Elliptic curve data - 72963.p1

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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': '72963i', 'Clabel': '72963i2', 'Cnumber': 2, 'abc_quality': 0.9003678870381097, 'absD': 1379612314837654227, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 8844, 'ainvs': [1, -1, 0, -479727, 114848014], 'analytic_rank': 1, 'bad_primes': [3, 11, 67], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 72963, 'degree': 691200, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2133169365329030085345932033', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 15, 'isogeny_degrees': [1, 2], 'jinv': [9454162623625, 1068251283], 'lmfdb_iso': '72963.p', 'lmfdb_label': '72963.p1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -440, 3009], 'min_quad_twist_disc': 33, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '132.6.0.?', '268.6.0.?', '8844.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '6.2731655655545701157750885520', 'prec': 100}, 'semistable': False, 'serre_invariants': [[3, 8, 8107], [11, 72, 603], [67, 68, 1089]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.46506315579966289080599879586', 'prec': 103}, 'szpiro_ratio': 4.541690387783249, '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, 0, 0, 0, -3, 0, 0, 0, 0, -4, 0, 0, -1, 2, 0, 2, 0], 'aplist': [1, 0, 0, 0, 0, -4, 2, 2, -2, -2, 8, -6, -6, 12, 6, -4, 6, 4, -1, -2, 10, -8, 8, 6, -14], 'class_deg': 2, 'class_size': 2, 'conductor': 72963, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '72963.p', 'trace_hash': 1200312353913013982}
• 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': '0.011954662933599058744840976368', 'prec': 107}, 'conductor': 72963, 'gens': [[2579, 65893, 2]], 'heights': [{'__RealLiteral__': 0, 'data': '6.2731655655545701157750885520', 'prec': 100}], 'lmfdb_label': '72963.p1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.26167692755033297806273572384', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.5661707648354673850972470852819764944', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[2003, -2003, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '3': 'a', '5': [1, 1, 0], '7': [1, 1, 0], '11': 'a', '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0], '67': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '72963.p1'}
• ec_torsion_growth •

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

  
  
