88219, -14388, 4281, -468, 105, -6, 1], 'lmfdb_label': '66139.a1', 'torsion': [9]}
  • id: 3152635
    {'degree': 12, 'field': [7613086009, 0, -1021824937, 0, 57492606, 0, -1729985, 0, 29310, 0, -265, 0, 1], 'lmfdb_label': '66139.a1', 'torsion': [2, 6]}
  • id: 3152637
    {'degree': 18, 'field': [-15691946657841, -28691307470799, 9038703505860, 3541533633750, 1834611427053, -1710096070323, 68696388436, 118492263933, -12762386478, -3683287511, 500528088, 64399029, -9358660, -669711, 92649, 3806, -474, -9, 1], 'lmfdb_label': '66139.a1', 'torsion': [18]}
  • id: 3152636
    {'degree': 18, 'field': [36433640532, -3609269336, 20824644556, -2476575140, 5483653802, -719387386, 872654667, -110188543, 91186225, -9926074, 6348139, -552367, 289648, -18845, 8313, -362, 137, -3, 1], 'lmfdb_label': '66139.a1', 'torsion': [6]}
• 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: 1597534
    {'conductor': 66139, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '66139.a1', 'prime': 19, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1597535
    {'conductor': 66139, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '66139.a1', 'prime': 59, '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: 2101681
    {'adelic_gens': [[27613, 7257, 43719, 14456], [31, 36, 54712, 53773], [1, 54, 0, 1], [57526, 16461, 33217, 18940], [28, 27, 729, 703], [42065, 0, 0, 60533], [1, 0, 54, 1], [60481, 54, 60480, 55]], 'adelic_image': '60534.1296.43.?', 'conductor': 66139, 'lmfdb_label': '66139.a1', 'prime': 0}
  • id: 276699
    {'conductor': 66139, 'elladic_image': '27.36.0.1', 'lmfdb_label': '66139.a1', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 3375949
    {'lmfdb_iso': '66139.a', 'p': 5, 'prec': 20, 'unit': 1740740874819, 'val': 2}
  • id: 3375950
    {'lmfdb_iso': '66139.a', 'p': 7, 'prec': 20, 'unit': 11368164376962395, 'val': 1}
  • id: 3375948
    {'lmfdb_iso': '66139.a', 'p': 11, 'prec': 20, 'unit': 51994810786245582285, 'val': 1}
  • id: 3375955
    {'lmfdb_iso': '66139.a', 'p': 13, 'prec': 20, 'unit': 726130367325172575755, 'val': 1}
  • id: 3375957
    {'lmfdb_iso': '66139.a', 'p': 17, 'prec': 20, 'unit': 191559074927479068172306, 'val': 1}
  • id: 3375954
    {'lmfdb_iso': '66139.a', 'p': 29, 'prec': 20, 'unit': 3501021561186182078627500072, 'val': 1}
  • id: 3375951
    {'lmfdb_iso': '66139.a', 'p': 31, 'prec': 20, 'unit': 6288492474179553371363053726, 'val': 1}
  • id: 3375965
    {'lmfdb_iso': '66139.a', 'p': 37, 'prec': 20, 'unit': 39840576807033006148322402111, 'val': 1}
  • id: 3375952
    {'lmfdb_iso': '66139.a', 'p': 41, 'prec': 20, 'unit': 416197215397324696554699824915, 'val': 1}
  • id: 3375953
    {'lmfdb_iso': '66139.a', 'p': 43, 'prec': 20, 'unit': 98218553537237079326456398286191, 'val': -1}
  • id: 3375956
    {'lmfdb_iso': '66139.a', 'p': 47, 'prec': 20, 'unit': 3327583000180333276683421416751, 'val': 1}
  • id: 3375959
    {'lmfdb_iso': '66139.a', 'p': 53, 'prec': 20, 'unit': 285456187083558189380681259543288, 'val': 1}
  • id: 3375964
    {'lmfdb_iso': '66139.a', 'p': 61, 'prec': 20, 'unit': 93056512420351142953507563383637632, 'val': -1}
  • id: 3375958
    {'lmfdb_iso': '66139.a', 'p': 67, 'prec': 20, 'unit': 21067049170549452354302242244106860, 'val': 1}
  • id: 3375962
    {'lmfdb_iso': '66139.a', 'p': 71, 'prec': 20, 'unit': 82642533026361608014375194272776388, 'val': 1}
  • id: 3375960
    {'lmfdb_iso': '66139.a', 'p': 73, 'prec': 20, 'unit': 147423014874610797150429832469274946, 'val': 1}
  • id: 3375963
    {'lmfdb_iso': '66139.a', 'p': 79, 'prec': 20, 'unit': 337648257369118712291194000208341438, 'val': 1}
  • id: 3375947
    {'lmfdb_iso': '66139.a', 'p': 83, 'prec': 20, 'unit': 276334009226198986856846262287018461, 'val': 1}
  • id: 3375961
    {'lmfdb_iso': '66139.a', 'p': 89, 'prec': 20, 'unit': 2643873493369383582582885546596099902, 'val': 1}
  • id: 3375946
    {'lmfdb_iso': '66139.a', 'p': 97, 'prec': 20, 'unit': 42217015882784670202965518908699614228, 'val': 1}