Elliptic curve data - 19110.b3

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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': '19110c', 'Clabel': '19110c2', 'Cnumber': 2, 'abc_quality': 1.11183271776232, 'absD': 30811831982604036000, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 10920, 'ainvs': [1, 1, 0, -784123, -10387523], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 13], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 19110, 'degree': 518400, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4290349837745431115682726711', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [453198971846635561, 261896250564000], 'lmfdb_iso': '19110.b', 'lmfdb_label': '19110.b3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -16003, 27998], 'min_quad_twist_disc': -7, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '21.8.0-3.a.1.1', '40.6.0.b.1', '42.24.0-6.a.1.3', '120.24.0.?', '156.24.0.?', '840.48.0.?', '1092.48.0.?', '1560.48.1.?', '10920.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 245], [3, 4, 1274], [5, 6, 1911], [7, 26, 390], [13, 14, 1470]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.4560799092468864590155962994', 'prec': 100}, 'szpiro_ratio': 5.308454405668486, '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, 0, -1, -1, 0, 1, 1, 0, -1, -2, -1], 'aplist': [-1, -1, -1, 0, 0, -1, 0, -2, -6, 0, -8, 2, -6, -4, 0, -6, 0, -14, -4, 0, 4, -16, 12, 6, 4], 'class_deg': 6, 'class_size': 4, 'conductor': 19110, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '19110.b', 'trace_hash': 848186474981030379}
• 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': '0.0077654570212224111941039352013', 'prec': 110}, 'conductor': 19110, 'gens': [], 'heights': [], 'lmfdb_label': '19110.b3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.17537029115868445539789620831', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.35074058231736891079579241662267246926', 'prec': 133}, 'tamagawa_product': 8, 'torsion_generators': [[-53, 53, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [5, 0], '3': [0, 0], '5': [0, 0], '7': 'a', '13': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '19110.b3'}
• ec_torsion_growth •

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

  
  
  • id: 975981
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '19110.b3', 'torsion': [2, 2]}
  • id: 975982
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '19110.b3', 'torsion': [6]}
  • id: 975984
    {'degree': 4, 'field': [134, 16, -15, -2, 1], 'lmfdb_label': '19110.b3', 'torsion': [2, 6]}
  • id: 975983
    {'degree': 4, 'field': [1960, 0, 77, 0, 1], 'lmfdb_label': '19110.b3', 'torsion': [4]}
  • id: 975985
    {'degree': 6, 'field': [-27, -9, -44, -51, 2, -3, 1], 'lmfdb_label': '19110.b3', 'torsion': [6]}
  • id: 975988
    {'degree': 8, 'field': [3592, 1120, -950, -326, 129, 38, -8, -4, 1], 'lmfdb_label': '19110.b3', 'torsion': [12]}
  • id: 975986
    {'degree': 8, 'field': [129600, 0, -6400, 0, -760, 0, -80, 0, 1], 'lmfdb_label': '19110.b3', 'torsion': [2, 4]}
  • id: 975987
    {'degree': 8, 'field': [8008900, 0, 399060, 0, 8909, 0, 114, 0, 1], 'lmfdb_label': '19110.b3', 'torsion': [2, 4]}
  • id: 975990
    {'degree': 12, 'field': [-6170321, 5241786, 621157, -1322934, 79476, 125754, -17575, -5478, 1152, 186, -47, -6, 1], 'lmfdb_label': '19110.b3', 'torsion': [2, 6]}
  • id: 975989
    {'degree': 12, 'field': [25, 435, 2513, -174, 807, -39, 328, -195, -9, 12, -1, -3, 1], 'lmfdb_label': '19110.b3', 'torsion': [3, 6]}
  • id: 975992
    {'degree': 16, 'field': [5948721, 0, 6015916, 0, 1169970, 0, -38536, 0, 70219, 0, -536, 0, -190, 0, 36, 0, 1], 'lmfdb_label': '19110.b3', 'torsion': [2, 12]}
  • id: 975993
    {'degree': 16, 'field': [16815556, 50422736, 77772832, 72157160, 46555088, 21634760, 7314360, 1675964, 268301, 4396, 6744, -164, 1394, -188, 64, -8, 1], 'lmfdb_label': '19110.b3', 'torsion': [2, 12]}
  • id: 975991
    {'degree': 16, 'field': [2145671992, -9831141584, 11454256380, -603251068, 359989761, 67293312, -37102436, -9066820, 7630884, -1259000, 360154, -37152, 2556, -524, 60, -4, 1], 'lmfdb_label': '19110.b3', 'torsion': [8]}
  • id: 975994
    {'degree': 18, 'field': [37348684, 15606360, -6630900, 7579026, 11837676, 2939352, -983039, -46389, 274350, 51738, -5661, 2223, 1768, -117, 141, 18, 24, -3, 1], 'lmfdb_label': '19110.b3', 'torsion': [18]}
• 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: 430875
    {'conductor': 19110, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '19110.b3', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 430876
    {'conductor': 19110, 'conductor_valuation': 1, 'discriminant_valuation': 18, 'j_denominator_valuation': 18, 'kodaira_symbol': 22, 'lmfdb_label': '19110.b3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 430877
    {'conductor': 19110, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '19110.b3', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 430878
    {'conductor': 19110, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '19110.b3', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 430879
    {'conductor': 19110, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '19110.b3', 'prime': 13, '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: 1791594
    {'adelic_gens': [[1, 6, 6, 37], [1, 12, 0, 1], [3130, 4683, 6993, 7792], [3119, 0, 0, 10919], [3130, 4683, 5901, 7792], [6315, 9688, 4718, 1877], [4201, 7812, 1806, 3193], [10909, 12, 10908, 13], [1, 0, 12, 1], [8849, 3122, 8064, 1], [11, 2, 10870, 10911]], 'adelic_image': '10920.96.1.?', 'conductor': 19110, 'lmfdb_label': '19110.b3', 'prime': 0}
  • id: 89130
    {'conductor': 19110, 'elladic_image': '2.3.0.1', 'lmfdb_label': '19110.b3', 'modell_image': '2B', 'prime': 2}
  • id: 89131
    {'conductor': 19110, 'elladic_image': '3.4.0.1', 'lmfdb_label': '19110.b3', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 19110.b does not appear in ec_padic