Elliptic curve data - 303450.bc5

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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': '303450bc', 'Clabel': '303450bc1', 'Cnumber': 1, 'abc_quality': 1.0214246831520672, 'absD': 20919897414359580672000000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 1360, 'ainvs': [1, 1, 0, -507513050, 4394954356500], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 17], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 303450, 'degree': 141557760, 'elladic_images': ['16.48.0.102'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.7607338267282580258341059145', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 28, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [38331145780597164097, 55468445663232], 'lmfdb_iso': '303450.bc', 'lmfdb_label': '303450.bc5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -70244, 7127525], 'min_quad_twist_disc': 85, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.bb.1', '16.48.0.z.1', '20.12.0-4.c.1.2', '34.6.0.a.1', '40.48.0-8.bb.1.2', '68.12.0.g.1', '80.96.0.?', '136.48.0.?', '272.96.1.?', '340.24.0.?', '680.96.0.?', '1360.192.1.?'], '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, 7225], [3, 4, 50575], [5, 14, 12138], [7, 8, 43350], [17, 162, 1050]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.5394081984830997984089589390', 'prec': 100}, 'szpiro_ratio': 5.683978482896629, '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, 0, 1, 1, -1, 1, 0, -4, -1, 2, -1, 0, 1, 0, -1, 4, 0], 'aplist': [-1, -1, 0, 1, -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': 303450, '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': '303450.bc', 'trace_hash': 491839761309427564}
• 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': '0.00054133748670449760169139175607', 'prec': 113}, 'conductor': 303450, 'gens': [], 'heights': [], 'lmfdb_label': '303450.bc5', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.068069506231277578827100885474', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0891120997004412612336141675806873215', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[13380, -6690, 1]], 'xcoord_integral_points': [13380]}
• lmfdb_label 303450.bc5 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 12826702
    {'degree': 2, 'field': [-21, -1, 1], 'lmfdb_label': '303450.bc5', 'torsion': [8]}
  • id: 12826701
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '303450.bc5', 'torsion': [2, 2]}
  • id: 12826703
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '303450.bc5', 'torsion': [4]}
  • id: 12826704
    {'degree': 4, 'field': [9, 0, -11, 0, 1], 'lmfdb_label': '303450.bc5', 'torsion': [2, 8]}
  • id: 12826708
    {'degree': 8, 'field': [-4099116, -116019, -137096, -36774, -1815, -423, -54, 0, 1], 'lmfdb_label': '303450.bc5', 'torsion': [6]}
  • id: 12826707
    {'degree': 8, 'field': [-33124, 30576, 2590, -9184, 1985, 290, -93, -2, 1], 'lmfdb_label': '303450.bc5', 'torsion': [16]}
  • id: 12826706
    {'degree': 8, 'field': [829, -238, 788, -374, 105, -34, 12, 0, 1], 'lmfdb_label': '303450.bc5', 'torsion': [8]}
  • id: 12826705
    {'degree': 8, 'field': [1636, -124, -534, 290, 41, -22, 12, -4, 1], 'lmfdb_label': '303450.bc5', 'torsion': [2, 4]}
  • id: 12826709
    {'degree': 16, 'field': [441, 0, 3124, 0, 6898, 0, 1940, 0, -685, 0, -52, 0, 50, 0, -8, 0, 1], 'lmfdb_label': '303450.bc5', 'torsion': [4, 8]}
  • id: 12826711
    {'degree': 16, 'field': [14519, 124604, 183798, -410408, -391534, 579480, 167550, -319780, 6043, 69984, -9666, -6756, 1308, 284, -64, -4, 1], 'lmfdb_label': '303450.bc5', 'torsion': [2, 16]}
  • id: 12826715
    {'degree': 16, 'field': [369344, -2777552, 9899308, -22638998, -61029063, 90281314, -24207832, -11112784, 5601570, -45112, -228746, -2378, 7896, -32, -118, -2, 1], 'lmfdb_label': '303450.bc5', 'torsion': [12]}
  • id: 12826712
    {'degree': 16, 'field': [2782561, -1483014, 1883338, -769430, 415048, -166156, 89672, -19802, 19641, -3764, 1984, -514, 160, -46, 6, -4, 1], 'lmfdb_label': '303450.bc5', 'torsion': [16]}
  • id: 12826710
    {'degree': 16, 'field': [41967275, -550529700, 2197108410, -2315138280, 1065905226, -234575888, 8097874, 12826540, -4547693, 506888, 101010, -39700, 2848, 724, -112, -4, 1], 'lmfdb_label': '303450.bc5', 'torsion': [2, 16]}
  • id: 12826713
    {'degree': 16, 'field': [115906756, 0, -829079401, 0, -45456758, 0, -3685983, 0, 399195, 0, 11973, 0, 1387, 0, -34, 0, 1], 'lmfdb_label': '303450.bc5', 'torsion': [2, 6]}
  • id: 12826714
    {'degree': 16, 'field': [45193657744, 0, -15188041253, 0, 2445719986, 0, -233680467, 0, 14022675, 0, -535791, 0, 12679, 0, -170, 0, 1], 'lmfdb_label': '303450.bc5', 'torsion': [24]}
• 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: 7514450
    {'conductor': 303450, 'conductor_valuation': 1, 'discriminant_valuation': 24, 'j_denominator_valuation': 24, 'kodaira_symbol': 28, 'lmfdb_label': '303450.bc5', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 7514451
    {'conductor': 303450, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '303450.bc5', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 7514452
    {'conductor': 303450, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '303450.bc5', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 7514453
    {'conductor': 303450, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '303450.bc5', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 7514454
    {'conductor': 303450, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '303450.bc5', 'prime': 17, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 3571305
    {'adelic_gens': [[15, 2, 1262, 1347], [543, 0, 0, 1359], [1, 16, 0, 1], [1201, 560, 1330, 111], [1345, 16, 1344, 17], [1, 560, 340, 341], [5, 4, 1356, 1357], [1, 0, 16, 1], [1064, 815, 545, 534]], 'adelic_image': '1360.192.1.?', 'conductor': 303450, 'lmfdb_label': '303450.bc5', 'prime': 0}
  • id: 1068196
    {'conductor': 303450, 'elladic_image': '16.48.0.102', 'lmfdb_label': '303450.bc5', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 303450.bc does not appear in ec_padic