Elliptic curve data - 2178.b3

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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': '2178c', 'Clabel': '2178c1', 'Cnumber': 1, 'abc_quality': 0.9258126221887728, 'absD': 1534263947172, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 264, 'ainvs': [1, -1, 0, -6012, 170748], 'analytic_rank': 1, 'bad_primes': [2, 3, 11], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 2178, 'degree': 3840, 'elladic_images': ['8.6.0.4', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0888706622439055104680924364', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [18609625, 1188], 'lmfdb_iso': '2178.b', 'lmfdb_label': '2178.b3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -6, 4], 'min_quad_twist_disc': 33, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.24.0-6.a.1.1', '8.6.0.d.1', '24.48.0-24.bx.1.2', '33.8.0-3.a.1.1', '66.48.0-66.b.1.2', '264.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 9, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.67332407801527524105707663771', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.65938311848933460726050197104', 'prec': 107}, 'szpiro_ratio': 4.907290967511425, '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, 0, 0, -2, -1, 0, 0, 0, 0, 4, 2, 0, 1, -6, 0, 4, 0], 'aplist': [-1, 0, 0, -2, 0, 4, -6, 4, -6, 6, 8, -10, 6, -8, 6, 0, 0, -8, -4, -6, -2, -14, -12, 6, 14], 'class_deg': 6, 'class_size': 4, 'conductor': 2178, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '2178.b', 'trace_hash': 1881539073645770731}
• 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': '0.11329714334197278138730454797', 'prec': 103}, 'conductor': 2178, 'gens': [[58, 92, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.67332407801527524105707663771', 'prec': 103}], 'lmfdb_label': '2178.b3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.83253487486399895363420441197', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.2422631081334585670027446105051312974', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[36, -18, 1]], 'xcoord_integral_points': [-63, 18, 36, 58, 157]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': 'a', '5': [1, 7, 0], '7': [1, 0], '11': 'a', '13': [1, 0], '17': [1, 0], '19': [3, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '2178.b3'}
• ec_torsion_growth •

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

  
  
