Elliptic curve data - 84966.cr3

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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': '84966da5', 'Cnumber': 5, 'abc_quality': 1.0817271650752718, 'absD': 596136658835743544641501531901448, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 1904, 'ainvs': [1, 1, 1, -4143565539, 1179186740968137], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 17], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 84966, 'degree': 424673280, 'elladic_images': ['16.48.0.204'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.9686907158787824552122508018', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 69, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [-2770540998624539614657, 209924951154647363208], 'lmfdb_iso': '84966.cr', 'lmfdb_label': '84966.cr3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -292604, -699871003], 'min_quad_twist_disc': -119, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.k.1', '16.48.0.e.1', '56.48.0-8.k.1.5', '112.96.0.?', '136.48.0.?', '272.96.1.?', '476.12.0.?', '952.96.0.?', '1904.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '34.693126836213004514000111233', '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': '2.5791289693230177625348071211', 'prec': 100}, 'szpiro_ratio': 7.306634721116032, '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, -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': '0.000048333704170044428722445692506', 'prec': 117}, 'conductor': 84966, 'gens': [[108345202723959421, 50786576560031714564434216, 1086405]], 'heights': [{'__RealLiteral__': 0, 'data': '34.693126836213004514000111233', 'prec': 100}], 'lmfdb_label': '84966.cr3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.013442544406826409471830071167', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.5963667772894519681476808109379452778', 'prec': 130}, 'tamagawa_product': 48, 'torsion_generators': [[-474653, 474649, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [11, 1], '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.cr3'}
• ec_torsion_growth •

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

  
  
  • id: 3984968
    {'degree': 2, 'field': [-119, 0, 1], 'lmfdb_label': '84966.cr3', 'torsion': [4]}
  • id: 3984967
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '84966.cr3', 'torsion': [2, 2]}
  • id: 3984969
    {'degree': 2, 'field': [238, 0, 1], 'lmfdb_label': '84966.cr3', 'torsion': [4]}
  • id: 3984971
    {'degree': 4, 'field': [25, 0, -24, 0, 1], 'lmfdb_label': '84966.cr3', 'torsion': [8]}
  • id: 3984972
    {'degree': 4, 'field': [242, -38, 39, -2, 1], 'lmfdb_label': '84966.cr3', 'torsion': [8]}
  • id: 3984970
    {'degree': 4, 'field': [3481, 0, 120, 0, 1], 'lmfdb_label': '84966.cr3', 'torsion': [2, 4]}
  • id: 3984977
    {'degree': 8, 'field': [86, -1019, 1064, -91, 49, -7, 7, -4, 1], 'lmfdb_label': '84966.cr3', 'torsion': [6]}
  • id: 3984974
    {'degree': 8, 'field': [5184, 0, 0, 0, 94, 0, 0, 0, 1], 'lmfdb_label': '84966.cr3', 'torsion': [8]}
  • id: 3984975
    {'degree': 8, 'field': [11762, 3092, -2730, -700, 291, 68, -18, -4, 1], 'lmfdb_label': '84966.cr3', 'torsion': [2, 8]}
  • id: 3984976
    {'degree': 8, 'field': [130202, 22136, -20514, -3184, 1443, 176, -54, -4, 1], 'lmfdb_label': '84966.cr3', 'torsion': [16]}
  • id: 3984973
    {'degree': 8, 'field': [813366, -107288, 112692, -10928, 5765, -364, 126, -4, 1], 'lmfdb_label': '84966.cr3', 'torsion': [2, 4]}
  • id: 3984982
    {'degree': 16, 'field': [1507202, -6630000, 14177148, -14978360, 16269458, -8485992, 6395124, -1710404, 1164267, -149804, 109200, -5508, 5266, -68, 120, 0, 1], 'lmfdb_label': '84966.cr3', 'torsion': [2, 16]}
  • id: 3984979
    {'degree': 16, 'field': [1679616, 0, -933120, 0, 259200, 0, -147600, 0, 55489, 0, -4100, 0, 200, 0, -20, 0, 1], 'lmfdb_label': '84966.cr3', 'torsion': [2, 8]}
  • id: 3984983
    {'degree': 16, 'field': [4944774, -4663572, 5950445, -2513644, 1054256, 387142, -361697, 183760, -24639, -17046, 6531, -2072, 679, -182, 46, -8, 1], 'lmfdb_label': '84966.cr3', 'torsion': [2, 6]}
  • id: 3984984
    {'degree': 16, 'field': [44520352, -57860336, 25676916, 59289804, -17206746, -14213970, 3553297, 1012504, -250314, -540, -1179, 624, -13, -70, 30, -8, 1], 'lmfdb_label': '84966.cr3', 'torsion': [12]}
  • id: 3984980
    {'degree': 16, 'field': [274193441, -349401544, -94723256, 119601392, -8022552, -35888088, -9825688, 1185376, 1132270, -85272, -136328, 8432, 8104, -136, -168, 0, 1], 'lmfdb_label': '84966.cr3', 'torsion': [16]}
  • id: 3984981
    {'degree': 16, 'field': [3716085564, -6587923104, 5233449872, -2626651328, 831175432, -154298816, 20839168, -265216, 1404000, -126448, 71288, -12320, 1308, -224, 0, 0, 1], 'lmfdb_label': '84966.cr3', 'torsion': [16]}
  • id: 3984985
    {'degree': 16, 'field': [6536715388, -2646178724, 2930249841, -572555556, 297629886, -14525658, 6377767, -1375376, 412023, -36990, -1017, 4512, -661, -70, 30, -8, 1], 'lmfdb_label': '84966.cr3', 'torsion': [12]}
  • id: 3984978
    {'degree': 16, 'field': [504993111858, -147794395992, 166477562132, -38693513976, 22722522122, -4214368208, 1681971216, -247197880, 74004611, -8431656, 1984792, -167352, 31714, -1792, 276, -8, 1], 'lmfdb_label': '84966.cr3', 'torsion': [4, 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: 2072158
    {'conductor': 84966, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '84966.cr3', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 2072159
    {'conductor': 84966, 'conductor_valuation': 1, 'discriminant_valuation': 32, 'j_denominator_valuation': 32, 'kodaira_symbol': 36, 'lmfdb_label': '84966.cr3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2072160
    {'conductor': 84966, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '84966.cr3', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2072161
    {'conductor': 84966, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '84966.cr3', '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: 2223748
    {'adelic_gens': [[5, 4, 1900, 1901], [1763, 1344, 224, 587], [1, 16, 0, 1], [543, 0, 0, 1903], [1716, 1701, 567, 1506], [1, 0, 16, 1], [1889, 16, 1888, 17], [1198, 1701, 1337, 1506], [15, 2, 1806, 1891]], 'adelic_image': '1904.192.1.?', 'conductor': 84966, 'lmfdb_label': '84966.cr3', 'prime': 0}
  • id: 346984
    {'conductor': 84966, 'elladic_image': '16.48.0.204', 'lmfdb_label': '84966.cr3', 'modell_image': '2B', '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}