Elliptic curve data - 1248.b2

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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': '1248h', 'Clabel': '1248h3', 'Cnumber': 3, 'abc_quality': 1.069422794221752, 'absD': 3158618112, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 312, 'ainvs': [0, -1, 0, -369, 513], 'analytic_rank': 1, 'bad_primes': [2, 3, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 1248, 'degree': 768, 'elladic_images': ['4.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.51271634234938137039558294885', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 4], 'jinv': [1360251712, 771147], 'lmfdb_iso': '1248.b', 'lmfdb_label': '1248.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -369, 513], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '12.24.0-12.h.1.2', '104.24.0.?', '312.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 9, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.7482494487637116152547544864', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 3], [3, 4, 416], [13, 14, 96]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.18043083821056393902164917261', 'prec': 107}, 'szpiro_ratio': 4.11663302972232, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
• 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, 0, -1, 0, -2, 0, 0, 0, 1, 0, 4, 0, 1, 0, 2, 0, -6, 0, -8, 0], 'aplist': [0, -1, -2, 0, 4, 1, -6, -8, 8, 2, 8, -10, 6, -4, 0, -14, -12, -10, -8, 0, -14, -4, 4, -10, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 1248, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '1248.b', 'trace_hash': 1985730887369394816}
• 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': '0.35864125324678496749312727713', 'prec': 103}, 'conductor': 1248, 'gens': [[1, 12, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.7482494487637116152547544864', 'prec': 100}], 'lmfdb_label': '1248.b2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.2206352993932699825054064318', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.1339749893058123379666515085619856063', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-7, 52, 1]], 'xcoord_integral_points': [-7, 1, 19, 32, 71]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [7, 0], '7': [1, 1, 0], '11': [1, 0], '13': [2, 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, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '1248.b2'}
• ec_torsion_growth •

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

  
  
  • id: 62081
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '1248.b2', 'torsion': [2, 4]}
  • id: 62082
    {'degree': 4, 'field': [27, 0, -2, 0, 1], 'lmfdb_label': '1248.b2', 'torsion': [8]}
  • id: 62086
    {'degree': 8, 'field': [-27, 0, 112, 0, -18, 0, 0, 0, 1], 'lmfdb_label': '1248.b2', 'torsion': [12]}
  • id: 62083
    {'degree': 8, 'field': [9, 0, 0, 0, 3, 0, 0, 0, 1], 'lmfdb_label': '1248.b2', 'torsion': [4, 4]}
  • id: 62084
    {'degree': 8, 'field': [900, 0, 768, 0, 124, 0, -16, 0, 1], 'lmfdb_label': '1248.b2', 'torsion': [2, 8]}
  • id: 62085
    {'degree': 8, 'field': [1764, 0, -1728, 0, 492, 0, -48, 0, 1], 'lmfdb_label': '1248.b2', 'torsion': [2, 8]}
  • id: 62088
    {'degree': 16, 'field': [1, 0, -8, 0, 10, 0, 128, 0, -289, 0, 128, 0, 10, 0, -8, 0, 1], 'lmfdb_label': '1248.b2', 'torsion': [2, 12]}
  • id: 62087
    {'degree': 16, 'field': [531441, 0, -157464, 0, 399492, 0, -647352, 0, 354294, 0, -23976, 0, 548, 0, -8, 0, 1], 'lmfdb_label': '1248.b2', 'torsion': [16]}
• 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: 18533
    {'conductor': 1248, 'conductor_valuation': 5, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '1248.b2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 18534
    {'conductor': 1248, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '1248.b2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 18535
    {'conductor': 1248, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '1248.b2', 'prime': 13, 'reduction_type': 1, '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: 1672413
    {'adelic_gens': [[7, 6, 306, 307], [212, 1, 127, 6], [1, 0, 8, 1], [1, 8, 0, 1], [203, 198, 122, 275], [1, 4, 4, 17], [145, 8, 268, 33], [120, 281, 265, 252], [305, 8, 304, 9]], 'adelic_image': '312.48.0.?', 'conductor': 1248, 'lmfdb_label': '1248.b2', 'prime': 0}
  • id: 5972
    {'conductor': 1248, 'elladic_image': '4.12.0.7', 'lmfdb_label': '1248.b2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 31208
    {'lmfdb_iso': '1248.b', 'p': 5, 'prec': 20, 'unit': 3625957518229, 'val': 2}
  • id: 31214
    {'lmfdb_iso': '1248.b', 'p': 11, 'prec': 20, 'unit': 16720180504261522195, 'val': 1}
  • id: 31215
    {'lmfdb_iso': '1248.b', 'p': 17, 'prec': 20, 'unit': 64980527083773441927791, 'val': 1}
  • id: 31216
    {'lmfdb_iso': '1248.b', 'p': 19, 'prec': 20, 'unit': 1951141508869496383516884, 'val': 1}
  • id: 31219
    {'lmfdb_iso': '1248.b', 'p': 23, 'prec': 20, 'unit': 10848580077386032315272860, 'val': 1}
  • id: 31212
    {'lmfdb_iso': '1248.b', 'p': 29, 'prec': 20, 'unit': 2499753086801128857628822663, 'val': 1}
  • id: 31209
    {'lmfdb_iso': '1248.b', 'p': 31, 'prec': 20, 'unit': 21412231363349312355950001445, 'val': 1}
  • id: 31223
    {'lmfdb_iso': '1248.b', 'p': 37, 'prec': 20, 'unit': 337551804064839068631208751645, 'val': 1}
  • id: 31210
    {'lmfdb_iso': '1248.b', 'p': 41, 'prec': 20, 'unit': 1106488553357419156744460003569, 'val': 1}
  • id: 31211
    {'lmfdb_iso': '1248.b', 'p': 43, 'prec': 20, 'unit': 1369254324316424664728226276254, 'val': 1}
  • id: 31217
    {'lmfdb_iso': '1248.b', 'p': 53, 'prec': 20, 'unit': 300745777217152588117141832641088, 'val': 1}
  • id: 31221
    {'lmfdb_iso': '1248.b', 'p': 59, 'prec': 20, 'unit': 961441938907187635044372085570207, 'val': 1}
  • id: 31222
    {'lmfdb_iso': '1248.b', 'p': 61, 'prec': 20, 'unit': 585154862878895221058908985868124, 'val': 1}
  • id: 31207
    {'lmfdb_iso': '1248.b', 'p': 67, 'prec': 20, 'unit': 39006545241781335751735567571841097, 'val': 1}
  • id: 31218
    {'lmfdb_iso': '1248.b', 'p': 73, 'prec': 20, 'unit': 406012153587619941512961668647962, 'val': 1}
  • id: 31213
    {'lmfdb_iso': '1248.b', 'p': 79, 'prec': 20, 'unit': 946826226350929109217855160251754706, 'val': 1}
  • id: 31206
    {'lmfdb_iso': '1248.b', 'p': 83, 'prec': 20, 'unit': 2604450885469249983399657058338027788, 'val': 1}
  • id: 31220
    {'lmfdb_iso': '1248.b', 'p': 89, 'prec': 20, 'unit': 7374977180978314546269441365072993249, 'val': 1}
  • id: 31205
    {'lmfdb_iso': '1248.b', 'p': 97, 'prec': 20, 'unit': 6378682102933110278174804954143592091, 'val': 1}