Elliptic curve data - 392.d4

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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': '392a', 'Clabel': '392a1', 'Cnumber': 1, 'abc_quality': 0.8915192755066496, 'absD': 210827008, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 56, 'ainvs': [0, 0, 0, 49, -686], 'analytic_rank': 1, 'bad_primes': [2, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 392, 'degree': 96, 'elladic_images': ['8.24.0.51'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.27777506716912385478890071327', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 3, 'isogeny_degrees': [1, 2, 4], 'jinv': [432, 7], 'lmfdb_iso': '392.d', 'lmfdb_label': '392.d4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, 1, 2], 'min_quad_twist_disc': -7, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '8.24.0-8.p.1.8', '14.6.0.b.1', '28.24.0-28.g.1.2', '56.48.0-56.bn.1.4'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 9, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.8919590029013207883469938310', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1572781277318296707085970728', 'prec': 103}, 'szpiro_ratio': 4.45214118997548, '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, -2, 0, 0, 0, -3, 0, -4, 0, -2, 0, 0, 0, 6, 0, -8, 0], 'aplist': [0, 0, -2, 0, -4, -2, 6, -8, 0, 6, -8, -2, -2, -4, 8, 6, 0, 6, -4, -8, -10, 16, -8, 6, 6], 'class_deg': 4, 'class_size': 4, 'conductor': 392, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '392.d', 'trace_hash': 171845760336522473}
• 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': '0.57375653118783894446137498368', 'prec': 103}, 'conductor': 392, 'gens': [[9, 22, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.8919590029013207883469938310', 'prec': 100}], 'lmfdb_label': '392.d4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.86788635344346877622337901890', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.6420053998925684615630104991172591612', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[21, 98, 1]], 'xcoord_integral_points': [7, 9, 21, 70, 105]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 1, 0], '5': [1, 0], '7': 'a', '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '392.d4'}
• ec_torsion_growth •

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

  
  
  • id: 17073
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '392.d4', 'torsion': [2, 4]}
  • id: 17074
    {'degree': 4, 'field': [-14, -28, -14, 0, 1], 'lmfdb_label': '392.d4', 'torsion': [8]}
  • id: 17078
    {'degree': 8, 'field': [1, -4, 4, -10, 4, -10, 4, -4, 1], 'lmfdb_label': '392.d4', 'torsion': [12]}
  • id: 17075
    {'degree': 8, 'field': [1, -2, 2, 4, -1, 4, 2, -2, 1], 'lmfdb_label': '392.d4', 'torsion': [4, 4]}
  • id: 17077
    {'degree': 8, 'field': [1, 0, -10, 0, 34, 0, -10, 0, 1], 'lmfdb_label': '392.d4', 'torsion': [2, 8]}
  • id: 17076
    {'degree': 8, 'field': [1, 0, 2, 0, 10, 0, 2, 0, 1], 'lmfdb_label': '392.d4', 'torsion': [2, 8]}
  • id: 17079
    {'degree': 16, 'field': [-686, 0, 8232, 16464, 7056, -9800, -10584, -784, 3318, 1512, -196, -280, -28, 0, 0, 0, 1], 'lmfdb_label': '392.d4', 'torsion': [16]}
  • id: 17080
    {'degree': 16, 'field': [9, 0, -36, 0, 324, 0, -72, 0, 30, 0, 12, 0, -12, 0, 0, 0, 1], 'lmfdb_label': '392.d4', 'torsion': [2, 12]}
• 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: 4009
    {'conductor': 392, 'conductor_valuation': 3, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -5, 'lmfdb_label': '392.d4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4010
    {'conductor': 392, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '392.d4', 'prime': 7, '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: 1667480
    {'adelic_gens': [[43, 38, 26, 51], [32, 53, 27, 54], [25, 24, 6, 31], [49, 8, 48, 9], [1, 0, 8, 1], [1, 4, 4, 17], [7, 6, 50, 51], [1, 8, 0, 1]], 'adelic_image': '56.48.0.?', 'conductor': 392, 'lmfdb_label': '392.d4', 'prime': 0}
  • id: 1665
    {'conductor': 392, 'elladic_image': '8.24.0.51', 'lmfdb_label': '392.d4', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 5103
    {'lmfdb_iso': '392.d', 'p': 5, 'prec': 20, 'unit': 5581105134299, 'val': 1}
  • id: 5102
    {'lmfdb_iso': '392.d', 'p': 11, 'prec': 20, 'unit': 39707177801364606527, 'val': 1}
  • id: 5109
    {'lmfdb_iso': '392.d', 'p': 13, 'prec': 20, 'unit': 22249774164019452065, 'val': 1}
  • id: 5111
    {'lmfdb_iso': '392.d', 'p': 17, 'prec': 20, 'unit': 113779041314068103226971, 'val': 1}
  • id: 5112
    {'lmfdb_iso': '392.d', 'p': 19, 'prec': 20, 'unit': 1591711133029548854341520, 'val': 1}
  • id: 5108
    {'lmfdb_iso': '392.d', 'p': 29, 'prec': 20, 'unit': 5269160424369951168816214213, 'val': 1}
  • id: 5105
    {'lmfdb_iso': '392.d', 'p': 31, 'prec': 20, 'unit': 3716558194519472290668397868, 'val': 1}
  • id: 5119
    {'lmfdb_iso': '392.d', 'p': 37, 'prec': 20, 'unit': 400475599874965886047205303326, 'val': 1}
  • id: 5106
    {'lmfdb_iso': '392.d', 'p': 41, 'prec': 20, 'unit': 1294780944017666414864322773551, 'val': 1}
  • id: 5107
    {'lmfdb_iso': '392.d', 'p': 43, 'prec': 20, 'unit': 7770183940460936479466935687358, 'val': 1}
  • id: 5110
    {'lmfdb_iso': '392.d', 'p': 47, 'prec': 20, 'unit': 31510220907570795621656538479509, 'val': 1}
  • id: 5113
    {'lmfdb_iso': '392.d', 'p': 53, 'prec': 20, 'unit': 341744734577639414413946485434503, 'val': 1}
  • id: 5118
    {'lmfdb_iso': '392.d', 'p': 61, 'prec': 20, 'unit': 2968242408791902802541186608712346, 'val': 1}
  • id: 5101
    {'lmfdb_iso': '392.d', 'p': 67, 'prec': 20, 'unit': 1056869293209319720704182421623602, 'val': 1}
  • id: 5104
    {'lmfdb_iso': '392.d', 'p': 71, 'prec': 20, 'unit': 71414394275304512592005569478290213, 'val': 1}
  • id: 5114
    {'lmfdb_iso': '392.d', 'p': 73, 'prec': 20, 'unit': 80633040103372455660046986625378686, 'val': 1}
  • id: 5117
    {'lmfdb_iso': '392.d', 'p': 79, 'prec': 20, 'unit': 755881418384500932279725927701444503, 'val': 1}
  • id: 5115
    {'lmfdb_iso': '392.d', 'p': 83, 'prec': 20, 'unit': 1599125928133060861520156746174660273, 'val': 1}
  • id: 5116
    {'lmfdb_iso': '392.d', 'p': 89, 'prec': 20, 'unit': 10100273504189998197510913017461674495, 'val': 1}
  • id: 5100
    {'lmfdb_iso': '392.d', 'p': 97, 'prec': 20, 'unit': 1065126617183258475274089393294078847, 'val': 1}