Elliptic curve data - 21168.v1

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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': '21168g', 'Clabel': '21168g1', 'Cnumber': 1, 'abc_quality': 0.7417960936614756, 'absD': 159385218048, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 6, 'ainvs': [0, 0, 0, 1029, -14406], 'analytic_rank': 1, 'bad_primes': [2, 3, 7], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 21168, 'degree': 16128, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.83538726755251584027399616199', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 21, 'isogeny_degrees': [1], 'jinv': [756, 1], 'lmfdb_iso': '21168.v', 'lmfdb_label': '21168.v1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, 189, 1134], 'min_quad_twist_disc': -84, 'modell_images': [], 'modm_images': ['6.2.0.a.1'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.61030560677952191741990100721', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.3141618877846748771594104108', 'prec': 103}, 'szpiro_ratio': 3.2804356480063546, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 0, 0, 0, 0, -4, 0, -1, 0, 0, 0, 0, 0, 4, 0], 'aplist': [0, 0, -2, 0, -4, -1, 0, 4, 6, 0, -5, 1, 4, 1, 4, 6, 0, -3, -11, -14, -14, -13, 14, -6, 9], 'class_deg': 1, 'class_size': 1, 'conductor': 21168, 'isogeny_matrix': [[1]], 'lmfdb_iso': '21168.v', 'trace_hash': 2110507764332842820}
• 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': '0.18810131812855813153099376921', 'prec': 103}, 'conductor': 21168, 'gens': [[49, 392, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.61030560677952191741990100721', 'prec': 103}], 'lmfdb_label': '21168.v1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.54583910788129002650974973907', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.9975440152738036040301633658136667627', 'prec': 130}, 'tamagawa_product': 12, 'torsion_generators': [], 'xcoord_integral_points': [49]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [3, 0], '7': 'a', '11': [1, 0], '13': [1, 0], '17': [1, 1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 1, 0], '31': [1, 0], '37': [1, 0], '41': [3, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '21168.v1'}
• ec_torsion_growth •

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

  
  
  • id: 1076613
    {'degree': 3, 'field': [-7, 0, 0, 1], 'lmfdb_label': '21168.v1', 'torsion': [2]}
  • id: 1076614
    {'degree': 6, 'field': [64, -24, -15, 7, 6, -3, 1], 'lmfdb_label': '21168.v1', 'torsion': [2, 2]}
  • id: 1076615
    {'degree': 8, 'field': [1, -2, 4, 10, -2, 10, 4, -2, 1], 'lmfdb_label': '21168.v1', 'torsion': [3]}
  • id: 1076616
    {'degree': 12, 'field': [-300, 0, -261, 0, 93, 0, -66, 0, 30, 0, -9, 0, 1], 'lmfdb_label': '21168.v1', 'torsion': [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: 481342
    {'conductor': 21168, 'conductor_valuation': 4, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -6, 'lmfdb_label': '21168.v1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 481343
    {'conductor': 21168, 'conductor_valuation': 3, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '21168.v1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 481344
    {'conductor': 21168, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '21168.v1', 'prime': 7, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 3}
• ec_galrep •

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

  
  {'adelic_gens': [[5, 2, 5, 3], [1, 1, 5, 0], [1, 2, 0, 1], [5, 2, 4, 3], [1, 0, 2, 1]], 'adelic_image': '6.2.0.?', 'conductor': 21168, 'lmfdb_label': '21168.v1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 991062
    {'lmfdb_iso': '21168.v', 'p': 5, 'prec': 20, 'unit': 3592526795048, 'val': 2}
  • id: 991061
    {'lmfdb_iso': '21168.v', 'p': 11, 'prec': 20, 'unit': 34531364195974580712, 'val': 1}
  • id: 991067
    {'lmfdb_iso': '21168.v', 'p': 13, 'prec': 20, 'unit': 1314845263765713398508, 'val': 1}
  • id: 991069
    {'lmfdb_iso': '21168.v', 'p': 19, 'prec': 20, 'unit': 1424602841572117173883305, 'val': 1}
  • id: 991072
    {'lmfdb_iso': '21168.v', 'p': 23, 'prec': 20, 'unit': 71043199038461328884986587, 'val': 1}
  • id: 991064
    {'lmfdb_iso': '21168.v', 'p': 31, 'prec': 20, 'unit': 2866245903455241331030096773, 'val': 1}
  • id: 991077
    {'lmfdb_iso': '21168.v', 'p': 37, 'prec': 20, 'unit': 14326909786490706992718552351336, 'val': -1}
  • id: 991065
    {'lmfdb_iso': '21168.v', 'p': 41, 'prec': 20, 'unit': 94368884989139636278205718219, 'val': 2}
  • id: 991066
    {'lmfdb_iso': '21168.v', 'p': 43, 'prec': 20, 'unit': 184501808679418965992475582067758, 'val': -1}
  • id: 991068
    {'lmfdb_iso': '21168.v', 'p': 47, 'prec': 20, 'unit': 34848868704116121941046093983919, 'val': 1}
  • id: 991070
    {'lmfdb_iso': '21168.v', 'p': 53, 'prec': 20, 'unit': 247616156775733632635872053746541, 'val': 1}
  • id: 991075
    {'lmfdb_iso': '21168.v', 'p': 61, 'prec': 20, 'unit': 7681588500181327217673793607665326, 'val': 1}
  • id: 991060
    {'lmfdb_iso': '21168.v', 'p': 67, 'prec': 20, 'unit': 45531914399853456977586174468596795, 'val': 1}
  • id: 991063
    {'lmfdb_iso': '21168.v', 'p': 71, 'prec': 20, 'unit': 125598825846306397212370457752862298, 'val': 1}
  • id: 991071
    {'lmfdb_iso': '21168.v', 'p': 73, 'prec': 20, 'unit': 173960573827365635652559053194824376, 'val': 1}
  • id: 991074
    {'lmfdb_iso': '21168.v', 'p': 79, 'prec': 20, 'unit': 383853637742919227401020745596830421, 'val': 1}
  • id: 991076
    {'lmfdb_iso': '21168.v', 'p': 83, 'prec': 20, 'unit': 1196387288905887592137627234755264960, 'val': 1}
  • id: 991073
    {'lmfdb_iso': '21168.v', 'p': 89, 'prec': 20, 'unit': 804877450568723433007720532049532139, 'val': 1}
  • id: 991059
    {'lmfdb_iso': '21168.v', 'p': 97, 'prec': 20, 'unit': 22884584630233687850959061231249891127, 'val': 1}