Elliptic curve data - 3192.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': '3192m', 'Clabel': '3192m1', 'Cnumber': 1, 'abc_quality': 1.0271363895982601, 'absD': 3724700112, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1596, 'ainvs': [0, -1, 0, -106435, -13329764], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 19], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 3192, 'degree': 11520, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3474214656909987995353164300', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [8334147900493981696, 232793757], 'lmfdb_iso': '3192.a', 'lmfdb_label': '3192.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -106435, -13329764], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.c.1', '266.6.0.?', '1596.12.0.?'], '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': '8.0628169707200053054932845563', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 133], [3, 4, 1064], [5, 2, 456], [7, 8, 456], [19, 20, 168]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1163724055043503630629057228', 'prec': 100}, 'szpiro_ratio': 5.74332763417528, '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, 0, -1, 0, -4, 0, -1, 0, 1, 0, 0, 0, -2, 0, 4, 0, 4, 0, 1, 0], 'aplist': [0, -1, -4, -1, 0, -2, 4, 1, 4, 4, 0, -10, 10, 4, -6, 0, 4, -10, -4, -2, -2, 4, -14, -6, -18], 'class_deg': 2, 'class_size': 2, 'conductor': 3192, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '3192.a', 'trace_hash': 3111885833162928}
• 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': '0.067552991395983874263672198067', 'prec': 107}, 'conductor': 3192, 'gens': [[4301, 281199, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '8.0628169707200053054932845563', 'prec': 100}], 'lmfdb_label': '3192.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.26431882756547432288162334201', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.1311543285757211148181181260327613371', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[-188, 0, 1]], 'xcoord_integral_points': [-188, 4301]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [1, 0], '7': [1, 0], '11': [1, 1, 0], '13': [1, 0], '17': [1, 0], '19': [2, 0], '23': [1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '3192.a1'}
• ec_torsion_growth •

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

  
  
  • id: 166648
    {'degree': 2, 'field': [-33, -1, 1], 'lmfdb_label': '3192.a1', 'torsion': [2, 2]}
  • id: 166649
    {'degree': 4, 'field': [7, 5, -4, -2, 1], 'lmfdb_label': '3192.a1', 'torsion': [4]}
  • id: 166650
    {'degree': 8, 'field': [9, 0, -33, 0, 124, 0, 11, 0, 1], 'lmfdb_label': '3192.a1', 'torsion': [2, 4]}
  • id: 166651
    {'degree': 8, 'field': [9, 0, 5786, 0, -949, 0, 22, 0, 1], 'lmfdb_label': '3192.a1', 'torsion': [2, 4]}
  • id: 166652
    {'degree': 8, 'field': [121, -154, 252, -174, 70, -30, -12, -2, 1], 'lmfdb_label': '3192.a1', 'torsion': [6]}
  • id: 166654
    {'degree': 16, 'field': [-39171572, -74090104, -29427908, -7391800, -1032932, 5850856, 1023056, 217568, -165762, -61412, 2788, -8350, 492, -172, 2, 0, 1], 'lmfdb_label': '3192.a1', 'torsion': [2, 6]}
  • id: 166653
    {'degree': 16, 'field': [961, 1674, 16656, -28992, 45592, 68460, 53550, 55410, 24318, 6558, 4008, 960, -143, -96, -18, 0, 1], 'lmfdb_label': '3192.a1', '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: 57731
    {'conductor': 3192, 'conductor_valuation': 3, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '3192.a1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 57732
    {'conductor': 3192, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '3192.a1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 57733
    {'conductor': 3192, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '3192.a1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 57734
    {'conductor': 3192, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '3192.a1', 'prime': 19, 'reduction_type': 1, '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

  
  
  • id: 1684715
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [533, 4, 1066, 9], [1593, 4, 1592, 5], [422, 1, 587, 0], [230, 1, 683, 0], [401, 1198, 1196, 399]], 'adelic_image': '1596.12.0.?', 'conductor': 3192, 'lmfdb_label': '3192.a1', 'prime': 0}
  • id: 15986
    {'conductor': 3192, 'elladic_image': '2.3.0.1', 'lmfdb_label': '3192.a1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 104840
    {'lmfdb_iso': '3192.a', 'p': 5, 'prec': 20, 'unit': 70767577024254, 'val': -1}
  • id: 104830
    {'lmfdb_iso': '3192.a', 'p': 13, 'prec': 20, 'unit': 171278015031395127927, 'val': 1}
  • id: 104832
    {'lmfdb_iso': '3192.a', 'p': 17, 'prec': 20, 'unit': 111427134812254238005555, 'val': 1}
  • id: 104836
    {'lmfdb_iso': '3192.a', 'p': 23, 'prec': 20, 'unit': 62156989710640018309495913, 'val': 1}
  • id: 104829
    {'lmfdb_iso': '3192.a', 'p': 29, 'prec': 20, 'unit': 5574252825455162150085669538, 'val': 1}
  • id: 104825
    {'lmfdb_iso': '3192.a', 'p': 37, 'prec': 20, 'unit': 418564674864091765428897152227, 'val': 1}
  • id: 104827
    {'lmfdb_iso': '3192.a', 'p': 41, 'prec': 20, 'unit': 1297925064752888878044723064426, 'val': 1}
  • id: 104828
    {'lmfdb_iso': '3192.a', 'p': 43, 'prec': 20, 'unit': 5889113229149965910987970304352, 'val': 1}
  • id: 104838
    {'lmfdb_iso': '3192.a', 'p': 47, 'prec': 20, 'unit': 44499062400581158937858003407090, 'val': 1}
  • id: 104834
    {'lmfdb_iso': '3192.a', 'p': 59, 'prec': 20, 'unit': 3965331601399052057447434898066471, 'val': 1}
  • id: 104839
    {'lmfdb_iso': '3192.a', 'p': 61, 'prec': 20, 'unit': 7013343972994205073741556368222978, 'val': 1}
  • id: 104824
    {'lmfdb_iso': '3192.a', 'p': 67, 'prec': 20, 'unit': 48339092123172195090094829191082129, 'val': 1}
  • id: 104826
    {'lmfdb_iso': '3192.a', 'p': 71, 'prec': 20, 'unit': 39947586734648556127650657695696710, 'val': 1}
  • id: 104835
    {'lmfdb_iso': '3192.a', 'p': 73, 'prec': 20, 'unit': 71596448922960474680945841475633816, 'val': 1}
  • id: 104831
    {'lmfdb_iso': '3192.a', 'p': 79, 'prec': 20, 'unit': 446341432555844669006075201276971562, 'val': 1}
  • id: 104833
    {'lmfdb_iso': '3192.a', 'p': 83, 'prec': 20, 'unit': 2148536771009680680353834321913939055, 'val': 1}
  • id: 104837
    {'lmfdb_iso': '3192.a', 'p': 89, 'prec': 20, 'unit': 3511812258340676897638287006089004309, 'val': 1}
  • id: 104823
    {'lmfdb_iso': '3192.a', 'p': 97, 'prec': 20, 'unit': 1669263040451575834597227412979564899, 'val': 1}