  • id: 3459127
    {'degree': 2, 'field': [-67, 0, 1], 'lmfdb_label': '72963.p1', 'torsion': [2, 2]}
  • id: 3459128
    {'degree': 4, 'field': [-2, 19, -13, -1, 1], 'lmfdb_label': '72963.p1', 'torsion': [4]}
  • id: 3459131
    {'degree': 8, 'field': [-198293, 46169, -47666, 2993, -1493, -7, 7, -4, 1], 'lmfdb_label': '72963.p1', 'torsion': [6]}
  • id: 3459129
    {'degree': 8, 'field': [4356, 0, -4224, 0, 1093, 0, -70, 0, 1], 'lmfdb_label': '72963.p1', 'torsion': [2, 4]}
  • id: 3459130
    {'degree': 8, 'field': [2155837761, 0, -11850960, 0, 180163, 0, -536, 0, 1], 'lmfdb_label': '72963.p1', 'torsion': [2, 4]}
  • id: 3459132
    {'degree': 16, 'field': [-80325084413, -94131653210, 3901698978, 15623562422, -4149409515, 922275354, -60036356, -12011968, 2543118, -1088318, 167926, -26754, -1791, 1006, -108, -4, 1], 'lmfdb_label': '72963.p1', 'torsion': [8]}
  • id: 3459133
    {'degree': 16, 'field': [4158783189, -1301243526, 1599769329, -608460294, 323447478, 4784202, -53413803, 55340430, -27721517, 9618454, -2286407, 200206, -35309, 868, -104, -8, 1], 'lmfdb_label': '72963.p1', 'torsion': [2, 6]}
• 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: 1771325
    {'conductor': 72963, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '72963.p1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1771326
    {'conductor': 72963, 'conductor_valuation': 2, 'discriminant_valuation': 12, 'j_denominator_valuation': 6, 'kodaira_symbol': -10, 'lmfdb_label': '72963.p1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1771327
    {'conductor': 72963, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '72963.p1', 'prime': 67, '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: 2146535
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [2212, 6637, 6633, 2212], [5897, 4, 2950, 9], [1, 2, 2, 5], [1, 4, 0, 1], [8714, 1, 4487, 0], [805, 4, 1610, 9], [8841, 4, 8840, 5]], 'adelic_image': '8844.12.0.?', 'conductor': 72963, 'lmfdb_label': '72963.p1', 'prime': 0}
  • id: 302916
    {'conductor': 72963, 'elladic_image': '2.3.0.1', 'lmfdb_label': '72963.p1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 3747023
    {'lmfdb_iso': '72963.p', 'p': 13, 'prec': 20, 'unit': 207448407431761330727, 'val': 1}
  • id: 3747025
    {'lmfdb_iso': '72963.p', 'p': 17, 'prec': 20, 'unit': 93561017680770340046170, 'val': 1}
  • id: 3747026
    {'lmfdb_iso': '72963.p', 'p': 19, 'prec': 20, 'unit': 1605890472669774971829396, 'val': 1}
  • id: 3747029
    {'lmfdb_iso': '72963.p', 'p': 23, 'prec': 20, 'unit': 33696800702477509307860113, 'val': 1}
  • id: 3747022
    {'lmfdb_iso': '72963.p', 'p': 29, 'prec': 20, 'unit': 3569218433074607154627872257, 'val': 1}
  • id: 3747033
    {'lmfdb_iso': '72963.p', 'p': 31, 'prec': 20, 'unit': 10906892390865599901739997727, 'val': 1}
  • id: 3747018
    {'lmfdb_iso': '72963.p', 'p': 37, 'prec': 20, 'unit': 217450686894825630795633571189, 'val': 1}
  • id: 3747020
    {'lmfdb_iso': '72963.p', 'p': 41, 'prec': 20, 'unit': 738892368213499115125207378675, 'val': 1}
  • id: 3747021
    {'lmfdb_iso': '72963.p', 'p': 43, 'prec': 20, 'unit': 3042197349180300171159185177145, 'val': 1}
  • id: 3747031
    {'lmfdb_iso': '72963.p', 'p': 47, 'prec': 20, 'unit': 26054989003011723394190270096022, 'val': 1}
  • id: 3747027
    {'lmfdb_iso': '72963.p', 'p': 53, 'prec': 20, 'unit': 127405518525923290980318226413705, 'val': 1}
  • id: 3747017
    {'lmfdb_iso': '72963.p', 'p': 59, 'prec': 20, 'unit': 2939328870394823337647069120807467, 'val': 1}
  • id: 3747032
    {'lmfdb_iso': '72963.p', 'p': 61, 'prec': 20, 'unit': 3910678112247324162323844899987220, 'val': 1}
  • id: 3747019
    {'lmfdb_iso': '72963.p', 'p': 71, 'prec': 20, 'unit': 94229934491713123626809747780557378, 'val': 1}
  • id: 3747028
    {'lmfdb_iso': '72963.p', 'p': 73, 'prec': 20, 'unit': 161795169653654106951220908034629437, 'val': 1}
  • id: 3747024
    {'lmfdb_iso': '72963.p', 'p': 79, 'prec': 20, 'unit': 104359967557193467175921062546894594, 'val': 1}
  • id: 3747016
    {'lmfdb_iso': '72963.p', 'p': 83, 'prec': 20, 'unit': 116086837206723340925588782139802031, 'val': 1}
  • id: 3747030
    {'lmfdb_iso': '72963.p', 'p': 89, 'prec': 20, 'unit': 45861778818626526724036118124271856, 'val': 2}
  • id: 3747015
    {'lmfdb_iso': '72963.p', 'p': 97, 'prec': 20, 'unit': 41894301295022399157858432731927174292, 'val': 1}