Elliptic curve data - 48510.cp1

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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': '48510da', 'Clabel': '48510da4', 'Cnumber': 4, 'abc_quality': 0.973105158996098, 'absD': 88106467303053322200, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1848, 'ainvs': [1, -1, 1, -5372933, 4773660581], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 48510, 'degree': 2359296, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.6730671515783893457835346084', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 67, 'isogeny_degrees': [1, 2, 4], 'jinv': [200005594092187129, 1027287538200], 'lmfdb_iso': '48510.cp', 'lmfdb_label': '48510.cp1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -12183, 510237], 'min_quad_twist_disc': 21, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0.bb.1', '56.12.0-4.c.1.5', '88.12.0.?', '168.24.0.?', '264.24.0.?', '616.24.0.?', '924.12.0.?', '1848.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 4851], [3, 8, 2695], [5, 6, 9702], [7, 32, 990], [11, 12, 4410]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1508059327166778475332356182', 'prec': 100}, 'szpiro_ratio': 5.385246807318771, '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, -1, 0, 0, 1, 0, -1, -1, 0, 6, 0, 0, 1, 6, 0, 0, -1], 'aplist': [1, 0, -1, 0, -1, 6, 6, 0, 4, -2, 0, -2, -2, -8, 12, 6, 4, -2, -12, 4, 6, 8, 12, -6, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 48510, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '48510.cp', 'trace_hash': 676046133061221199}
• 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': '0.0047665414347633592887758597124', 'prec': 110}, 'conductor': 48510, 'gens': [], 'heights': [], 'lmfdb_label': '48510.cp1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.19221283401809428352217502177', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.6131080164342628045322005225736056166', 'prec': 130}, 'tamagawa_product': 96, 'torsion_generators': [[5643, -5647, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [6, 0], '3': 'a', '5': [0, 0], '7': 'a', '11': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '48510.cp1'}
• ec_torsion_growth •

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

  
  
  • id: 2361926
    {'degree': 2, 'field': [-231, 0, 1], 'lmfdb_label': '48510.cp1', 'torsion': [4]}
  • id: 2361927
    {'degree': 2, 'field': [-42, 0, 1], 'lmfdb_label': '48510.cp1', 'torsion': [4]}
  • id: 2361925
    {'degree': 2, 'field': [-22, 0, 1], 'lmfdb_label': '48510.cp1', 'torsion': [2, 2]}
  • id: 2361928
    {'degree': 4, 'field': [25, 0, -32, 0, 1], 'lmfdb_label': '48510.cp1', 'torsion': [2, 4]}
  • id: 2361930
    {'degree': 8, 'field': [576, 0, -59952, 0, 7633, 0, -197, 0, 1], 'lmfdb_label': '48510.cp1', 'torsion': [8]}
  • id: 2361931
    {'degree': 8, 'field': [4456, -2048, 2584, -1112, 657, -124, 46, -4, 1], 'lmfdb_label': '48510.cp1', 'torsion': [8]}
  • id: 2361932
    {'degree': 8, 'field': [8015, 9639, 12607, 4424, 1092, -392, -31, -3, 1], 'lmfdb_label': '48510.cp1', 'torsion': [6]}
  • id: 2361929
    {'degree': 8, 'field': [594636, 425040, 134920, 14080, -488, -440, 20, 0, 1], 'lmfdb_label': '48510.cp1', 'torsion': [2, 4]}
  • id: 2361934
    {'degree': 16, 'field': [46656, 0, -2567808, 0, 16244704, 0, -26883072, 0, 4861044, 0, -345512, 0, 11592, 0, -180, 0, 1], 'lmfdb_label': '48510.cp1', 'torsion': [2, 8]}
  • id: 2361935
    {'degree': 16, 'field': [2240602, -3882424, 6865812, -6644408, 5011938, -2002896, 589456, 137704, -116085, 44312, 712, -4536, 210, 224, -12, -8, 1], 'lmfdb_label': '48510.cp1', 'torsion': [2, 8]}
  • id: 2361938
    {'degree': 16, 'field': [14561731584, 0, -4793207424, 0, 310510720, 0, -26226528, 0, 828720, 0, -96248, 0, 2220, 0, -84, 0, 1], 'lmfdb_label': '48510.cp1', 'torsion': [12]}
  • id: 2361933
    {'degree': 16, 'field': [62473002916, 49049403040, 19255068800, 10850762560, 3502982924, 96525440, -61564800, -17490880, 3355101, 817960, 96800, -11440, -2406, -440, 0, 0, 1], 'lmfdb_label': '48510.cp1', 'torsion': [4, 4]}
  • id: 2361936
    {'degree': 16, 'field': [226158129675, -662504261850, 267460400175, 29515121010, -29112153675, 1732873440, 1001509758, -143679084, 968762, 3130236, -927986, -24440, 24483, 326, -229, -6, 1], 'lmfdb_label': '48510.cp1', 'torsion': [2, 6]}
  • id: 2361937
    {'degree': 16, 'field': [22416182850000, -24916916396880, 7846158208296, -806862594504, 18868569456, 6581083092, -2852154122, -22777050, 53506555, -4998610, 1233745, -4750, -7538, -268, -53, -6, 1], 'lmfdb_label': '48510.cp1', 'torsion': [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: 1159104
    {'conductor': 48510, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '48510.cp1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 1159105
    {'conductor': 48510, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '48510.cp1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1159106
    {'conductor': 48510, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '48510.cp1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1159107
    {'conductor': 48510, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '48510.cp1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1159108
    {'conductor': 48510, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '48510.cp1', 'prime': 11, '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: 1986969
    {'adelic_gens': [[960, 833, 91, 78], [1, 0, 8, 1], [1, 8, 0, 1], [1841, 8, 1840, 9], [1, 4, 4, 17], [7, 6, 1842, 1843], [1688, 1323, 1253, 1058], [263, 0, 0, 1847], [1231, 784, 700, 1287], [232, 371, 763, 792]], 'adelic_image': '1848.48.0.?', 'conductor': 48510, 'lmfdb_label': '48510.cp1', 'prime': 0}
  • id: 209078
    {'conductor': 48510, 'elladic_image': '4.6.0.1', 'lmfdb_label': '48510.cp1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 48510.cp does not appear in ec_padic