Elliptic curve data - 84966.cr4

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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': '84966da', 'Clabel': '84966da2', 'Cnumber': 2, 'abc_quality': 1.0972067382550121, 'absD': 127143428114514212586055471104, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 952, 'ainvs': [1, 1, 1, -1284742859, -4454988308359], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 17], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 84966, 'degree': 106168320, 'elladic_images': ['8.48.0.97'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.2755435353188371457950186803', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 69, 'isogeny_degrees': [1, 2, 4], 'jinv': [82582985847542515777, 44772582831427584], 'lmfdb_iso': '84966.cr', 'lmfdb_label': '84966.cr4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -90724, 2605541], 'min_quad_twist_disc': -119, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.48.0.i.1', '28.24.0-4.b.1.2', '56.96.0-8.i.1.8', '68.24.0.c.1', '136.96.1.?', '476.48.0.?', '952.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '8.6732817090532511285000278082', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 14161], [3, 4, 14161], [7, 32, 1734], [17, 162, 294]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.8859817887630724531175749996', 'prec': 100}, 'szpiro_ratio': 6.56696334067714, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, -2, -1, 0, 1, 1, -2, -4, -1, 2, 0, 2, 1, 0, 1, -4, -2], 'aplist': [1, -1, -2, 0, -4, 2, 0, -4, -8, -6, 0, 2, 10, -4, 0, 6, 4, 6, -12, 8, -6, 0, 12, 6, 2], 'class_deg': 8, 'class_size': 6, 'conductor': 84966, 'isogeny_matrix': [[1, 2, 4, 4, 8, 8], [2, 1, 2, 2, 4, 4], [4, 2, 1, 4, 8, 8], [4, 2, 4, 1, 2, 2], [8, 4, 8, 2, 1, 4], [8, 4, 8, 2, 4, 1]], 'lmfdb_iso': '84966.cr', 'trace_hash': 1650855162204231907}
• 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': '0.00019333481668017771488978277003', 'prec': 113}, 'conductor': 84966, 'gens': [[82197, 21061102, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '8.6732817090532511285000278082', 'prec': 100}], 'lmfdb_label': '84966.cr4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.026885088813652818943660142334', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.5963667772894519681476808109379452778', 'prec': 130}, 'tamagawa_product': 384, 'torsion_generators': [[-33965, 16982, 1], [-3501, 1750, 1]], 'xcoord_integral_points': [-33965, -3501, 82197]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [11, 0], '3': [1, 0], '5': [3, 0], '7': 'a', '11': [3, 0], '13': [1, 0], '17': 'a', '19': [1, 0], '23': [1, 0], '29': [3, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '84966.cr4'}
• ec_torsion_growth •

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

  
  
  • id: 3984922
    {'degree': 2, 'field': [30, -1, 1], 'lmfdb_label': '84966.cr4', 'torsion': [2, 4]}
  • id: 3984924
    {'degree': 4, 'field': [2, 22, -21, -2, 1], 'lmfdb_label': '84966.cr4', 'torsion': [2, 4]}
  • id: 3984923
    {'degree': 4, 'field': [242, -38, 39, -2, 1], 'lmfdb_label': '84966.cr4', 'torsion': [2, 4]}
  • id: 3984925
    {'degree': 4, 'field': [1022, -56, 57, -2, 1], 'lmfdb_label': '84966.cr4', 'torsion': [2, 8]}
  • id: 3984926
    {'degree': 8, 'field': [72, -288, 470, -390, 261, -82, 32, -4, 1], 'lmfdb_label': '84966.cr4', 'torsion': [4, 4]}
  • id: 3984929
    {'degree': 8, 'field': [86, -1019, 1064, -91, 49, -7, 7, -4, 1], 'lmfdb_label': '84966.cr4', 'torsion': [2, 6]}
  • id: 3984927
    {'degree': 8, 'field': [616, -952, 422, -170, 165, -34, 24, 0, 1], 'lmfdb_label': '84966.cr4', 'torsion': [2, 8]}
  • id: 3984928
    {'degree': 8, 'field': [2500, 0, -1052, 0, 101, 0, -2, 0, 1], 'lmfdb_label': '84966.cr4', 'torsion': [2, 8]}
  • id: 3984930
    {'degree': 16, 'field': [4096, 0, -92160, 0, 214416, 0, -53184, 0, -5159, 0, 936, 0, -54, 0, -24, 0, 1], 'lmfdb_label': '84966.cr4', 'torsion': [2, 8]}
  • id: 3984932
    {'degree': 16, 'field': [5184, 0, -8288, 0, 5044, 0, -1816, 0, 593, 0, 296, 0, 122, 0, 16, 0, 1], 'lmfdb_label': '84966.cr4', 'torsion': [4, 8]}
  • id: 3984933
    {'degree': 16, 'field': [5576, -23936, 68280, -139264, 221138, -252648, 203936, -104928, 26887, 3032, -4056, 1840, -246, -56, 28, -8, 1], 'lmfdb_label': '84966.cr4', 'torsion': [2, 16]}
  • id: 3984931
    {'degree': 16, 'field': [109600, 273600, 238752, 126336, 219858, 83892, 64566, 22248, 22105, 936, 4698, -120, 552, -12, 36, 0, 1], 'lmfdb_label': '84966.cr4', 'torsion': [4, 8]}
  • id: 3984934
    {'degree': 16, 'field': [746496, 0, -99252, 0, -89955, 0, 125820, 0, 95748, 0, 13666, 0, 660, 0, 0, 0, 1], 'lmfdb_label': '84966.cr4', 'torsion': [2, 12]}
• 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: 2072146
    {'conductor': 84966, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '84966.cr4', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
  • id: 2072147
    {'conductor': 84966, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '84966.cr4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2072148
    {'conductor': 84966, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '84966.cr4', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 2072149
    {'conductor': 84966, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '84966.cr4', 'prime': 17, '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: 2223749
    {'adelic_gens': [[543, 0, 0, 951], [945, 8, 944, 9], [547, 378, 812, 29], [1, 0, 8, 1], [1, 8, 0, 1], [617, 308, 308, 477], [5, 4, 948, 949], [489, 266, 630, 685]], 'adelic_image': '952.192.1.?', 'conductor': 84966, 'lmfdb_label': '84966.cr4', 'prime': 0}
  • id: 346985
    {'conductor': 84966, 'elladic_image': '8.48.0.97', 'lmfdb_label': '84966.cr4', 'modell_image': '2Cs', 'prime': 2}
• ec_padic •

