Elliptic curve data - 51480.bb4

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '51480bu', 'Clabel': '51480bu1', 'Cnumber': 1, 'abc_quality': 0.9550957138890439, 'absD': 30345227955900000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 3432, 'ainvs': [0, 0, 0, -822207, -390626494], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 11, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 51480, 'degree': 1376256, 'elladic_images': ['4.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4435050976859057687502500590', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 27, 'isogeny_degrees': [1, 2, 4], 'jinv': [-329381898333928144, 162600887109375], 'lmfdb_iso': '51480.bb', 'lmfdb_label': '51480.bb4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -91356, 14498100], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '78.6.0.?', '156.24.0.?', '264.24.0.?', '1144.24.0.?', '3432.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.4321008329785540501078060262', 'prec': 100}, 'szpiro_ratio': 4.893531345682957, '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, 0, 0, 1, 0, -4, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 4, 0], 'aplist': [0, 0, 1, -4, 1, 1, 2, 4, 4, -6, 0, 10, 10, 4, 0, -10, 12, -2, 8, 8, -2, -16, 12, 10, -14], 'class_deg': 4, 'class_size': 4, 'conductor': 51480, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '51480.bb', 'trace_hash': 250021476196467731}
• 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': '0.0075439437089880661892845627456', 'prec': 110}, 'conductor': 51480, 'gens': [], 'heights': [], 'lmfdb_label': '51480.bb4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.077455299338461193586429753420', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.4785695788307581947657521094229239310', 'prec': 130}, 'tamagawa_product': 512, 'torsion_generators': [[2737, 133650, 1]], 'xcoord_integral_points': [1087, 2737]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '11': [1, 0], '13': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '51480.bb4'}
• ec_torsion_growth •

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

  
  
  • id: 2495276
    {'degree': 2, 'field': [10, -1, 1], 'lmfdb_label': '51480.bb4', 'torsion': [2, 4]}
  • id: 2495277
    {'degree': 4, 'field': [510, -132, -18, 0, 1], 'lmfdb_label': '51480.bb4', 'torsion': [8]}
  • id: 2495281
    {'degree': 8, 'field': [-1299571, 271336, -78182, -8204, 1400, 374, -94, -2, 1], 'lmfdb_label': '51480.bb4', 'torsion': [12]}
  • id: 2495278
    {'degree': 8, 'field': [100, -20, 2, 34, -11, -10, 8, -4, 1], 'lmfdb_label': '51480.bb4', 'torsion': [4, 4]}
  • id: 2495280
    {'degree': 8, 'field': [3025, 0, 10274, 0, 8754, 0, -94, 0, 1], 'lmfdb_label': '51480.bb4', 'torsion': [2, 8]}
  • id: 2495279
    {'degree': 8, 'field': [203401, 0, 5830, 0, 1698, 0, 70, 0, 1], 'lmfdb_label': '51480.bb4', 'torsion': [2, 8]}
  • id: 2495283
    {'degree': 16, 'field': [564536356362, 1501799978052, 1030961837322, -5439376818, -65422409832, -5482291536, 236945424, 115999122, 36638727, -676512, -206292, 28698, 6916, -74, -106, -4, 1], 'lmfdb_label': '51480.bb4', 'torsion': [2, 12]}
  • id: 2495282
    {'degree': 16, 'field': [74432182924000, -188350054006400, 35249915405760, -9869092245760, 2463415366784, 1386345232320, 71171457760, 4979230336, 46817928, 50912416, 3563632, 2290416, 104216, 7808, 672, -8, 1], 'lmfdb_label': '51480.bb4', '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: 1232425
    {'conductor': 51480, 'conductor_valuation': 3, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -5, 'lmfdb_label': '51480.bb4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1232426
    {'conductor': 51480, 'conductor_valuation': 2, 'discriminant_valuation': 13, 'j_denominator_valuation': 7, 'kodaira_symbol': -11, 'lmfdb_label': '51480.bb4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1232427
    {'conductor': 51480, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '51480.bb4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 1232428
    {'conductor': 51480, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '51480.bb4', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1232429
    {'conductor': 51480, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '51480.bb4', 'prime': 13, '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: 2006183
    {'adelic_gens': [[7, 6, 3426, 3427], [2153, 2148, 2150, 431], [3425, 8, 3424, 9], [937, 8, 316, 33], [1, 0, 8, 1], [3011, 3006, 434, 2147], [1, 8, 0, 1], [1, 4, 4, 17], [268, 1, 2399, 6], [1136, 3429, 1139, 3430]], 'adelic_image': '3432.48.0.?', 'conductor': 51480, 'lmfdb_label': '51480.bb4', 'prime': 0}
  • id: 220462
    {'conductor': 51480, 'elladic_image': '4.12.0.7', 'lmfdb_label': '51480.bb4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 51480.bb does not appear in ec_padic