Elliptic curve data - 4176.k1

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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': '4176b', 'Clabel': '4176b2', 'Cnumber': 2, 'abc_quality': 0.8661276626980977, 'absD': 33901369344, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 696, 'ainvs': [0, 0, 0, -891, 5130], 'analytic_rank': 1, 'bad_primes': [2, 3, 29], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 4176, 'degree': 2688, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.71675512413547334931281688152', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2], 'jinv': [1940598, 841], 'lmfdb_iso': '4176.k', 'lmfdb_label': '4176.k1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -891, -5130], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '24.6.0.a.1', '232.6.0.?', '348.6.0.?', '696.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 7, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.86770336313187442353469525352', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 3], [3, 2, 464], [29, 30, 144]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.74258900787889211953274649084', 'prec': 107}, 'szpiro_ratio': 3.837137767778619, '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, 0, 0, -2, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, -6, 0, 0, 0], 'aplist': [0, 0, -2, 4, 0, 2, -6, 0, -4, -1, -6, 4, -6, -4, 0, 2, 2, 0, -12, 0, 14, -10, -6, 6, 2], 'class_deg': 2, 'class_size': 2, 'conductor': 4176, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '4176.k', 'trace_hash': 1750735483580863781}
• 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': '0.23847036115308689844808579250', 'prec': 103}, 'conductor': 4176, 'gens': [[33, 108, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.86770336313187442353469525352', 'prec': 103}], 'lmfdb_label': '4176.k1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.0493780223038038175750538466', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.6421953565987428078536217377199508947', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[6, 0, 1]], 'xcoord_integral_points': [-23, 6, 33, 55]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [1, 0], '11': [1, 1, 0], '13': [3, 0], '17': [1, 0], '19': [1, 1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '4176.k1'}
• ec_torsion_growth •

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

  
  
  • id: 218120
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '4176.k1', 'torsion': [2, 2]}
  • id: 218121
    {'degree': 4, 'field': [64, -37, 9, -1, 1], 'lmfdb_label': '4176.k1', 'torsion': [4]}
  • id: 218124
    {'degree': 8, 'field': [-108, 0, 36, 0, -36, 0, 0, 0, 1], 'lmfdb_label': '4176.k1', 'torsion': [6]}
  • id: 218123
    {'degree': 8, 'field': [256, 0, 160, 0, 144, 0, 10, 0, 1], 'lmfdb_label': '4176.k1', 'torsion': [2, 4]}
  • id: 218122
    {'degree': 8, 'field': [529, 0, -356, 0, 96, 0, -20, 0, 1], 'lmfdb_label': '4176.k1', 'torsion': [2, 4]}
  • id: 218126
    {'degree': 16, 'field': [314721, 0, -403416, 0, 200484, 0, -55980, 0, 11334, 0, -2256, 0, 328, 0, -28, 0, 1], 'lmfdb_label': '4176.k1', 'torsion': [2, 6]}
  • id: 218125
    {'degree': 16, 'field': [17572864, 0, -4892216, 0, 1546562, 0, -286535, 0, 54517, 0, -7036, 0, 710, 0, -43, 0, 1], 'lmfdb_label': '4176.k1', 'torsion': [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: 78561
    {'conductor': 4176, 'conductor_valuation': 4, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '4176.k1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 78562
    {'conductor': 4176, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '4176.k1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 78563
    {'conductor': 4176, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '4176.k1', 'prime': 29, '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: 1691183
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [2, 1, 347, 0], [1, 2, 2, 5], [1, 4, 0, 1], [553, 4, 410, 9], [236, 1, 463, 0], [693, 4, 692, 5], [436, 265, 609, 88]], 'adelic_image': '696.12.0.?', 'conductor': 4176, 'lmfdb_label': '4176.k1', 'prime': 0}
  • id: 20819
    {'conductor': 4176, 'elladic_image': '2.3.0.1', 'lmfdb_label': '4176.k1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 147261
    {'lmfdb_iso': '4176.k', 'p': 5, 'prec': 20, 'unit': 9546717468086, 'val': 1}
  • id: 147262
    {'lmfdb_iso': '4176.k', 'p': 7, 'prec': 20, 'unit': 4293866983164018, 'val': 1}
  • id: 147266
    {'lmfdb_iso': '4176.k', 'p': 13, 'prec': 20, 'unit': 111439870436230832966, 'val': 2}
  • id: 147268
    {'lmfdb_iso': '4176.k', 'p': 17, 'prec': 20, 'unit': 118506227951779129402099, 'val': 1}
  • id: 147272
    {'lmfdb_iso': '4176.k', 'p': 23, 'prec': 20, 'unit': 34151977176401641382649307, 'val': 1}
  • id: 147263
    {'lmfdb_iso': '4176.k', 'p': 31, 'prec': 20, 'unit': 10815839929171707312178664701, 'val': 1}
  • id: 147275
    {'lmfdb_iso': '4176.k', 'p': 37, 'prec': 20, 'unit': 296677661893202325469416113697, 'val': 1}
  • id: 147264
    {'lmfdb_iso': '4176.k', 'p': 41, 'prec': 20, 'unit': 3442079892312162908686982363273, 'val': 1}
  • id: 147265
    {'lmfdb_iso': '4176.k', 'p': 43, 'prec': 20, 'unit': 744435319340498524649503972007, 'val': 1}
  • id: 147270
    {'lmfdb_iso': '4176.k', 'p': 53, 'prec': 20, 'unit': 211870590179298568604199740834750, 'val': 1}
  • id: 147274
    {'lmfdb_iso': '4176.k', 'p': 59, 'prec': 20, 'unit': 255703237347366945066166842453742, 'val': 1}
  • id: 147260
    {'lmfdb_iso': '4176.k', 'p': 67, 'prec': 20, 'unit': 48278868051293331989648532563669636, 'val': 1}
  • id: 147271
    {'lmfdb_iso': '4176.k', 'p': 73, 'prec': 20, 'unit': 45729556102813764739864858458280088, 'val': 1}
  • id: 147267
    {'lmfdb_iso': '4176.k', 'p': 79, 'prec': 20, 'unit': 657642253932866945616448765683981367, 'val': 1}
  • id: 147269
    {'lmfdb_iso': '4176.k', 'p': 83, 'prec': 20, 'unit': 1845303223313383094842238472457385495, 'val': 1}
  • id: 147273
    {'lmfdb_iso': '4176.k', 'p': 89, 'prec': 20, 'unit': 3970365780814437925788420400331826913, 'val': 1}
  • id: 147259
    {'lmfdb_iso': '4176.k', 'p': 97, 'prec': 20, 'unit': 52258991725109152506529740293906421981, 'val': 1}