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

  
  
  • id: 4386194
    {'lmfdb_iso': '84966.cr', 'p': 5, 'prec': 20, 'unit': 1010138752034, 'val': 2}
  • id: 4386200
    {'lmfdb_iso': '84966.cr', 'p': 11, 'prec': 20, 'unit': 3216860634590158433, 'val': 2}
  • id: 4386198
    {'lmfdb_iso': '84966.cr', 'p': 13, 'prec': 20, 'unit': 296872380486001984977, 'val': 1}
  • id: 4386201
    {'lmfdb_iso': '84966.cr', 'p': 19, 'prec': 20, 'unit': 407572464652580465499411, 'val': 1}
  • id: 4386204
    {'lmfdb_iso': '84966.cr', 'p': 23, 'prec': 20, 'unit': 34522142123014911845105478, 'val': 1}
  • id: 4386199
    {'lmfdb_iso': '84966.cr', 'p': 29, 'prec': 20, 'unit': 101169577863989328676854333, 'val': 2}
  • id: 4386208
    {'lmfdb_iso': '84966.cr', 'p': 37, 'prec': 20, 'unit': 490067690869611988822916275948, 'val': 1}
  • id: 4386196
    {'lmfdb_iso': '84966.cr', 'p': 41, 'prec': 20, 'unit': 432612485887521470600187881893, 'val': 1}
  • id: 4386197
    {'lmfdb_iso': '84966.cr', 'p': 43, 'prec': 20, 'unit': 4082597386763843667418030291785, 'val': 1}
  • id: 4386202
    {'lmfdb_iso': '84966.cr', 'p': 53, 'prec': 20, 'unit': 63737894048598733908243183349793, 'val': 1}
  • id: 4386206
    {'lmfdb_iso': '84966.cr', 'p': 59, 'prec': 20, 'unit': 324387727560995429653053010586435, 'val': 1}
  • id: 4386207
    {'lmfdb_iso': '84966.cr', 'p': 61, 'prec': 20, 'unit': 5164761653864208103929633826569865, 'val': 1}
  • id: 4386193
    {'lmfdb_iso': '84966.cr', 'p': 67, 'prec': 20, 'unit': 30714344918892231606637004070168843, 'val': 1}
  • id: 4386195
    {'lmfdb_iso': '84966.cr', 'p': 71, 'prec': 20, 'unit': 68126545580724781902808066459285996, 'val': 1}
  • id: 4386203
    {'lmfdb_iso': '84966.cr', 'p': 73, 'prec': 20, 'unit': 150296777874462537373686005250221453, 'val': 1}
  • id: 4386192
    {'lmfdb_iso': '84966.cr', 'p': 83, 'prec': 20, 'unit': 816011460558663736936912262407822913, 'val': 1}
  • id: 4386205
    {'lmfdb_iso': '84966.cr', 'p': 89, 'prec': 20, 'unit': 4429790794639773571937714986946743267, 'val': 1}
  • id: 4386191
    {'lmfdb_iso': '84966.cr', 'p': 97, 'prec': 20, 'unit': 53814681425338189266323639788803735796, 'val': 1}