Elliptic curve data - 67270.x1

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '67270bc', 'Clabel': '67270bc2', 'Cnumber': 2, 'abc_quality': 0.9452930887207672, 'absD': 4170740, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 4340, 'ainvs': [1, 0, 0, -23146, 1353456], 'analytic_rank': 1, 'bad_primes': [2, 5, 7, 31], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 67270, 'degree': 98304, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.92233055564718798537691453672', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 23, 'isogeny_degrees': [1, 2], 'jinv': [46032827294719, 140], 'lmfdb_iso': '67270.x', 'lmfdb_label': '67270.x1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -23146, 1353456], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '124.6.0.?', '140.6.0.?', '2170.6.0.?', '4340.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.88901674417679138051378217932', 'prec': 103}, 'semistable': False, 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.063833754525901423894623455584', 'prec': 107}, 'szpiro_ratio': 3.756798589772292, '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, -2, 1, -1, -2, -1, 1, 1, -1, 2, -2, 4, -1, 2, 1, -8, 1, 0, -1], 'aplist': [1, -2, -1, -1, 2, 4, -8, 0, 4, 0, 0, -6, 2, 0, 8, 6, 0, -2, -8, -8, 4, -10, 2, -2, 10], 'class_deg': 2, 'class_size': 2, 'conductor': 67270, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '67270.x', 'trace_hash': 75099708629146262}
• 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': '0.15807888296137786920591727252', 'prec': 103}, 'conductor': 67270, 'gens': [[80, 84, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.88901674417679138051378217932', 'prec': 103}], 'lmfdb_label': '67270.x1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.6336287950597635551265527578', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.8092934103099430844566183383428830257', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[351, -351, 2]], 'xcoord_integral_points': [80, 88]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [17, 0], '3': [1, 0], '5': [1, 0], '7': [3, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 1, 0], '23': [1, 0], '29': [1, 1, 0], '31': 'a', '37': [1, 0], '41': [1, 0], '43': [1, 1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '67270.x1'}
• ec_torsion_growth •

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

  
  
  • id: 3204814
    {'degree': 2, 'field': [-271, -1, 1], 'lmfdb_label': '67270.x1', 'torsion': [2, 2]}
  • id: 3204815
    {'degree': 4, 'field': [1085, 0, 62, 0, 1], 'lmfdb_label': '67270.x1', 'torsion': [4]}
  • id: 3204818
    {'degree': 8, 'field': [20736, 0, -6912, -4464, -1368, -372, -48, 0, 1], 'lmfdb_label': '67270.x1', 'torsion': [6]}
  • id: 3204817
    {'degree': 8, 'field': [48209, -14882, 16692, -3714, 2093, -286, 100, -4, 1], 'lmfdb_label': '67270.x1', 'torsion': [2, 4]}
  • id: 3204816
    {'degree': 8, 'field': [4247721, 0, -442998, 0, 14759, 0, -202, 0, 1], 'lmfdb_label': '67270.x1', 'torsion': [2, 4]}
  • id: 3204819
    {'degree': 16, 'field': [7432508944, 0, -2206947296, 0, 1094454648, 0, -81396088, 0, 4496865, 0, -180908, 0, 5662, 0, -116, 0, 1], 'lmfdb_label': '67270.x1', 'torsion': [8]}
  • id: 3204820
    {'degree': 16, 'field': [195689447424, 0, -63692780544, 0, -555621120, 0, -322693632, 0, 613440, 0, 98208, 0, -2448, 0, 0, 0, 1], 'lmfdb_label': '67270.x1', 'torsion': [2, 6]}
• 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: 1627206
    {'conductor': 67270, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '67270.x1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1627207
    {'conductor': 67270, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '67270.x1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1627208
    {'conductor': 67270, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '67270.x1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1627209
    {'conductor': 67270, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '67270.x1', 'prime': 31, 'reduction_type': 0, '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: 2109313
    {'adelic_gens': [[2244, 1, 3779, 0], [1, 2, 2, 5], [622, 1, 1859, 0], [1, 4, 0, 1], [3474, 1, 2603, 0], [1, 0, 4, 1], [4337, 4, 4336, 5], [3, 4, 8, 11], [3257, 1086, 1084, 3255]], 'adelic_image': '4340.12.0.?', 'conductor': 67270, 'lmfdb_label': '67270.x1', 'prime': 0}
  • id: 281303
    {'conductor': 67270, 'elladic_image': '2.3.0.1', 'lmfdb_label': '67270.x1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 3438332
    {'lmfdb_iso': '67270.x', 'p': 11, 'prec': 20, 'unit': 40858489550344848809, 'val': 1}
  • id: 3438333
    {'lmfdb_iso': '67270.x', 'p': 13, 'prec': 20, 'unit': 552102422741316503066, 'val': 1}
  • id: 3438335
    {'lmfdb_iso': '67270.x', 'p': 17, 'prec': 20, 'unit': 4045861654491669033120, 'val': 1}
  • id: 3438339
    {'lmfdb_iso': '67270.x', 'p': 23, 'prec': 20, 'unit': 15823455589826755751067310, 'val': 1}
  • id: 3438329
    {'lmfdb_iso': '67270.x', 'p': 37, 'prec': 20, 'unit': 335162289343555309113608380472, 'val': 1}
  • id: 3438331
    {'lmfdb_iso': '67270.x', 'p': 41, 'prec': 20, 'unit': 2825299991108671504704443995249, 'val': 1}
  • id: 3438334
    {'lmfdb_iso': '67270.x', 'p': 47, 'prec': 20, 'unit': 34635621264544473402475744539459, 'val': 1}
  • id: 3438337
    {'lmfdb_iso': '67270.x', 'p': 53, 'prec': 20, 'unit': 381451098425910069311828858162325, 'val': 1}
  • id: 3438342
    {'lmfdb_iso': '67270.x', 'p': 61, 'prec': 20, 'unit': 4037682191473432617738318831362564, 'val': 1}
  • id: 3438328
    {'lmfdb_iso': '67270.x', 'p': 67, 'prec': 20, 'unit': 18713077533789003659787015262047169, 'val': 1}
  • id: 3438330
    {'lmfdb_iso': '67270.x', 'p': 71, 'prec': 20, 'unit': 39961156605862231894351744509933692, 'val': 1}
  • id: 3438338
    {'lmfdb_iso': '67270.x', 'p': 73, 'prec': 20, 'unit': 91584449776002984157192040752886706, 'val': 1}
  • id: 3438341
    {'lmfdb_iso': '67270.x', 'p': 79, 'prec': 20, 'unit': 138927381889106373331547308980477129, 'val': 1}
  • id: 3438336
    {'lmfdb_iso': '67270.x', 'p': 83, 'prec': 20, 'unit': 2616825340259925444639821924192976970, 'val': 1}
  • id: 3438340
    {'lmfdb_iso': '67270.x', 'p': 89, 'prec': 20, 'unit': 9151753560691842343680157923714278176, 'val': 1}
  • id: 3438327
    {'lmfdb_iso': '67270.x', 'p': 97, 'prec': 20, 'unit': 21219554389002607684947071815746668038, 'val': 1}