Elliptic curve data - 1045.b3

Formats: - HTML - YAML - JSON - 2023-06-04T12:02:01.310924

• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  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
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '1045b', 'Clabel': '1045b1', 'Cnumber': 1, 'absD': 47155625, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1672, 'ainvs': [1, -1, 0, -982409, -374543312], 'analytic_rank': 1, 'bad_primes': [5, 11, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 1045, 'degree': 4416, 'elladic_images': ['8.12.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7158240888248362330886097080', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 4], 'jinv': [104857852278310619039721, 47155625], 'lmfdb_iso': '1045.b', 'lmfdb_label': '1045.b3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -982409, -374543312], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.5', '44.12.0-4.c.1.2', '76.12.0.?', '88.24.0.?', '152.24.0.?', '418.6.0.?', '836.24.0.?', '1672.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '6.6552718759833089389679662935', 'prec': 100}, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.7158240888248362330886097080', 'prec': 100}, '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, -3, -3, 1, -1, 0, 2, 0, 0, -1, -6, -3, 1, -1], 'aplist': [1, 0, 1, 0, -1, 2, -6, 1, -8, -6, 4, -2, -10, 4, 0, -2, -8, 14, 8, -4, 2, -16, -4, 10, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 1045, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '1045.b', 'trace_hash': 89484167820100000}
• 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': '0.032333605306219705031373156762', 'prec': 107}, 'conductor': 1045, 'gens': [[13348, 1000658, 3]], 'heights': [{'__RealLiteral__': 0, 'data': '6.6552718759833089389679662935', 'prec': 100}], 'lmfdb_label': '1045.b3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.15164442574914819669892743864', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.0277046455138353542434232563698642628', 'prec': 130}, 'tamagawa_product': 12, 'torsion_generators': [[-572, 286, 1]], 'xcoord_integral_points': [-572]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 0], '3': [3, 3, 0], '5': [2, 0], '7': [3, 1, 0], '11': [1, 0], '13': [3, 0], '17': [1, 0], '19': [2, 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': '1045.b3'}
• ec_torsion_growth •

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

  
  
  • id: 50883
    {'degree': 2, 'field': [-52, -1, 1], 'lmfdb_label': '1045.b3', 'torsion': [2, 2]}
  • id: 50885
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '1045.b3', 'torsion': [4]}
  • id: 50884
    {'degree': 2, 'field': [5, -1, 1], 'lmfdb_label': '1045.b3', 'torsion': [4]}
  • id: 50886
    {'degree': 4, 'field': [4, 0, 15, 0, 1], 'lmfdb_label': '1045.b3', 'torsion': [2, 4]}
  • id: 50887
    {'degree': 4, 'field': [17, 13, -2, -1, 1], 'lmfdb_label': '1045.b3', 'torsion': [8]}
  • id: 50891
    {'degree': 8, 'field': [-3, 0, 3, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '1045.b3', 'torsion': [6]}
  • id: 50889
    {'degree': 8, 'field': [25, -70, 98, 192, 159, 40, 2, -2, 1], 'lmfdb_label': '1045.b3', 'torsion': [8]}
  • id: 50888
    {'degree': 8, 'field': [1126, -25178, -6583, 2788, 1172, -68, -58, -2, 1], 'lmfdb_label': '1045.b3', 'torsion': [2, 4]}
  • id: 50890
    {'degree': 8, 'field': [1472, 480, -575, 92, 114, -34, 8, -2, 1], 'lmfdb_label': '1045.b3', 'torsion': [2, 8]}
  • id: 50892
    {'degree': 16, 'field': [1, 0, 0, 0, -414, 0, 0, 0, 46195, 0, 0, 0, -414, 0, 0, 0, 1], 'lmfdb_label': '1045.b3', 'torsion': [4, 4]}
  • id: 50897
    {'degree': 16, 'field': [121, 0, 682, 0, 1951, 0, 1579, 0, -659, 0, -194, 0, 31, 0, 13, 0, 1], 'lmfdb_label': '1045.b3', 'torsion': [12]}
  • id: 50896
    {'degree': 16, 'field': [298615, -817030, 1390940, -1362714, 1266743, -844388, 539998, -267792, 129772, -50118, 18850, -5584, 1598, -336, 68, -8, 1], 'lmfdb_label': '1045.b3', 'torsion': [12]}
  • id: 50893
    {'degree': 16, 'field': [1638400, -1269760, 492032, -126656, 21924, -78300, 58994, 20258, 17253, -10170, 2216, -598, 47, -20, 8, -4, 1], 'lmfdb_label': '1045.b3', 'torsion': [2, 8]}
  • id: 50894
    {'degree': 16, 'field': [2650777, -305002, 3450662, -255956, 2048551, -189156, 829898, -155658, 249070, -29674, 44496, -2728, 2569, -144, 72, -2, 1], 'lmfdb_label': '1045.b3', 'torsion': [16]}
  • id: 50895
    {'degree': 16, 'field': [3685582681, 0, -2339734903, 0, 560816161, 0, -68680936, 0, 4994716, 0, -221734, 0, 6136, 0, -97, 0, 1], 'lmfdb_label': '1045.b3', 'torsion': [2, 6]}
• 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: 14672
    {'conductor': 1045, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '1045.b3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 14673
    {'conductor': 1045, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '1045.b3', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 14674
    {'conductor': 1045, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '1045.b3', 'prime': 19, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
• ec_galrep •

