Elliptic curve data - 1369.b1

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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': '1369c', 'Clabel': '1369c2', 'Cnumber': 2, 'abc_quality': 1.116627416496341, 'absD': 1369, 'adelic_genus': 6, 'adelic_index': 192, 'adelic_level': 2072, 'ainvs': [1, -1, 1, -1663, -25680], 'analytic_rank': 1, 'bad_primes': [37], 'class_deg': 7, 'class_size': 2, 'cm': 0, 'conductor': 1369, 'degree': 252, 'elladic_images': ['4.2.0.1', '7.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.26169607405070362892002534856', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 7, 'iso_nlabel': 1, 'isogeny_degrees': [1, 7], 'jinv': [-371323264041, 1], 'lmfdb_iso': '1369.b', 'lmfdb_label': '1369.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -1663, -25680], 'min_quad_twist_disc': 1, 'modell_images': ['7B'], 'modm_images': ['4.2.0.a.1', '7.8.0.a.1', '28.16.0.a.1', '56.32.0.b.1', '259.48.0.?', '296.4.0.?', '1036.96.2.?', '2072.192.6.?'], 'nonmax_primes': [2, 7], 'nonmax_rad': 14, 'num_bad_primes': 1, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.5879433756730922486890682491', 'prec': 100}, 'semistable': False, 'serre_invariants': [[37, 254, 1]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.34012357805666711180799059661', 'prec': 107}, 'szpiro_ratio': 4.688859661303817, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 2, 3, -3, 1, -2, 0, 2, -2, 0, -1, -3, 3, 6, 1], 'aplist': [-1, 0, -1, 2, -2, 2, -3, 6, 4, -9, 10, 0, -9, -2, 6, -2, 4, -1, -10, 6, -10, -10, -12, -7, -7], 'class_deg': 7, 'class_size': 2, 'conductor': 1369, 'isogeny_matrix': [[1, 7], [7, 1]], 'lmfdb_iso': '1369.b', 'trace_hash': 1165286420399210022}
• 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': '0.59250726283334364728250995730', 'prec': 103}, 'conductor': 1369, 'gens': [[75, 479, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '4.5879433756730922486890682491', 'prec': 100}], 'lmfdb_label': '1369.b1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.37382375965132293176986151217', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.7150822417614972297962238812747055669', 'prec': 130}, 'tamagawa_product': 1, 'torsion_generators': [], 'xcoord_integral_points': [75]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'o?', '3': [1, 1, 0], '5': [1, 0], '7': [1, 1], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [3, 0], '37': 'a', '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '1369.b1'}
• ec_torsion_growth •

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

  
  
  • id: 69112
    {'degree': 3, 'field': [26, -12, -1, 1], 'lmfdb_label': '1369.b1', 'torsion': [2]}
  • id: 69113
    {'degree': 6, 'field': [676, 0, 196, 0, 25, 0, 1], 'lmfdb_label': '1369.b1', 'torsion': [2, 2]}
  • id: 69114
    {'degree': 6, 'field': [23605, -1, 1051, 398, 22, -1, 1], 'lmfdb_label': '1369.b1', 'torsion': [7]}
  • id: 69115
    {'degree': 8, 'field': [-173, 104, -62, -85, 46, -7, 7, -4, 1], 'lmfdb_label': '1369.b1', 'torsion': [3]}
  • id: 69116
    {'degree': 12, 'field': [-1296, 1080, -5112, 2988, -656, -682, 474, -385, -47, 94, -6, -5, 1], 'lmfdb_label': '1369.b1', 'torsion': [4]}
  • id: 69117
    {'degree': 18, 'field': [48545701, -89197653, 308234022, -63215993, 78810363, 60163387, -7168923, -1237625, 3071651, -593050, 42724, -10592, 19025, -1701, 1451, -16, 48, -1, 1], 'lmfdb_label': '1369.b1', 'torsion': [14]}
• 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

