Elliptic curve data - 12870.c7

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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': '12870p', 'Clabel': '12870p1', 'Cnumber': 1, 'abc_quality': 0.9585908886289013, 'absD': 5902788722688000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 17160, 'ainvs': [1, -1, 0, -102780, 12157776], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 11, 13], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 12870, 'degree': 110592, 'elladic_images': ['4.6.0.1', '3.8.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7855114749657531054328353801', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 2, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [164711681450297281, 8097103872000], 'lmfdb_iso': '12870.c', 'lmfdb_label': '12870.c7', 'lmfdb_number': 7, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -11420, -450288], 'min_quad_twist_disc': -3, 'modell_images': ['2B', '3B.1.2'], 'modm_images': ['2.3.0.a.1', '3.8.0-3.a.1.1', '4.6.0.c.1', '6.24.0-6.a.1.2', '12.48.0-12.g.1.10', '24.96.0-24.bt.1.20', '52.12.0-4.c.1.2', '156.96.0.?', '312.192.1.?', '440.12.0.?', '660.96.0.?', '1320.192.1.?', '4290.48.0.?', '5720.24.0.?', '8580.192.1.?', '17160.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.2362053306316982597352127616', 'prec': 100}, 'szpiro_ratio': 4.8860124462465455, '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, 0, 1, -1, 0, -4, -1, 0, 1, 1, 0, 1, 4, 0, 1, 6, 0, -4, -1], 'aplist': [-1, 0, -1, -4, 1, 1, 6, -4, 0, 6, -4, 2, 6, -4, 0, 6, -12, -10, -4, 0, 2, 8, -12, 6, -10], 'class_deg': 12, 'class_size': 8, 'conductor': 12870, 'isogeny_matrix': [[1, 2, 4, 4, 3, 6, 12, 12], [2, 1, 2, 2, 6, 3, 6, 6], [4, 2, 1, 4, 12, 6, 3, 12], [4, 2, 4, 1, 12, 6, 12, 3], [3, 6, 12, 12, 1, 2, 4, 4], [6, 3, 6, 6, 2, 1, 2, 2], [12, 6, 3, 12, 4, 2, 1, 4], [12, 6, 12, 3, 4, 2, 4, 1]], 'lmfdb_iso': '12870.c', 'trace_hash': 463400990941157455}
• 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': '0.028127066378201012558769745521', 'prec': 107}, 'conductor': 12870, 'gens': [], 'heights': [], 'lmfdb_label': '12870.c7', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.42066793980675354163480667642', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.84133587961350708326961335283824307224', 'prec': 133}, 'tamagawa_product': 8, 'torsion_generators': [[216, -108, 1]], 'xcoord_integral_points': [216]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [7, 0], '3': 'a', '5': [0, 0], '11': [1, 0], '13': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '12870.c7'}
• ec_torsion_growth •

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

  
  