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

  
  
  • id: 1671142
    {'adelic_gens': [[1665, 8, 1664, 9], [1, 0, 8, 1], [7, 6, 1666, 1667], [1, 8, 0, 1], [1, 4, 4, 17], [217, 212, 214, 1047], [1372, 1, 783, 6], [1467, 1466, 1058, 219], [624, 3, 181, 2]], 'adelic_image': '1672.48.0.?', 'conductor': 1045, 'lmfdb_label': '1045.b3', 'prime': 0}
  • id: 4917
    {'conductor': 1045, 'elladic_image': '8.12.0.6', 'lmfdb_label': '1045.b3', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 23994
    {'lmfdb_iso': '1045.b', 'p': 13, 'prec': 20, 'unit': 48387134605679768859, 'val': 2}
  • id: 23996
    {'lmfdb_iso': '1045.b', 'p': 17, 'prec': 20, 'unit': 191137214908475878334340, 'val': 1}
  • id: 24000
    {'lmfdb_iso': '1045.b', 'p': 23, 'prec': 20, 'unit': 52267404802528728270645215, 'val': 1}
  • id: 23993
    {'lmfdb_iso': '1045.b', 'p': 29, 'prec': 20, 'unit': 345046209706737764912339412, 'val': 1}
  • id: 24004
    {'lmfdb_iso': '1045.b', 'p': 31, 'prec': 20, 'unit': 3004674695648024654684704016, 'val': 1}
  • id: 23989
    {'lmfdb_iso': '1045.b', 'p': 37, 'prec': 20, 'unit': 320574506802793872928771388581, 'val': 1}
  • id: 23991
    {'lmfdb_iso': '1045.b', 'p': 41, 'prec': 20, 'unit': 4066735298071223100663364986338, 'val': 1}
  • id: 23992
    {'lmfdb_iso': '1045.b', 'p': 43, 'prec': 20, 'unit': 5125273204847364618594856219046, 'val': 1}
  • id: 23998
    {'lmfdb_iso': '1045.b', 'p': 53, 'prec': 20, 'unit': 377670065232759768866330635460617, 'val': 1}
  • id: 24002
    {'lmfdb_iso': '1045.b', 'p': 59, 'prec': 20, 'unit': 1000491486374762276172043146605379, 'val': 1}
  • id: 24003
    {'lmfdb_iso': '1045.b', 'p': 61, 'prec': 20, 'unit': 5754969843246982122878775838516038, 'val': 1}
  • id: 23988
    {'lmfdb_iso': '1045.b', 'p': 67, 'prec': 20, 'unit': 28301498713088840152661408571871441, 'val': 1}
  • id: 23990
    {'lmfdb_iso': '1045.b', 'p': 71, 'prec': 20, 'unit': 60039084190142991816179459684766854, 'val': 1}
  • id: 23999
    {'lmfdb_iso': '1045.b', 'p': 73, 'prec': 20, 'unit': 42145099187000600724663795378224926, 'val': 1}
  • id: 23995
    {'lmfdb_iso': '1045.b', 'p': 79, 'prec': 20, 'unit': 906478283758850273845027919743210644, 'val': 1}
  • id: 23997
    {'lmfdb_iso': '1045.b', 'p': 83, 'prec': 20, 'unit': 2526386986941259054610109443020715574, 'val': 1}
  • id: 24001
    {'lmfdb_iso': '1045.b', 'p': 89, 'prec': 20, 'unit': 2614586800384778664805849348530802313, 'val': 1}
  • id: 23987
    {'lmfdb_iso': '1045.b', 'p': 97, 'prec': 20, 'unit': 8905861191286106034753378051279609720, 'val': 1}