Elliptic curve data - 177870.dg2

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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': '177870gp', 'Clabel': '177870gp3', 'Cnumber': 3, 'abc_quality': 1.0750149448569075, 'absD': 96502726449866996083440, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 18480, 'ainvs': [1, 0, 1, -70110549, 225454928752], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 177870, 'degree': 35389440, 'elladic_images': ['8.12.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.2870887442197995206735885728', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 84, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [182864522286982801, 463015182960], 'lmfdb_iso': '177870.dg', 'lmfdb_label': '177870.dg2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -11825, 488927], 'min_quad_twist_disc': 77, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '24.24.0.by.2', '40.24.0.cb.2', '60.12.0.h.1', '112.24.0.?', '120.48.0.?', '176.24.0.?', '308.12.0.?', '336.48.0.?', '528.48.0.?', '560.48.0.?', '616.24.0.?', '880.48.0.?', '1232.48.0.?', '1680.96.0.?', '1848.48.0.?', '2640.96.1.?', '3080.48.0.?', '3696.96.0.?', '4620.24.0.?', '6160.96.0.?', '9240.96.0.?', '18480.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 88935], [3, 4, 59290], [5, 6, 35574], [7, 26, 3630], [11, 72, 1470]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1151860332929575960899404121', 'prec': 100}, 'szpiro_ratio': 5.44390755998796, '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, 0, -1, 1, 1, 0, 1, 6, 0, -1, 1, 2, -1, -4, -1], 'aplist': [-1, 1, -1, 0, 0, 6, 2, -4, 0, 10, 0, 6, 2, -4, 8, -10, 4, -2, -4, -8, 2, 8, -12, 6, -18], 'class_deg': 8, 'class_size': 6, 'conductor': 177870, 'isogeny_matrix': [[1, 8, 2, 4, 4, 8], [8, 1, 4, 8, 2, 4], [2, 4, 1, 2, 2, 4], [4, 8, 2, 1, 4, 8], [4, 2, 2, 4, 1, 2], [8, 4, 4, 8, 2, 1]], 'lmfdb_iso': '177870.dg', 'trace_hash': 306853768274905050}
• 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': '0.0013959536343084853740443479717', 'prec': 110}, 'conductor': 177870, 'gens': [], 'heights': [], 'lmfdb_label': '177870.dg2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.10700675329002743536294994450', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.5681620789606584487107986679870123034', 'prec': 130}, 'tamagawa_product': 96, 'torsion_generators': [[20071, -20075, 2]], 'xcoord_integral_points': []}
• lmfdb_label 177870.dg2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7881417
    {'degree': 2, 'field': [-1155, 0, 1], 'lmfdb_label': '177870.dg2', 'torsion': [4]}
  • id: 7881416
    {'degree': 2, 'field': [-19, -1, 1], 'lmfdb_label': '177870.dg2', 'torsion': [4]}
  • id: 7881415
    {'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '177870.dg2', 'torsion': [2, 2]}
  • id: 7881418
    {'degree': 4, 'field': [1, 68, -67, -2, 1], 'lmfdb_label': '177870.dg2', 'torsion': [2, 4]}
  • id: 7881419
    {'degree': 4, 'field': [253, 44, -43, -2, 1], 'lmfdb_label': '177870.dg2', 'torsion': [8]}
  • id: 7881420
    {'degree': 4, 'field': [324, 0, -41, 0, 1], 'lmfdb_label': '177870.dg2', 'torsion': [8]}
  • id: 7881424
    {'degree': 8, 'field': [-25212, -99, 6504, -775, 247, 23, 25, -4, 1], 'lmfdb_label': '177870.dg2', 'torsion': [6]}
  • id: 7881423
    {'degree': 8, 'field': [44100, 0, -24360, 0, 2629, 0, -94, 0, 1], 'lmfdb_label': '177870.dg2', 'torsion': [2, 8]}
  • id: 7881421
    {'degree': 8, 'field': [311161, 247860, 74108, 8280, 1749, -180, 62, 0, 1], 'lmfdb_label': '177870.dg2', 'torsion': [2, 4]}
  • id: 7881422
    {'degree': 8, 'field': [35868121, 0, 1770692, 0, 35694, 0, 308, 0, 1], 'lmfdb_label': '177870.dg2', 'torsion': [8]}
  • id: 7881429
    {'degree': 16, 'field': [-5707225590, -2663010570, 2572978881, 871527030, -352399080, 19572828, 5569303, -28166176, 5390175, 1281390, -271473, -32868, 6897, 570, -120, -4, 1], 'lmfdb_label': '177870.dg2', 'torsion': [2, 6]}
  • id: 7881430
    {'degree': 16, 'field': [-1668112, 8543984, -5830815, -5095644, 1697346, 1076802, -422681, -2912, 67299, -36050, -1073, 4440, -649, -70, 30, -8, 1], 'lmfdb_label': '177870.dg2', 'torsion': [12]}
  • id: 7881427
    {'degree': 16, 'field': [961, -14198, 56208, -622, -210054, 129504, 215110, -180418, -41169, 61312, -4070, -7074, 1158, 310, -66, -4, 1], 'lmfdb_label': '177870.dg2', 'torsion': [16]}
  • id: 7881431
    {'degree': 16, 'field': [904920, -6353220, 18476601, -33680340, 40692450, -28613712, 9980173, 3390034, 11945, -1248750, 265097, 11162, -4563, 80, -10, -4, 1], 'lmfdb_label': '177870.dg2', 'torsion': [12]}
  • id: 7881428
    {'degree': 16, 'field': [2926991936, -447030144, 429990176, 39422944, -32992372, 15716856, -4854626, -364728, 137083, -33644, 10306, -2648, 1048, -308, 64, -8, 1], 'lmfdb_label': '177870.dg2', 'torsion': [16]}
  • id: 7881426
    {'degree': 16, 'field': [14056710721, 0, 7780170216, 0, 1540401370, 0, 157937364, 0, 10037739, 0, 408564, 0, 10510, 0, 156, 0, 1], 'lmfdb_label': '177870.dg2', 'torsion': [2, 8]}
  • id: 7881425
    {'degree': 16, 'field': [31028546761, 11427730620, 6389301306, 1350600240, 1206133720, 172179240, 102292614, 9458520, 8333589, 99480, 399834, -2400, 10780, -60, 156, 0, 1], 'lmfdb_label': '177870.dg2', 'torsion': [4, 4]}
• 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: 4403125
    {'conductor': 177870, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '177870.dg2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4403126
    {'conductor': 177870, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '177870.dg2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 4403127
    {'conductor': 177870, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '177870.dg2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 4403128
    {'conductor': 177870, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '177870.dg2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4403129
    {'conductor': 177870, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '177870.dg2', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 2809538
    {'adelic_gens': [[1, 16, 0, 1], [18465, 16, 18464, 17], [16178, 4627, 10255, 9262], [13199, 0, 0, 18479], [15, 2, 18382, 18467], [1, 13216, 11228, 8709], [5, 4, 18476, 18477], [1, 0, 16, 1], [11096, 15841, 9583, 13210], [6719, 5264, 952, 5151], [3536, 5285, 7875, 2626]], 'adelic_image': '18480.192.1.?', 'conductor': 177870, 'lmfdb_label': '177870.dg2', 'prime': 0}
  • id: 668538
    {'conductor': 177870, 'elladic_image': '8.12.0.5', 'lmfdb_label': '177870.dg2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 177870.dg does not appear in ec_padic