Elliptic curve data - 177744.dd1

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '177744x', 'Clabel': '177744x6', 'Cnumber': 6, 'abc_quality': 1.0156853826442096, 'absD': 386616818768022654271488, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 2576, 'ainvs': [0, 1, 0, -669790352, -6672162455532], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 23], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 177744, 'degree': 51904512, 'elladic_images': ['16.48.0.114'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.6768688415643578662456001194', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 8, 'intrinsic_torsion': 2, 'iso_nlabel': 81, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [54804145548726848737, 637608031452], 'lmfdb_iso': '177744.dd', 'lmfdb_label': '177744.dd1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -79134, -8601153], 'min_quad_twist_disc': 92, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0-8.n.1.7', '16.48.0-16.e.2.1', '28.12.0.h.1', '56.48.0-56.bj.1.2', '92.12.0.?', '112.96.0.?', '184.48.0.?', '368.96.0.?', '644.24.0.?', '1288.96.0.?', '2576.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '24.280129905553922175563109774', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 3703], [3, 4, 59248], [7, 8, 25392], [23, 288, 336]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.4159745530398377114249915820', 'prec': 100}, 'szpiro_ratio': 6.0043374415185715, '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, 2, 0, 1, 0, 1, 0, -4, 0, -2, 0, 2, 0, 6, 0, 4, 0], 'aplist': [0, 1, 2, 1, -4, -2, 6, 4, 0, -2, 8, -6, -6, -4, 8, -6, -4, 10, 4, 8, -6, 0, -12, -2, -10], 'class_deg': 8, 'class_size': 6, 'conductor': 177744, 'isogeny_matrix': [[1, 8, 2, 4, 8, 4], [8, 1, 4, 2, 4, 8], [2, 4, 1, 2, 4, 2], [4, 2, 2, 1, 2, 4], [8, 4, 4, 2, 1, 8], [4, 8, 2, 4, 8, 1]], 'lmfdb_iso': '177744.dd', 'trace_hash': 2090745402359908086}
• 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': '0.00064019503674056855593319554761', 'prec': 113}, 'conductor': 177744, 'gens': [[-563193176204, 1588121655542794, 6135]], 'heights': [{'__RealLiteral__': 0, 'data': '24.280129905553922175563109774', 'prec': 100}], 'lmfdb_label': '177744.dd1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.029676667846779339606792305505', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '11.528853607740441055042889572716996336', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[-14981, 0, 1]], 'xcoord_integral_points': [-14981]}
• lmfdb_label 177744.dd1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7873111
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '177744.dd1', 'torsion': [2, 2]}
  • id: 7873113
    {'degree': 2, 'field': [6, -1, 1], 'lmfdb_label': '177744.dd1', 'torsion': [4]}
  • id: 7873112
    {'degree': 2, 'field': [161, 0, 1], 'lmfdb_label': '177744.dd1', 'torsion': [4]}
  • id: 7873116
    {'degree': 4, 'field': [18, -16, 17, -2, 1], 'lmfdb_label': '177744.dd1', 'torsion': [8]}
  • id: 7873115
    {'degree': 4, 'field': [78, -40, 41, -2, 1], 'lmfdb_label': '177744.dd1', 'torsion': [8]}
  • id: 7873114
    {'degree': 4, 'field': [162, 2, -1, -2, 1], 'lmfdb_label': '177744.dd1', 'torsion': [2, 4]}
  • id: 7873121
    {'degree': 8, 'field': [-64971, 129510, -44706, 11004, -624, -10, -48, 0, 1], 'lmfdb_label': '177744.dd1', 'torsion': [6]}
  • id: 7873119
    {'degree': 8, 'field': [162, -684, 1086, -844, 523, -124, 46, -4, 1], 'lmfdb_label': '177744.dd1', 'torsion': [2, 8]}
  • id: 7873117