  • id: 110624
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '2178.b3', 'torsion': [2, 6]}
  • id: 110625
    {'degree': 4, 'field': [1, -2, 5, -2, 1], 'lmfdb_label': '2178.b3', 'torsion': [4]}
  • id: 110626
    {'degree': 6, 'field': [15, -6, 23, -4, 9, -2, 1], 'lmfdb_label': '2178.b3', 'torsion': [6]}
  • id: 110627
    {'degree': 8, 'field': [4, 0, -79, 0, -45, 0, 23, 0, 1], 'lmfdb_label': '2178.b3', 'torsion': [2, 12]}
  • id: 110628
    {'degree': 8, 'field': [187, 88, -40, -92, 37, 8, 2, -4, 1], 'lmfdb_label': '2178.b3', 'torsion': [2, 12]}
  • id: 110629
    {'degree': 12, 'field': [36, -36, -12, -12, 52, -18, 23, -39, 18, -9, 8, -3, 1], 'lmfdb_label': '2178.b3', 'torsion': [6, 6]}
  • id: 110630
    {'degree': 16, 'field': [51756, -10320, 58648, -45920, 12678, 2872, -844, 5664, -5339, -500, 1762, -456, -141, 88, -6, -4, 1], 'lmfdb_label': '2178.b3', 'torsion': [8]}
  • id: 110631
    {'degree': 18, 'field': [729, 2187, -1458, -2673, 11178, 12393, 5130, -2187, 1782, 1287, 3861, 1404, -1068, -432, 0, 78, 9, -9, 1], 'lmfdb_label': '2178.b3', 'torsion': [2, 18]}
• 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: 36380
    {'conductor': 2178, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '2178.b3', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 36381
    {'conductor': 2178, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '2178.b3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 36382
    {'conductor': 2178, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '2178.b3', 'prime': 11, 'reduction_type': 0, '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: 1678144
    {'adelic_gens': [[214, 253, 99, 20], [253, 12, 252, 13], [134, 261, 219, 8], [15, 58, 230, 5], [133, 12, 6, 73], [1, 0, 12, 1], [11, 2, 214, 255], [1, 6, 6, 37], [1, 12, 0, 1]], 'adelic_image': '264.96.1.?', 'conductor': 2178, 'lmfdb_label': '2178.b3', 'prime': 0}
  • id: 10712
    {'conductor': 2178, 'elladic_image': '8.6.0.4', 'lmfdb_label': '2178.b3', 'modell_image': '2B', 'prime': 2}
  • id: 10713
    {'conductor': 2178, 'elladic_image': '3.4.0.1', 'lmfdb_label': '2178.b3', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 64819
    {'lmfdb_iso': '2178.b', 'p': 7, 'prec': 20, 'unit': 4733917036902062, 'val': 1}
  • id: 64823
    {'lmfdb_iso': '2178.b', 'p': 13, 'prec': 20, 'unit': 534425278979363908254, 'val': 1}
  • id: 64825
    {'lmfdb_iso': '2178.b', 'p': 17, 'prec': 20, 'unit': 232738510502679628123994, 'val': 1}
  • id: 64826
    {'lmfdb_iso': '2178.b', 'p': 19, 'prec': 20, 'unit': 37539646801610621067071, 'val': 2}
  • id: 64828
    {'lmfdb_iso': '2178.b', 'p': 23, 'prec': 20, 'unit': 69731302777042717344121632, 'val': 1}
  • id: 64822
    {'lmfdb_iso': '2178.b', 'p': 29, 'prec': 20, 'unit': 4862172188477876170236351120, 'val': 1}
  • id: 64833
    {'lmfdb_iso': '2178.b', 'p': 31, 'prec': 20, 'unit': 589527804319077714401648826, 'val': 1}
  • id: 64818
    {'lmfdb_iso': '2178.b', 'p': 37, 'prec': 20, 'unit': 198967888693154377512350083363, 'val': 1}
  • id: 64820
    {'lmfdb_iso': '2178.b', 'p': 41, 'prec': 20, 'unit': 3794366951632934149810641230327, 'val': 1}
  • id: 64821
    {'lmfdb_iso': '2178.b', 'p': 43, 'prec': 20, 'unit': 5061967979879965323158120132853, 'val': 1}
  • id: 64824
    {'lmfdb_iso': '2178.b', 'p': 47, 'prec': 20, 'unit': 37807458090552598670694674312699, 'val': 1}
  • id: 64832
    {'lmfdb_iso': '2178.b', 'p': 61, 'prec': 20, 'unit': 3553920229639603598791482009970114, 'val': 1}
  • id: 64817
    {'lmfdb_iso': '2178.b', 'p': 67, 'prec': 20, 'unit': 35716218934607271394284273696573894, 'val': 1}
  • id: 64830
    {'lmfdb_iso': '2178.b', 'p': 71, 'prec': 20, 'unit': 89728374497656915191707462981134519, 'val': 1}
  • id: 64827
    {'lmfdb_iso': '2178.b', 'p': 73, 'prec': 20, 'unit': 223129496983927045255470293673195710, 'val': 1}
  • id: 64831
    {'lmfdb_iso': '2178.b', 'p': 79, 'prec': 20, 'unit': 123436564281973993667965983804405010, 'val': 1}
  • id: 64816
    {'lmfdb_iso': '2178.b', 'p': 83, 'prec': 20, 'unit': 2658532458602766491971760917889734949, 'val': 1}
  • id: 64829
    {'lmfdb_iso': '2178.b', 'p': 89, 'prec': 20, 'unit': 10511035686934997067329461004620302011, 'val': 1}
  • id: 64815
    {'lmfdb_iso': '2178.b', 'p': 97, 'prec': 20, 'unit': 39315278034250370754872399715570436077, 'val': 1}