Elliptic curve data - 190740.p2

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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': '190740z', 'Clabel': '190740z2', 'Cnumber': 2, 'abc_quality': 0.9214349789031259, 'absD': 100937520541440, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 11220, 'ainvs': [0, -1, 0, -207020, 36320760], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 11, 17], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 190740, 'degree': 1327104, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7199083245374406023516065278', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 15, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [158792223184, 16335], 'lmfdb_iso': '190740.p', 'lmfdb_label': '190740.p2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -716, 7140], 'min_quad_twist_disc': 17, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '44.6.0.c.1', '51.8.0-3.a.1.2', '60.24.0.r.1', '102.24.0.?', '132.24.0.?', '660.48.1.?', '1020.48.0.?', '2244.48.0.?', '11220.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 4335], [3, 4, 63580], [5, 6, 38148], [11, 12, 17340], [17, 146, 660]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.15879646786396431071798219544', 'prec': 107}, 'szpiro_ratio': 3.975380016305414, '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, 1, 0, 4, 0, 1, 0, 1, 0, -4, 0, -1, 0, 0, 0, 2, 0], 'aplist': [0, -1, 1, 4, 1, -4, 0, 2, 0, 0, 4, 10, 0, -4, 12, 6, 12, 10, -4, 0, -8, 10, -6, -6, 10], 'class_deg': 6, 'class_size': 4, 'conductor': 190740, 'isogeny_matrix': [[1, 3, 6, 2], [3, 1, 2, 6], [6, 2, 1, 3], [2, 6, 3, 1]], 'lmfdb_iso': '190740.p', 'trace_hash': 2153474579810805581}
• 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': '0.032070564956580487079506747837', 'prec': 107}, 'conductor': 190740, 'gens': [], 'heights': [], 'lmfdb_label': '190740.p2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.57314910338028039169287717292', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.4388946202816823501572630375010609423', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [[261, 0, 1]], 'xcoord_integral_points': [261]}
• lmfdb_label 190740.p2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8401007
    {'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '190740.p2', 'torsion': [2, 2]}
  • id: 8401008
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '190740.p2', 'torsion': [6]}
  • id: 8401010
    {'degree': 4, 'field': [106, 38, -37, -2, 1], 'lmfdb_label': '190740.p2', 'torsion': [2, 6]}
  • id: 8401009
    {'degree': 4, 'field': [4335, 0, 119, 0, 1], 'lmfdb_label': '190740.p2', 'torsion': [4]}
  • id: 8401011
    {'degree': 6, 'field': [12105, -405, 1920, -213, 112, -1, 1], 'lmfdb_label': '190740.p2', 'torsion': [6]}
  • id: 8401013
    {'degree': 8, 'field': [-15315359, -4878308, -748138, -182120, -29564, -2440, -202, -4, 1], 'lmfdb_label': '190740.p2', 'torsion': [2, 4]}
  • id: 8401014
    {'degree': 8, 'field': [3953, -62, 188, -250, 121, 2, 4, -4, 1], 'lmfdb_label': '190740.p2', 'torsion': [12]}
  • id: 8401012
    {'degree': 8, 'field': [26373765, -6918780, 40084, 56650, 13391, -1346, -94, -2, 1], 'lmfdb_label': '190740.p2', 'torsion': [2, 4]}
  • id: 8401016
    {'degree': 12, 'field': [5689989, -3735828, 4510503, -1597830, 922150, -153648, 61031, -8826, 2730, -360, 83, -6, 1], 'lmfdb_label': '190740.p2', 'torsion': [2, 6]}
  • id: 8401015
    {'degree': 12, 'field': [110481121, 47583297, 9395927, 1104588, -680655, -64359, 38404, -10029, 345, -42, 17, -3, 1], 'lmfdb_label': '190740.p2', 'torsion': [3, 6]}
  • id: 8401019
    {'degree': 16, 'field': [-9453464, 29086352, 4000856, -47824032, -18856984, 42856336, -865136, -10149096, 904777, 996144, -109196, -46384, 5486, 1008, -124, -8, 1], 'lmfdb_label': '190740.p2', 'torsion': [2, 12]}
  • id: 8401018
    {'degree': 16, 'field': [216119401, 0, 24986444, 0, 14766602, 0, 50880, 0, 208931, 0, -240, 0, 962, 0, 44, 0, 1], 'lmfdb_label': '190740.p2', 'torsion': [2, 12]}
  • id: 8401017
    {'degree': 16, 'field': [515709036355984, 0, 16228365042080, 0, 35382022656, 0, -1812947456, 0, 36541132, 0, 826432, 0, -168, 0, -76, 0, 1], 'lmfdb_label': '190740.p2', 'torsion': [8]}
  • id: 8401020
    {'degree': 18, 'field': [-1719721352, -695664096, 824386080, 122697196, 3009852, 42902520, -16632402, 7560552, -4108308, 254217, -39165, 28608, -14718, 462, -198, 32, -6, -3, 1], 'lmfdb_label': '190740.p2', '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: 4722947
    {'conductor': 190740, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '190740.p2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 4722948
    {'conductor': 190740, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '190740.p2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 4722949
    {'conductor': 190740, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '190740.p2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 4722950
    {'conductor': 190740, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '190740.p2', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4722951
    {'conductor': 190740, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '190740.p2', 'prime': 17, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 2888962
    {'adelic_gens': [[1990, 663, 9741, 9232], [7919, 0, 0, 11219], [1106, 9911, 5049, 6580], [1, 0, 12, 1], [7141, 2652, 10506, 4693], [11, 2, 11170, 11211], [11209, 12, 11208, 13], [1, 6, 6, 37], [1, 12, 0, 1], [6546, 1717, 6545, 10286]], 'adelic_image': '11220.96.1.?', 'conductor': 190740, 'lmfdb_label': '190740.p2', 'prime': 0}
  • id: 711356
    {'conductor': 190740, 'elladic_image': '2.3.0.1', 'lmfdb_label': '190740.p2', 'modell_image': '2B', 'prime': 2}
  • id: 711357
    {'conductor': 190740, 'elladic_image': '3.4.0.1', 'lmfdb_label': '190740.p2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 190740.p does not appear in ec_padic