  
  {'conductor': 1369, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '1369.b1', 'prime': 37, 'reduction_type': 0, '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: 1673213
    {'adelic_gens': [[1, 0, 28, 1], [1, 14, 14, 197], [297, 28, 0, 1], [1037, 5, 1043, 36], [2045, 28, 2044, 29], [1555, 28, 1813, 1], [565, 21, 1771, 1984], [1, 28, 0, 1], [8, 5, 1827, 1919]], 'adelic_image': '2072.192.6.?', 'conductor': 1369, 'lmfdb_label': '1369.b1', 'prime': 0}
  • id: 6673
    {'conductor': 1369, 'elladic_image': '4.2.0.1', 'lmfdb_label': '1369.b1', 'modell_image': '2G', 'prime': 2}
  • id: 6674
    {'conductor': 1369, 'elladic_image': '7.8.0.1', 'lmfdb_label': '1369.b1', 'modell_image': '7B', 'prime': 7}
• ec_padic •

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

  
  
  • id: 35544
    {'lmfdb_iso': '1369.b', 'p': 5, 'prec': 20, 'unit': 9364015982092, 'val': 1}
  • id: 35545
    {'lmfdb_iso': '1369.b', 'p': 7, 'prec': 20, 'unit': 4096677945410067, 'val': 1}
  • id: 35546
    {'lmfdb_iso': '1369.b', 'p': 11, 'prec': 20, 'unit': 47346101918957188962, 'val': 1}
  • id: 35547
    {'lmfdb_iso': '1369.b', 'p': 13, 'prec': 20, 'unit': 4389882784616862122, 'val': 1}
  • id: 35548
    {'lmfdb_iso': '1369.b', 'p': 17, 'prec': 20, 'unit': 135459844085014435636386, 'val': 1}
  • id: 35549
    {'lmfdb_iso': '1369.b', 'p': 19, 'prec': 20, 'unit': 1297776159979055075636143, 'val': 1}
  • id: 35550
    {'lmfdb_iso': '1369.b', 'p': 23, 'prec': 20, 'unit': 24967131136973274599078034, 'val': 1}
  • id: 35551
    {'lmfdb_iso': '1369.b', 'p': 29, 'prec': 20, 'unit': 111589857796362531170852046, 'val': 1}
  • id: 35552
    {'lmfdb_iso': '1369.b', 'p': 31, 'prec': 20, 'unit': 586560526283308657736802822, 'val': 2}
  • id: 35553
    {'lmfdb_iso': '1369.b', 'p': 41, 'prec': 20, 'unit': 2118144260905109605374366812287, 'val': 1}
  • id: 35554
    {'lmfdb_iso': '1369.b', 'p': 43, 'prec': 20, 'unit': 10539017820564547624733009124117, 'val': 1}
  • id: 35555
    {'lmfdb_iso': '1369.b', 'p': 47, 'prec': 20, 'unit': 14693601794947585263813058315476, 'val': 1}
  • id: 35556
    {'lmfdb_iso': '1369.b', 'p': 53, 'prec': 20, 'unit': 506913302695993600540767369324345, 'val': 1}
  • id: 35557
    {'lmfdb_iso': '1369.b', 'p': 59, 'prec': 20, 'unit': 538979322221496615938192302295789, 'val': 1}
  • id: 35558
    {'lmfdb_iso': '1369.b', 'p': 61, 'prec': 20, 'unit': 4815039213231832188869501971859848, 'val': 1}
  • id: 35559
    {'lmfdb_iso': '1369.b', 'p': 67, 'prec': 20, 'unit': 123351630331518781486132578927856, 'val': 1}
  • id: 35560
    {'lmfdb_iso': '1369.b', 'p': 71, 'prec': 20, 'unit': 4304660270766031892312253325918431, 'val': 1}
  • id: 35561
    {'lmfdb_iso': '1369.b', 'p': 73, 'prec': 20, 'unit': 111129033133485043518557017361671321, 'val': 1}
  • id: 35562
    {'lmfdb_iso': '1369.b', 'p': 79, 'prec': 20, 'unit': 866473633538161959973730947070881644, 'val': 1}
  • id: 35563
    {'lmfdb_iso': '1369.b', 'p': 83, 'prec': 20, 'unit': 1587931227299631392116231964669788325, 'val': 1}
  • id: 35564
    {'lmfdb_iso': '1369.b', 'p': 89, 'prec': 20, 'unit': 5283634830136805488010918396230801258, 'val': 1}
  • id: 35565
    {'lmfdb_iso': '1369.b', 'p': 97, 'prec': 20, 'unit': 23973370352797958397231993055216148837, 'val': 1}