Elliptic curve data - 12480.cn4

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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': '12480co', 'Clabel': '12480co1', 'Cnumber': 1, 'abc_quality': 1.1541079700404029, 'absD': 213890625000000, 'adelic_genus': 3, 'adelic_index': 192, 'adelic_level': 1040, 'ainvs': [0, 1, 0, 13044, -403506], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 12480, 'degree': 49152, 'elladic_images': ['8.24.0.69'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4372179322726098224278295356', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 65, 'isogeny_degrees': [1, 2, 4], 'jinv': [3834800837445824, 3342041015625], 'lmfdb_iso': '12480.cn', 'lmfdb_label': '12480.cn4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 52175, -3280223], 'min_quad_twist_disc': 8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0.d.1', '8.24.0-4.d.1.1', '40.48.0-40.bf.1.2', '52.24.0-4.d.1.2', '80.96.0.?', '104.48.0.?', '520.96.1.?', '1040.192.3.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.8551193641791950695033522127', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 1], [3, 4, 832], [5, 6, 2496], [13, 14, 960]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.0906443419926371677192134749', 'prec': 100}, 'szpiro_ratio': 4.245364207660031, '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, 0, 0, -1, 0, -1, 0, 2, 0, -8, 0], 'aplist': [0, 1, -1, 4, 0, -1, 2, -8, 4, -6, -8, -6, -6, 4, 4, -6, -8, 10, -4, 8, -14, 0, -12, -6, -6], 'class_deg': 4, 'class_size': 4, 'conductor': 12480, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '12480.cn', 'trace_hash': 1046727770531346927}
• 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': '0.056447974827166286601453539175', 'prec': 107}, 'conductor': 12480, 'gens': [[225, 3738, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '4.8551193641791950695033522127', 'prec': 100}], 'lmfdb_label': '12480.cn4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.30914968993432701220221989361', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.0038345841205802617039344165633139239', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[29, 0, 1]], 'xcoord_integral_points': [29, 225]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [1, 0], '7': [1, 0], '11': [1, 1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '12480.cn4'}
• ec_torsion_growth •

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

  
  
