Elliptic curve data - 82110.z2

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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': '82110y', 'Clabel': '82110y2', 'Cnumber': 2, 'abc_quality': 1.0096074627779512, 'absD': 84465268068629449376512200, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 2856, 'ainvs': [1, 0, 1, -548298544, 4921801751126], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 17, 23], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 82110, 'degree': 57729024, 'elladic_images': ['8.6.0.6', '3.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.8252302755729215313505878241', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 25, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [18229509733721637057438776494969, 84465268068629449376512200], 'lmfdb_iso': '82110.z', 'lmfdb_label': '82110.z2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -548298544, 4921801751126], 'min_quad_twist_disc': 1, 'modell_images': ['2B', '3B.1.1'], 'modm_images': ['2.3.0.a.1', '3.8.0-3.a.1.2', '6.24.0-6.a.1.4', '8.6.0.b.1', '24.48.0-24.y.1.15', '476.6.0.?', '952.12.0.?', '1428.48.0.?', '2856.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 6, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 1], [3, 4, 115], [5, 6, 16422], [7, 8, 11730], [17, 18, 4830], [23, 24, 3570]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '3.8252302755729215313505878241', 'prec': 100}, 'szpiro_ratio': 6.361061391318801, 'torsion': 6, 'torsion_primes': [2, 3], 'torsion_structure': [6]}
• 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, 1, -1, 1, 1, 6, 1, -4, -1, -1, 1, 1, -1, 2, -1], 'aplist': [-1, 1, -1, 1, 6, -4, 1, 2, -1, 0, 8, -4, 6, 8, 12, 6, -6, -10, -4, 0, 2, 8, 18, -6, 14], 'class_deg': 6, 'class_size': 4, 'conductor': 82110, 'isogeny_matrix': [[1, 3, 6, 2], [3, 1, 2, 6], [6, 2, 1, 3], [2, 6, 3, 1]], 'lmfdb_iso': '82110.z', 'trace_hash': 810450700091883430}
• 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': '0.00047582493683165805401946806116', 'prec': 113}, 'conductor': 82110, 'gens': [], 'heights': [], 'lmfdb_label': '82110.z2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.060987497890757498887384427323', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.9273998987563599465944525115056444784', 'prec': 130}, 'tamagawa_product': 1728, 'torsion_generators': [[-2924, 2550977, 1]], 'xcoord_integral_points': [-2924, 16354]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [8, 0], '3': [9, 0], '5': [0, 0], '7': [1, 0], '17': [1, 0], '23': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '82110.z2'}
• ec_torsion_growth •

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

  
  
  • id: 3859743
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '82110.z2', 'torsion': [2, 6]}
  • id: 3859744
    {'degree': 4, 'field': [50, 0, -9, 0, 1], 'lmfdb_label': '82110.z2', 'torsion': [12]}
  • id: 3859745
    {'degree': 6, 'field': [12288, 0, -383, 0, 1, 0, 1], 'lmfdb_label': '82110.z2', 'torsion': [3, 6]}
  • id: 3859746
    {'degree': 8, 'field': [1022, -364, 662, -480, 183, -4, 2, 0, 1], 'lmfdb_label': '82110.z2', 'torsion': [2, 12]}
  • id: 3859747
    {'degree': 8, 'field': [1351, -2548, 926, 776, -517, 32, 14, -4, 1], 'lmfdb_label': '82110.z2', 'torsion': [2, 12]}
  • id: 3859748
    {'degree': 9, 'field': [-49185157371, -16255086750, -1815188067, -37170085, 6557040, 274305, -14931, -1011, 0, 1], 'lmfdb_label': '82110.z2', 'torsion': [18]}
  • id: 3859749
    {'degree': 12, 'field': [161151004, -28191072, -7347970, 268560, -171837, -168, 26998, 4536, -735, -12, 8, 0, 1], 'lmfdb_label': '82110.z2', 'torsion': [6, 6]}
  • id: 3859750
    {'degree': 16, 'field': [195105024000000, 0, 29292364411200, 0, 1299997720976, 0, 10853539232, 0, 365645384, 0, -2985204, 0, 45289, 0, -278, 0, 1], 'lmfdb_label': '82110.z2', 'torsion': [24]}
  • id: 3859751
    {'degree': 18, 'field': [2253494141182759244881, 1505457016363618724448, 422243273381259745830, 60754567584715792914, 3851374800641391411, -91560195761995800, -28788556553147441, -875479119927552, 108803851669362, 8249930308410, -77893188333, -25284565404, -419376497, 43483734, 1595139, -29862, -2040, 0, 1], 'lmfdb_label': '82110.z2', 'torsion': [2, 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: 2000177
    {'conductor': 82110, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '82110.z2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 2000178
    {'conductor': 82110, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '82110.z2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
  • id: 2000179
    {'conductor': 82110, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '82110.z2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2000180
    {'conductor': 82110, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '82110.z2', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 2000181
    {'conductor': 82110, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '82110.z2', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 2000182
    {'conductor': 82110, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '82110.z2', 'prime': 23, '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: 2205446
    {'adelic_gens': [[10, 3, 1401, 2848], [2845, 12, 2844, 13], [2689, 12, 1854, 73], [843, 1312, 806, 1301], [1, 0, 12, 1], [1913, 2, 534, 13], [1, 6, 6, 37], [11, 2, 2806, 2847], [1, 12, 0, 1], [409, 12, 2454, 73]], 'adelic_image': '2856.96.1.?', 'conductor': 82110, 'lmfdb_label': '82110.z2', 'prime': 0}
  • id: 336475
    {'conductor': 82110, 'elladic_image': '8.6.0.6', 'lmfdb_label': '82110.z2', 'modell_image': '2B', 'prime': 2}
  • id: 336476
    {'conductor': 82110, 'elladic_image': '3.8.0.1', 'lmfdb_label': '82110.z2', 'modell_image': '3B.1.1', 'prime': 3}
• lmfdb_iso 82110.z does not appear in ec_padic