Elliptic curve data - 4650.x1

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• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  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
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '4650bd', 'Clabel': '4650bd2', 'Cnumber': 2, 'absD': 49818240000000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1240, 'ainvs': [1, 1, 1, -5461188, 4909955781], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 31], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 4650, 'degree': 99840, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2864422954146134653708761084', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 23, 'isogeny_degrees': [1, 2], 'jinv': [1152829477932246539641, 3188367360], 'lmfdb_iso': '4650.x', 'lmfdb_label': '4650.x1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -218448, 39279646], 'min_quad_twist_disc': 5, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '40.6.0.b.1', '124.6.0.?', '1240.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 10, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.39612412703278941597770964800', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.4817233391975632780704964418', 'prec': 100}, '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, 0, -1, -4, 1, 1, 0, 2, -1, -2, -4, 0, 1, 0, 1, 0, 0], 'aplist': [1, -1, 0, -4, 2, -2, 0, 0, 6, 0, 1, 2, -10, 4, -4, -6, -4, 0, -4, -16, -4, 4, -8, 6, -14], 'class_deg': 2, 'class_size': 2, 'conductor': 4650, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '4650.x', 'trace_hash': 1882000481353112646}
• 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': '0.010328124294185212436053994667', 'prec': 107}, 'conductor': 4650, 'gens': [[1405, 2897, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.39612412703278941597770964800', 'prec': 103}], 'lmfdb_label': '4650.x1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.41831522806529736356304299586', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.3083236180890913581510438562724289346', 'prec': 130}, 'tamagawa_product': 104, 'torsion_generators': [[5395, -5399, 2]], 'xcoord_integral_points': [-395, 969, 1341, 1349, 1405]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [9, 0], '3': [1, 0], '5': 'a', '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 1, 0], '19': [1, 1, 0], '23': [1, 0], '29': [1, 1, 0], '31': [2, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '4650.x1'}
• ec_torsion_growth •

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

  
  
  • id: 241875
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '4650.x1', 'torsion': [2, 2]}
  • id: 241876
    {'degree': 4, 'field': [10, 0, 3, 0, 1], 'lmfdb_label': '4650.x1', 'torsion': [4]}
  • id: 241879
    {'degree': 8, 'field': [-3424, -1856, 2072, -433, 220, -7, 7, -4, 1], 'lmfdb_label': '4650.x1', 'torsion': [6]}
  • id: 241877
    {'degree': 8, 'field': [-1944, 288, 856, 504, 49, -68, -6, -4, 1], 'lmfdb_label': '4650.x1', 'torsion': [2, 4]}
  • id: 241878
    {'degree': 8, 'field': [19600, 0, -3520, 0, 569, 0, -34, 0, 1], 'lmfdb_label': '4650.x1', 'torsion': [2, 4]}
  • id: 241881
    {'degree': 16, 'field': [648822784, 0, -670889984, 0, 99746560, 0, 1423968, 0, 692640, 0, 22488, 0, 532, 0, -20, 0, 1], 'lmfdb_label': '4650.x1', 'torsion': [2, 6]}
  • id: 241880
    {'degree': 16, 'field': [871430400, 0, -67383360, 0, 11959056, 0, -2347680, 0, 213736, 0, -4812, 0, -31, 0, -6, 0, 1], 'lmfdb_label': '4650.x1', '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: 88735
    {'conductor': 4650, 'conductor_valuation': 1, 'discriminant_valuation': 13, 'j_denominator_valuation': 13, 'kodaira_symbol': 17, 'lmfdb_label': '4650.x1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 13}
  • id: 88736
    {'conductor': 4650, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '4650.x1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 88737
    {'conductor': 4650, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '4650.x1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 88738
    {'conductor': 4650, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '4650.x1', 'prime': 31, 'reduction_type': 1, '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: 1694220
    {'adelic_gens': [[2, 1, 619, 0], [1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [777, 466, 464, 775], [994, 1, 743, 0], [1237, 4, 1236, 5], [561, 4, 1122, 9]], 'adelic_image': '1240.12.0.?', 'conductor': 4650, 'lmfdb_label': '4650.x1', 'prime': 0}
  • id: 23043
    {'conductor': 4650, 'elladic_image': '2.3.0.1', 'lmfdb_label': '4650.x1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 167945
    {'lmfdb_iso': '4650.x', 'p': 7, 'prec': 20, 'unit': 472942254893452, 'val': 1}
  • id: 167943
    {'lmfdb_iso': '4650.x', 'p': 11, 'prec': 20, 'unit': 37302827419689269334, 'val': 1}
  • id: 167948
    {'lmfdb_iso': '4650.x', 'p': 13, 'prec': 20, 'unit': 15484694025934901440850, 'val': 0}
  • id: 167954
    {'lmfdb_iso': '4650.x', 'p': 23, 'prec': 20, 'unit': 69333498705297669675227752, 'val': 1}
  • id: 167944
    {'lmfdb_iso': '4650.x', 'p': 37, 'prec': 20, 'unit': 378901077907725417010964576820, 'val': 1}
  • id: 167946
    {'lmfdb_iso': '4650.x', 'p': 41, 'prec': 20, 'unit': 4309207199283867854855939665935, 'val': 1}
  • id: 167947
    {'lmfdb_iso': '4650.x', 'p': 43, 'prec': 20, 'unit': 6183659489393914738094512004026, 'val': 1}
  • id: 167957
    {'lmfdb_iso': '4650.x', 'p': 47, 'prec': 20, 'unit': 12279285470938205824589218892594, 'val': 1}
  • id: 167952
    {'lmfdb_iso': '4650.x', 'p': 53, 'prec': 20, 'unit': 285811946462440290715847197384538, 'val': 1}
  • id: 167950
    {'lmfdb_iso': '4650.x', 'p': 59, 'prec': 20, 'unit': 3257862050813881841300655010452830, 'val': 1}
  • id: 167942
    {'lmfdb_iso': '4650.x', 'p': 67, 'prec': 20, 'unit': 15920573144467048297307180148160839, 'val': 1}
  • id: 167956
    {'lmfdb_iso': '4650.x', 'p': 71, 'prec': 20, 'unit': 42732395847240319268673760617783364, 'val': 1}
  • id: 167953
    {'lmfdb_iso': '4650.x', 'p': 73, 'prec': 20, 'unit': 244164090821877142344902264030445185, 'val': 1}
  • id: 167949
    {'lmfdb_iso': '4650.x', 'p': 79, 'prec': 20, 'unit': 35099832476373658607997717676377583, 'val': 1}
  • id: 167951
    {'lmfdb_iso': '4650.x', 'p': 83, 'prec': 20, 'unit': 2599492723856124291711230874853295081, 'val': 1}
  • id: 167955
    {'lmfdb_iso': '4650.x', 'p': 89, 'prec': 20, 'unit': 7767096092890157219748759793255537660, 'val': 1}
  • id: 167941
    {'lmfdb_iso': '4650.x', 'p': 97, 'prec': 20, 'unit': 24183682577283593403741772240167122778, 'val': 1}