  • id: 663133
    {'degree': 2, 'field': [-536, -1, 1], 'lmfdb_label': '12870.c7', 'torsion': [2, 2]}
  • id: 663134
    {'degree': 2, 'field': [-41, -1, 1], 'lmfdb_label': '12870.c7', 'torsion': [4]}
  • id: 663135
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '12870.c7', 'torsion': [4]}
  • id: 663136
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '12870.c7', 'torsion': [6]}
  • id: 663137
    {'degree': 3, 'field': [-143, 0, 0, 1], 'lmfdb_label': '12870.c7', 'torsion': [6]}
  • id: 663141
    {'degree': 4, 'field': [9, 3, 4, -1, 1], 'lmfdb_label': '12870.c7', 'torsion': [12]}
  • id: 663140
    {'degree': 4, 'field': [196, -14, -13, -1, 1], 'lmfdb_label': '12870.c7', 'torsion': [12]}
  • id: 663138
    {'degree': 4, 'field': [1444, 0, -89, 0, 1], 'lmfdb_label': '12870.c7', 'torsion': [2, 4]}
  • id: 663139
    {'degree': 4, 'field': [32041, -179, -178, -1, 1], 'lmfdb_label': '12870.c7', 'torsion': [2, 6]}
  • id: 663144
    {'degree': 6, 'field': [-9264, -13920, -5744, -1172, -61, -1, 1], 'lmfdb_label': '12870.c7', 'torsion': [12]}
  • id: 663145
    {'degree': 6, 'field': [-4096, -768, 720, -48, -45, -3, 1], 'lmfdb_label': '12870.c7', 'torsion': [12]}
  • id: 663142
    {'degree': 6, 'field': [768, 0, -95, 0, 1, 0, 1], 'lmfdb_label': '12870.c7', 'torsion': [3, 6]}
  • id: 663143
    {'degree': 6, 'field': [4096, -512, -736, 799, -46, -2, 1], 'lmfdb_label': '12870.c7', 'torsion': [2, 6]}
  • id: 663147
    {'degree': 8, 'field': [12996, 0, -7272, 0, 1069, 0, -58, 0, 1], 'lmfdb_label': '12870.c7', 'torsion': [8]}
  • id: 663149
    {'degree': 8, 'field': [83521, 0, -6069, 0, 152, 0, -21, 0, 1], 'lmfdb_label': '12870.c7', 'torsion': [2, 12]}
  • id: 663148
    {'degree': 8, 'field': [299209, 0, -26581, 0, 1800, 0, -61, 0, 1], 'lmfdb_label': '12870.c7', 'torsion': [24]}
  • id: 663146
    {'degree': 8, 'field': [331179616, -72754888, -2464315, 1593632, 98734, -5162, -490, -2, 1], 'lmfdb_label': '12870.c7', 'torsion': [2, 4]}
  • id: 663153
    {'degree': 12, 'field': [149109, 647898, -1634006, -962060, 96778, 75042, -29590, -8074, 3014, 924, 22, -2, 1], 'lmfdb_label': '12870.c7', 'torsion': [2, 12]}
  • id: 663152
    {'degree': 12, 'field': [898704, -890172, 283479, 10329, -33782, 2019, -1081, 1764, 57, -33, 14, -3, 1], 'lmfdb_label': '12870.c7', 'torsion': [3, 12]}
  • id: 663151
    {'degree': 12, 'field': [6012304, 0, 6291368, 0, 44433, 0, 48475, 0, 2952, 0, 83, 0, 1], 'lmfdb_label': '12870.c7', 'torsion': [3, 12]}
  • id: 663150
    {'degree': 12, 'field': [319551376, -107256, -268104, 714950, -268035, -107376, 35891, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '12870.c7', 'torsion': [6, 6]}
  • id: 663155
    {'degree': 16, 'field': [169937296, 0, -176329272, 0, 69536665, 0, -14172432, 0, 1666584, 0, -117138, 0, 4840, 0, -108, 0, 1], 'lmfdb_label': '12870.c7', 'torsion': [2, 8]}
  • id: 663158
    {'degree': 16, 'field': [395254161, 0, 147000114, 0, 34571545, 0, 5328186, 0, 602964, 0, 39806, 0, 1905, 0, 54, 0, 1], 'lmfdb_label': '12870.c7', 'torsion': [24]}
  • id: 663156
    {'degree': 16, 'field': [7525389001, -6235257873, 2749562738, -2110684095, 884475397, -64942176, 45136130, -17654754, -148028, -387390, 149978, 4416, 2485, -621, -22, -3, 1], 'lmfdb_label': '12870.c7', 'torsion': [2, 24]}
  • id: 663157
    {'degree': 16, 'field': [416123045776, 2283305848992, 5655767362188, 8118319721400, 5930956351705, 1315844088108, 132203640474, 4704179040, -582780246, -27723630, 4505526, 208956, 25630, 900, -138, -6, 1], 'lmfdb_label': '12870.c7', 'torsion': [2, 12]}
  • id: 663154
    {'degree': 16, 'field': [39438852161296, 0, 0, 0, 174385529704, 0, 0, 0, 402692721, 0, 0, 0, -28586, 0, 0, 0, 1], 'lmfdb_label': '12870.c7', 'torsion': [4, 4]}
  • id: 663159
    {'degree': 18, 'field': [512320919969911, 218677739083752, 81169301922696, 27713756783044, 6402912231054, 1406549126724, 273111198371, 40751189730, 5864200314, 728247292, 66429114, 6941394, 460469, 22614, 5214, -752, 72, -6, 1], 'lmfdb_label': '12870.c7', '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: 279030
    {'conductor': 12870, 'conductor_valuation': 1, 'discriminant_valuation': 24, 'j_denominator_valuation': 24, 'kodaira_symbol': 28, 'lmfdb_label': '12870.c7', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 279031
    {'conductor': 12870, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '12870.c7', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 279032
    {'conductor': 12870, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '12870.c7', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 279033
    {'conductor': 12870, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '12870.c7', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 279034
    {'conductor': 12870, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '12870.c7', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 1749362
    {'adelic_gens': [[4696, 3, 5781, 17074], [1, 24, 0, 1], [1, 0, 24, 1], [17137, 24, 17136, 25], [1, 12, 12, 145], [4297, 24, 4782, 1687], [7881, 5008, 3116, 629], [15, 106, 15854, 7931], [17144, 8559, 3145, 6094], [7936, 21, 2355, 16786], [10312, 3, 9837, 17074]], 'adelic_image': '17160.384.5.?', 'conductor': 12870, 'lmfdb_label': '12870.c7', 'prime': 0}
  • id: 61122
    {'conductor': 12870, 'elladic_image': '4.6.0.1', 'lmfdb_label': '12870.c7', 'modell_image': '2B', 'prime': 2}
  • id: 61123
    {'conductor': 12870, 'elladic_image': '3.8.0.2', 'lmfdb_label': '12870.c7', 'modell_image': '3B.1.2', 'prime': 3}
• lmfdb_iso 12870.c does not appear in ec_padic