Elliptic curve data - 48510.p3

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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': '48510y', 'Clabel': '48510y1', 'Cnumber': 1, 'abc_quality': 1.035653777739774, 'absD': 38462244393351905280000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1848, 'ainvs': [1, -1, 0, -17757315, 27216375381], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 48510, 'degree': 5160960, 'elladic_images': ['8.12.0.11'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.0851781893655168026257648653', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 15, 'isogeny_degrees': [1, 2, 4], 'jinv': [7220044159551112609, 448454983680000], 'lmfdb_iso': '48510.p', 'lmfdb_label': '48510.p3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -40266, 2921559], 'min_quad_twist_disc': 21, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.m.1', '66.6.0.a.1', '84.12.0.?', '132.12.0.?', '168.24.0.?', '264.24.0.?', '308.12.0.?', '616.24.0.?', '924.24.0.?', '1848.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 4851], [3, 8, 5390], [5, 6, 9702], [7, 26, 495], [11, 12, 4410]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.5629169705038053043754658751', 'prec': 100}, 'szpiro_ratio': 5.717631312785646, '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, -2, 0, 0, 1, 2, 0, -4, -1], 'aplist': [-1, 0, -1, 0, 1, -2, 2, -4, 4, -6, 0, -10, -6, -12, -4, 6, -4, -10, -12, 4, -10, 4, 4, 10, -18], '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.p', 'trace_hash': 293569726135198030}
• 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': '0.0020904908612667310630228840050', 'prec': 110}, 'conductor': 48510, 'gens': [], 'heights': [], 'lmfdb_label': '48510.p3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.11325746765735923533284943166', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.45302987062943694133139772665963982255', 'prec': 133}, 'tamagawa_product': 16, 'torsion_generators': [[2886, -1443, 1]], 'xcoord_integral_points': [2886]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [8, 0], '3': 'a', '5': [0, 0], '7': 'a', '11': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '48510.p3'}
• ec_torsion_growth •

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

  
  
  • id: 2360314
    {'degree': 2, 'field': [-19, -1, 1], 'lmfdb_label': '48510.p3', 'torsion': [4]}
  • id: 2360313
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '48510.p3', 'torsion': [2, 2]}
  • id: 2360315
    {'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '48510.p3', 'torsion': [4]}
  • id: 2360316
    {'degree': 4, 'field': [-17, 37, -16, -1, 1], 'lmfdb_label': '48510.p3', 'torsion': [2, 4]}
  • id: 2360320
    {'degree': 8, 'field': [-49922, 28325, -27608, -1435, 721, -7, 7, -4, 1], 'lmfdb_label': '48510.p3', 'torsion': [6]}
  • id: 2360319
    {'degree': 8, 'field': [729, 0, -426, 0, 175, 0, -22, 0, 1], 'lmfdb_label': '48510.p3', 'torsion': [8]}
  • id: 2360317
    {'degree': 8, 'field': [2046, 3366, 1749, 528, 196, 16, 18, -2, 1], 'lmfdb_label': '48510.p3', 'torsion': [2, 4]}
  • id: 2360318
    {'degree': 8, 'field': [51984, 0, -19728, 0, 2460, 0, -108, 0, 1], 'lmfdb_label': '48510.p3', 'torsion': [8]}
  • id: 2360324
    {'degree': 16, 'field': [-766115712, -2298901824, -2554138440, -1525212684, -710551620, -296028576, -66615740, -1409970, 516394, 274531, 142468, 18667, 265, 475, 19, -6, 1], 'lmfdb_label': '48510.p3', 'torsion': [2, 6]}
  • id: 2360325
    {'degree': 16, 'field': [-404161436, 1073057062, -1120515199, 532372296, -71586691, -18629956, -12372092, 16996692, -6390650, 1012620, -18662, -15332, 1592, 126, -31, -4, 1], 'lmfdb_label': '48510.p3', 'torsion': [12]}
  • id: 2360323
    {'degree': 16, 'field': [1089, 0, -189486, 0, 2658381, 0, -1818234, 0, 466492, 0, -56894, 0, 3453, 0, -98, 0, 1], 'lmfdb_label': '48510.p3', 'torsion': [2, 8]}
  • id: 2360326
    {'degree': 16, 'field': [142884, 0, -969213, 0, 897670, 0, -411159, 0, 74655, 0, -8431, 0, 735, 0, -42, 0, 1], 'lmfdb_label': '48510.p3', 'torsion': [12]}
  • id: 2360322
    {'degree': 16, 'field': [364681, 344530, 108075, -8694, -7851, -47676, -8378, 18328, 8598, -4008, -1266, 108, 341, -10, -21, -2, 1], 'lmfdb_label': '48510.p3', 'torsion': [2, 8]}
  • id: 2360321
    {'degree': 16, 'field': [1713481, 0, -897820, 0, 688930, 0, -63580, 0, 32803, 0, -7300, 0, 754, 0, -40, 0, 1], 'lmfdb_label': '48510.p3', '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: 1158379
    {'conductor': 48510, 'conductor_valuation': 1, 'discriminant_valuation': 28, 'j_denominator_valuation': 28, 'kodaira_symbol': 32, 'lmfdb_label': '48510.p3', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1158380
    {'conductor': 48510, 'conductor_valuation': 2, 'discriminant_valuation': 11, 'j_denominator_valuation': 5, 'kodaira_symbol': -9, 'lmfdb_label': '48510.p3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1158381
    {'conductor': 48510, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '48510.p3', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1158382
    {'conductor': 48510, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '48510.p3', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1158383
    {'conductor': 48510, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '48510.p3', '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: 1987121
    {'adelic_gens': [[1, 0, 8, 1], [1625, 1092, 1358, 1751], [1, 8, 0, 1], [1841, 8, 1840, 9], [1, 4, 4, 17], [7, 6, 1842, 1843], [1688, 1323, 1253, 1058], [608, 525, 875, 790], [1163, 630, 434, 827], [263, 0, 0, 1847]], 'adelic_image': '1848.48.0.?', 'conductor': 48510, 'lmfdb_label': '48510.p3', 'prime': 0}
  • id: 209250
    {'conductor': 48510, 'elladic_image': '8.12.0.11', 'lmfdb_label': '48510.p3', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 48510.p does not appear in ec_padic