Elliptic curve data - 112710.cb1

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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': '112710ci', 'Clabel': '112710ci4', 'Cnumber': 4, 'abc_quality': 0.9869421687813174, 'absD': 262141729396472250, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 26520, 'ainvs': [1, 1, 1, -345650, -74381083], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 13, 17], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 112710, 'degree': 1492992, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0964298845100634339807221776', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 6, 'iso_nlabel': 53, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [189208196468929, 10860320250], 'lmfdb_iso': '112710.cb', 'lmfdb_label': '112710.cb1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -1196, -15210], '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', '40.6.0.b.1', '51.8.0-3.a.1.1', '102.24.0.?', '120.24.0.?', '156.24.0.?', '1560.48.1.?', '2040.48.0.?', '2652.48.0.?', '26520.96.1.?'], '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, 1445], [3, 4, 578], [5, 6, 22542], [13, 14, 8670], [17, 146, 390]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.67982321248195539385595486866', 'prec': 103}, 'szpiro_ratio': 4.287370242674875, '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, -2, 1, 1, 1, 0, -1, 1, -2, -1, 1, 0, 1, 2, 1], 'aplist': [1, -1, 1, -2, 0, 1, 0, 2, 6, 0, 4, -2, 6, -4, 0, -6, 0, 10, 8, 0, -8, -8, -12, 6, -8], 'class_deg': 6, 'class_size': 4, 'conductor': 112710, 'isogeny_matrix': [[1, 3, 6, 2], [3, 1, 2, 6], [6, 2, 1, 3], [2, 6, 3, 1]], 'lmfdb_iso': '112710.cb', 'trace_hash': 1594404953944858996}
• 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': '0.015103031873069630718893310219', 'prec': 107}, 'conductor': 112710, 'gens': [], 'heights': [], 'lmfdb_label': '112710.cb1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.19760303224612265510672457945', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.5568545804302077919210424301232085195', 'prec': 130}, 'tamagawa_product': 72, 'torsion_generators': [[-1101, 1097, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [9, 0], '3': [6, 1], '5': [1, 0], '13': [1, 0], '17': 'a'}, 'iwp0': 5, 'lmfdb_label': '112710.cb1'}
• ec_torsion_growth •

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

  
  
  • id: 5179418
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '112710.cb1', 'torsion': [2, 2]}
  • id: 5179419
    {'degree': 2, 'field': [13, -1, 1], 'lmfdb_label': '112710.cb1', 'torsion': [6]}
  • id: 5179421
    {'degree': 4, 'field': [519, -6, 7, -2, 1], 'lmfdb_label': '112710.cb1', 'torsion': [2, 6]}
  • id: 5179420
    {'degree': 4, 'field': [11560, 0, -34, 0, 1], 'lmfdb_label': '112710.cb1', 'torsion': [4]}
  • id: 5179422
    {'degree': 6, 'field': [236, -372, 72, -1, -9, -3, 1], 'lmfdb_label': '112710.cb1', 'torsion': [6]}
  • id: 5179425
    {'degree': 8, 'field': [119565, -8406, 9324, -1866, 1009, -94, 36, -4, 1], 'lmfdb_label': '112710.cb1', 'torsion': [12]}
  • id: 5179423
    {'degree': 8, 'field': [1288225, 0, -110370, 0, 7106, 0, 78, 0, 1], 'lmfdb_label': '112710.cb1', 'torsion': [2, 4]}
  • id: 5179424
    {'degree': 8, 'field': [3775641, 2958800, -672696, -37840, -1454, -640, -56, 0, 1], 'lmfdb_label': '112710.cb1', 'torsion': [2, 4]}
  • id: 5179426
    {'degree': 12, 'field': [7804, -1128, 6516, -9520, 1860, 2832, 65, -726, 15, 100, -9, -6, 1], 'lmfdb_label': '112710.cb1', 'torsion': [3, 6]}
  • id: 5179427
    {'degree': 12, 'field': [4398346, 1369644, -1656054, 578600, -303510, 16404, -4459, -726, 15, 100, -9, -6, 1], 'lmfdb_label': '112710.cb1', 'torsion': [2, 6]}
  • id: 5179429
    {'degree': 16, 'field': [861392025, 2311416900, 3597753780, 812355300, 670889854, -58899584, 33631772, -20304588, 2112583, -1207672, 220276, -34924, 8962, -804, 152, -8, 1], 'lmfdb_label': '112710.cb1', 'torsion': [2, 12]}
  • id: 5179430
    {'degree': 16, 'field': [78371678151, -11054298816, 12911412468, -3890829192, 2397531676, -572607416, 242050160, -46048056, 14325049, -2016472, 547060, -81808, 16486, -1344, 212, -8, 1], 'lmfdb_label': '112710.cb1', 'torsion': [2, 12]}
  • id: 5179428
    {'degree': 16, 'field': [3027619957345, -79468771860, 163374513351, 2837383938, 803784394, -672954624, -160045407, -23427834, 7084266, 609324, 187785, -23106, -3350, 168, 15, -6, 1], 'lmfdb_label': '112710.cb1', 'torsion': [8]}
  • id: 5179431
    {'degree': 18, 'field': [409398811875, 188296342875, 113365746675, 36476747580, 25258901850, -6450618270, 5873063308, -1429425096, 564975495, -79680011, 20271825, -1324296, 238896, 4878, 438, -80, 21, -9, 1], 'lmfdb_label': '112710.cb1', '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: 2771005
    {'conductor': 112710, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '112710.cb1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 2771006
    {'conductor': 112710, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '112710.cb1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2771007
    {'conductor': 112710, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '112710.cb1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 2771008
    {'conductor': 112710, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '112710.cb1', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 2771009
    {'conductor': 112710, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '112710.cb1', 'prime': 17, '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: 2401565
    {'adelic_gens': [[15675, 22168, 1598, 17477], [14039, 0, 0, 26519], [1, 0, 12, 1], [1, 6, 6, 37], [24481, 4692, 3366, 1633], [26509, 12, 26508, 13], [1, 12, 0, 1], [23410, 7803, 19941, 3112], [11, 2, 26470, 26511], [23410, 7803, 22593, 3112], [17681, 4692, 20026, 1633]], 'adelic_image': '26520.96.1.?', 'conductor': 112710, 'lmfdb_label': '112710.cb1', 'prime': 0}
  • id: 446135
    {'conductor': 112710, 'elladic_image': '2.3.0.1', 'lmfdb_label': '112710.cb1', 'modell_image': '2B', 'prime': 2}
  • id: 446136
    {'conductor': 112710, 'elladic_image': '3.4.0.1', 'lmfdb_label': '112710.cb1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 112710.cb does not appear in ec_padic