Elliptic curve data - 19536.r2

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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': '19536p', 'Clabel': '19536p2', 'Cnumber': 2, 'abc_quality': 0.9418522684727934, 'absD': 123656315904, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 9768, 'ainvs': [0, 1, 0, -29304, 1920996], 'analytic_rank': 2, 'bad_primes': [2, 3, 11, 37], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 19536, 'degree': 49152, 'elladic_images': ['4.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.2057096820537371630426376770', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 17, 'isogeny_degrees': [1, 2], 'jinv': [2717811254229988, 120758121], 'lmfdb_iso': '19536.r', 'lmfdb_label': '19536.r2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -29304, -1920996], 'min_quad_twist_disc': -4, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0-2.a.1.1', '132.24.0.?', '296.24.0.?', '9768.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 33, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '1.2212849715670262831924813343', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 1], [3, 4, 6512], [11, 12, 1776], [37, 38, 528]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.62808703158711607186161090912', 'prec': 103}, 'szpiro_ratio': 4.298584417685089, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, 0, 1, 0, -2, 0, -4, 0, 1, 0, 1, 0, -2, 0, -2, 0, -6, 0, -8, 0], 'aplist': [0, 1, -2, -4, 1, -2, -6, -8, 0, -2, 0, 1, -6, -8, -12, -6, 0, -2, -4, 12, -6, 8, -4, -10, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 19536, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '19536.r', 'trace_hash': 124700896687296351}
• 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': '0.089687904394738988655026957207', 'prec': 107}, 'conductor': 19536, 'gens': [[66, 528, 1], [102, 60, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.0672116891040326697540416633', 'prec': 100}, {'__RealLiteral__': 0, 'data': '1.3046548642484262427370689673', 'prec': 100}], 'lmfdb_label': '19536.r2', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.98316433737676607649158092506', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.2043429789133879627517036854145986779', 'prec': 130}, 'tamagawa_product': 96, 'torsion_generators': [[98, 0, 1], [99, 0, 1]], 'xcoord_integral_points': [-198, -190, -144, 0, 24, 66, 90, 96, 98, 99, 102, 135, 198, 246, 627, 774, 1430, 10791]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [5, 0], '5': [2, 0], '7': [2, 0], '11': [3, 0], '13': [2, 0], '17': [2, 0], '19': [2, 0], '23': [2, 2, 0], '29': [2, 0], '31': [2, 2, 0], '37': [3, 0], '41': [2, 0], '43': [2, 0], '47': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '19536.r2'}
• ec_torsion_growth •

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

  
  
  • id: 998840
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '19536.r2', 'torsion': [2, 4]}
  • id: 998841
    {'degree': 4, 'field': [1369, 0, 0, 0, 1], 'lmfdb_label': '19536.r2', 'torsion': [2, 4]}
  • id: 998842
    {'degree': 4, 'field': [1681, 0, 214, 0, 1], 'lmfdb_label': '19536.r2', 'torsion': [2, 4]}
  • id: 998845
    {'degree': 8, 'field': [-3, 0, -4744, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '19536.r2', 'torsion': [2, 6]}
  • id: 998844
    {'degree': 8, 'field': [93, 1110, -1680, 1170, -659, 86, -24, -4, 1], 'lmfdb_label': '19536.r2', 'torsion': [2, 8]}
  • id: 998843
    {'degree': 8, 'field': [2098666, -173012, -126510, 2368, 3155, -148, 34, 0, 1], 'lmfdb_label': '19536.r2', 'torsion': [4, 4]}
  • id: 998848
    {'degree': 16, 'field': [-3119972136, 3926974608, -1293006416, 125212208, 57112048, -40025664, 8412312, -788040, -83870, 95984, -16310, 2484, -42, -198, 22, -4, 1], 'lmfdb_label': '19536.r2', 'torsion': [2, 12]}
  • id: 998846
    {'degree': 16, 'field': [87616, -700928, 2803712, -7009280, 11913408, -14004352, 11176960, -5543488, 1326688, 63872, -37760, 14048, -2232, -80, 32, -8, 1], 'lmfdb_label': '19536.r2', 'torsion': [2, 8]}
  • id: 998847
    {'degree': 16, 'field': [3561561198519489, 0, -247870671484392, 0, 10843846513896, 0, -131624454456, 0, 133441906, 0, 2705144, 0, 52392, 0, 296, 0, 1], 'lmfdb_label': '19536.r2', 'torsion': [2, 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: 442171
    {'conductor': 19536, 'conductor_valuation': 4, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -6, 'lmfdb_label': '19536.r2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 442172
    {'conductor': 19536, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '19536.r2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 442173
    {'conductor': 19536, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '19536.r2', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 442174
    {'conductor': 19536, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '19536.r2', 'prime': 37, '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: 1794653
    {'adelic_gens': [[1, 0, 4, 1], [2441, 9766, 0, 9767], [1, 4, 0, 1], [6217, 4, 2666, 9], [3257, 4, 6514, 9], [9765, 4, 9764, 5], [3961, 2, 0, 1], [4885, 2, 0, 1]], 'adelic_image': '9768.48.0.?', 'conductor': 19536, 'lmfdb_label': '19536.r2', 'prime': 0}
  • id: 91275
    {'conductor': 19536, 'elladic_image': '4.12.0.1', 'lmfdb_label': '19536.r2', 'modell_image': '2Cs', 'prime': 2}
• ec_padic •