    {'degree': 8, 'field': [772, 788, -610, -334, 113, 62, -16, -4, 1], 'lmfdb_label': '177744.dd1', 'torsion': [2, 4]}
  • id: 7873118
    {'degree': 8, 'field': [310249, 0, -40940, 0, 3230, 0, -92, 0, 1], 'lmfdb_label': '177744.dd1', 'torsion': [8]}
  • id: 7873120
    {'degree': 8, 'field': [157703364, 0, 3317888, 0, 13524, 0, 0, 0, 1], 'lmfdb_label': '177744.dd1', 'torsion': [16]}
  • id: 7873122
    {'degree': 16, 'field': [595984, 0, 1562784, 0, 1072956, 0, 371832, 0, 81553, 0, 11352, 0, 978, 0, 48, 0, 1], 'lmfdb_label': '177744.dd1', 'torsion': [4, 4]}
  • id: 7873124
    {'degree': 16, 'field': [1004004, 0, -1294568, 0, 1781824, 0, -521356, 0, 94373, 0, -10384, 0, 842, 0, -44, 0, 1], 'lmfdb_label': '177744.dd1', 'torsion': [2, 8]}
  • id: 7873125
    {'degree': 16, 'field': [1882384, 0, 0, 0, 0, 0, 0, 0, 167608, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '177744.dd1', 'torsion': [16]}
  • id: 7873130
    {'degree': 16, 'field': [2415312, -6128784, 9627732, -9431616, 11055456, -8335936, 4033544, -1160176, 401765, -84256, 27332, -6632, 1894, -392, 76, -8, 1], 'lmfdb_label': '177744.dd1', 'torsion': [12]}
  • id: 7873128
    {'degree': 16, 'field': [32764176, 0, 13304736, 0, 1221264, 0, -148207, 0, 6098, 0, -3799, 0, -311, 0, -14, 0, 1], 'lmfdb_label': '177744.dd1', 'torsion': [2, 6]}
  • id: 7873123
    {'degree': 16, 'field': [262529901, 110495376, -101164348, -19766824, 12576802, -3027416, 629832, 401280, -194837, 61816, -10920, -1120, 490, -168, 44, -8, 1], 'lmfdb_label': '177744.dd1', 'torsion': [2, 8]}
  • id: 7873126
    {'degree': 16, 'field': [671898241, 0, 0, 0, 0, 0, 0, 0, 3166594, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '177744.dd1', 'torsion': [16]}
  • id: 7873129
    {'degree': 16, 'field': [113254044474, -51944609256, 56447759304, -31348526894, 13580463244, -4262668770, 910361535, -145129692, 13659564, 353122, -151187, -18996, 4077, 414, -66, -8, 1], 'lmfdb_label': '177744.dd1', 'torsion': [12]}
  • id: 7873127
    {'degree': 16, 'field': [44791229390625, 0, -5206592584800, 0, 253930770576, 0, -6542602864, 0, 91902818, 0, -890848, 0, 15568, 0, 16, 0, 1], 'lmfdb_label': '177744.dd1', 'torsion': [2, 16]}
• 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: 4398357
    {'conductor': 177744, 'conductor_valuation': 4, 'discriminant_valuation': 14, 'j_denominator_valuation': 2, 'kodaira_symbol': -10, 'lmfdb_label': '177744.dd1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4398358
    {'conductor': 177744, 'conductor_valuation': 1, 'discriminant_valuation': 16, 'j_denominator_valuation': 16, 'kodaira_symbol': 20, 'lmfdb_label': '177744.dd1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 16}
  • id: 4398359
    {'conductor': 177744, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '177744.dd1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 4398360
    {'conductor': 177744, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '177744.dd1', 'prime': 23, '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: 2808691
    {'adelic_gens': [[211, 2560, 2384, 315], [1, 16, 0, 1], [15, 2, 2478, 2563], [384, 5, 691, 2562], [2561, 16, 2560, 17], [5, 4, 2572, 2573], [13, 16, 388, 329], [314, 1927, 2251, 1286], [1, 0, 16, 1]], 'adelic_image': '2576.192.1.?', 'conductor': 177744, 'lmfdb_label': '177744.dd1', 'prime': 0}
  • id: 668013
    {'conductor': 177744, 'elladic_image': '16.48.0.114', 'lmfdb_label': '177744.dd1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 177744.dd does not appear in ec_padic