  • id: 644614
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '12480.cn4', 'torsion': [4]}
  • id: 644613
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '12480.cn4', 'torsion': [2, 2]}
  • id: 644615
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '12480.cn4', 'torsion': [4]}
  • id: 644616
    {'degree': 4, 'field': [1, 0, 0, 0, 1], 'lmfdb_label': '12480.cn4', 'torsion': [2, 4]}
  • id: 644620
    {'degree': 8, 'field': [-588, 0, 872, 0, 84, 0, 0, 0, 1], 'lmfdb_label': '12480.cn4', 'torsion': [6]}
  • id: 644619
    {'degree': 8, 'field': [81, 0, -88, 0, 38, 0, -8, 0, 1], 'lmfdb_label': '12480.cn4', 'torsion': [8]}
  • id: 644617
    {'degree': 8, 'field': [81, 0, 0, 0, 31, 0, 0, 0, 1], 'lmfdb_label': '12480.cn4', 'torsion': [4, 4]}
  • id: 644618
    {'degree': 8, 'field': [28561, 0, -4394, 0, -1183, 0, -26, 0, 1], 'lmfdb_label': '12480.cn4', 'torsion': [8]}
  • id: 644621
    {'degree': 16, 'field': [1, 0, 0, 0, 18, 0, 0, 0, 43, 0, 0, 0, 18, 0, 0, 0, 1], 'lmfdb_label': '12480.cn4', 'torsion': [2, 8]}
  • id: 644623
    {'degree': 16, 'field': [1079957, -2041608, 778654, 957604, -636106, -226888, 195770, 53320, -27197, -15900, 3866, 1272, -56, -48, -16, 0, 1], 'lmfdb_label': '12480.cn4', 'torsion': [2, 6]}
  • id: 644624
    {'degree': 16, 'field': [1126953, 598752, 1210788, -617904, -135756, -114912, 119668, 62496, -55714, 24192, -5012, -1008, 292, 0, -4, 0, 1], 'lmfdb_label': '12480.cn4', 'torsion': [12]}
  • id: 644625
    {'degree': 16, 'field': [19416672, -6003072, -12026880, 1835712, 3440448, -68832, -505984, -40896, 25664, 7776, 2744, -576, -356, 0, 4, 0, 1], 'lmfdb_label': '12480.cn4', 'torsion': [12]}
  • id: 644622
    {'degree': 16, 'field': [113018161, 37888884, -15425620, -1037608, 2795432, -2397124, 1265020, -556252, 238563, -70508, 20220, -5356, 1152, -232, 40, -4, 1], 'lmfdb_label': '12480.cn4', 'torsion': [2, 8]}
• 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: 270407
    {'conductor': 12480, 'conductor_valuation': 6, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '12480.cn4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 270408
    {'conductor': 12480, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '12480.cn4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 270409
    {'conductor': 12480, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '12480.cn4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 270410
    {'conductor': 12480, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '12480.cn4', '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: 1746801
    {'adelic_gens': [[95, 166, 714, 947], [1, 16, 0, 1], [417, 16, 628, 65], [704, 309, 125, 424], [1, 12, 4, 49], [1, 0, 16, 1], [5, 16, 64, 205], [1025, 16, 1024, 17], [1029, 114, 318, 557]], 'adelic_image': '1040.192.3.?', 'conductor': 12480, 'lmfdb_label': '12480.cn4', 'prime': 0}
  • id: 59432
    {'conductor': 12480, 'elladic_image': '8.24.0.69', 'lmfdb_label': '12480.cn4', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 546550
    {'lmfdb_iso': '12480.cn', 'p': 7, 'prec': 20, 'unit': 5164588986512771, 'val': 1}
  • id: 546555
    {'lmfdb_iso': '12480.cn', 'p': 17, 'prec': 20, 'unit': 114594936782845964819537, 'val': 1}
  • id: 546546
    {'lmfdb_iso': '12480.cn', 'p': 19, 'prec': 20, 'unit': 1505080085906228120402909, 'val': 1}
  • id: 546559
    {'lmfdb_iso': '12480.cn', 'p': 23, 'prec': 20, 'unit': 55131423172874854373487530, 'val': 1}
  • id: 546553
    {'lmfdb_iso': '12480.cn', 'p': 29, 'prec': 20, 'unit': 1877899601720159182329608394, 'val': 1}
  • id: 546564
    {'lmfdb_iso': '12480.cn', 'p': 31, 'prec': 20, 'unit': 10471011619930229044451605830, 'val': 1}
  • id: 546549
    {'lmfdb_iso': '12480.cn', 'p': 37, 'prec': 20, 'unit': 553170293591038702630323808619, 'val': 1}
  • id: 546551
    {'lmfdb_iso': '12480.cn', 'p': 41, 'prec': 20, 'unit': 880743256011095091043363118199, 'val': 1}
  • id: 546552
    {'lmfdb_iso': '12480.cn', 'p': 43, 'prec': 20, 'unit': 4964214555454611620622969209486, 'val': 1}
  • id: 546554
    {'lmfdb_iso': '12480.cn', 'p': 47, 'prec': 20, 'unit': 26197503791356362268515842683784, 'val': 1}
  • id: 546557
    {'lmfdb_iso': '12480.cn', 'p': 53, 'prec': 20, 'unit': 447499132351354022706686638576533, 'val': 1}
  • id: 546562
    {'lmfdb_iso': '12480.cn', 'p': 59, 'prec': 20, 'unit': 2379850853008173645612549571464977, 'val': 1}
  • id: 546563
    {'lmfdb_iso': '12480.cn', 'p': 61, 'prec': 20, 'unit': 1759630620907497381732472822713034, 'val': 1}
  • id: 546548
    {'lmfdb_iso': '12480.cn', 'p': 67, 'prec': 20, 'unit': 30018336284465747418226642922876077, 'val': 1}
  • id: 546561
    {'lmfdb_iso': '12480.cn', 'p': 71, 'prec': 20, 'unit': 144877157785122420338852052298383552, 'val': 1}
  • id: 546558
    {'lmfdb_iso': '12480.cn', 'p': 73, 'prec': 20, 'unit': 32073955170456014722204741135562021, 'val': 1}
  • id: 546556
    {'lmfdb_iso': '12480.cn', 'p': 83, 'prec': 20, 'unit': 2273002174622731873088923850942180472, 'val': 1}
  • id: 546560
    {'lmfdb_iso': '12480.cn', 'p': 89, 'prec': 20, 'unit': 5004398912721174628486339888567002165, 'val': 1}
  • id: 546547
    {'lmfdb_iso': '12480.cn', 'p': 97, 'prec': 20, 'unit': 44599690251077262552826688499829266116, 'val': 1}