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

  
  
  • id: 905842
    {'lmfdb_iso': '19536.r', 'p': 5, 'prec': 20, 'unit': 13442810996281, 'val': 2}
  • id: 905843
    {'lmfdb_iso': '19536.r', 'p': 7, 'prec': 20, 'unit': 4859086173264117, 'val': 2}
  • id: 905847
    {'lmfdb_iso': '19536.r', 'p': 13, 'prec': 20, 'unit': 343229781591257136280, 'val': 2}
  • id: 905849
    {'lmfdb_iso': '19536.r', 'p': 17, 'prec': 20, 'unit': 171774085726941574977937, 'val': 2}
  • id: 905850
    {'lmfdb_iso': '19536.r', 'p': 19, 'prec': 20, 'unit': 1699847848367361934101528, 'val': 2}
  • id: 905846
    {'lmfdb_iso': '19536.r', 'p': 29, 'prec': 20, 'unit': 2218692416639452740747186411, 'val': 2}
  • id: 905844
    {'lmfdb_iso': '19536.r', 'p': 41, 'prec': 20, 'unit': 1262057176750080290965762165310, 'val': 2}
  • id: 905845
    {'lmfdb_iso': '19536.r', 'p': 43, 'prec': 20, 'unit': 7277643228039593788132023895237, 'val': 2}
  • id: 905848
    {'lmfdb_iso': '19536.r', 'p': 47, 'prec': 20, 'unit': 10304974540090698695199839074462, 'val': 2}
  • id: 905851
    {'lmfdb_iso': '19536.r', 'p': 53, 'prec': 20, 'unit': 467999628033106156453869564033587, 'val': 2}
  • id: 905856
    {'lmfdb_iso': '19536.r', 'p': 61, 'prec': 20, 'unit': 7520001447537427204608499802754229, 'val': 2}
  • id: 905841
    {'lmfdb_iso': '19536.r', 'p': 67, 'prec': 20, 'unit': 27217252796799403211420782291941213, 'val': 2}
  • id: 905854
    {'lmfdb_iso': '19536.r', 'p': 71, 'prec': 20, 'unit': 9598747064242144492510283742380935, 'val': 2}
  • id: 905852
    {'lmfdb_iso': '19536.r', 'p': 73, 'prec': 20, 'unit': 12428019266204949972118278941790714, 'val': 2}
  • id: 905855
    {'lmfdb_iso': '19536.r', 'p': 79, 'prec': 20, 'unit': 447126577527913800478748959991635001, 'val': 2}
  • id: 905840
    {'lmfdb_iso': '19536.r', 'p': 83, 'prec': 20, 'unit': 19997742568849914447685938230869939, 'val': 2}
  • id: 905853
    {'lmfdb_iso': '19536.r', 'p': 89, 'prec': 20, 'unit': 9518098820486348917195701991695117381, 'val': 2}
  • id: 905839
    {'lmfdb_iso': '19536.r', 'p': 97, 'prec': 20, 'unit': 30162711499354582623779450022440914633, 'val': 2}