Elliptic curve data - 1386.k4

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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': '1386l', 'Clabel': '1386l1', 'Cnumber': 1, 'abc_quality': 0.8499917728489924, 'absD': 2694384, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1848, 'ainvs': [1, -1, 1, 31, 33], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 1386, 'degree': 256, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.078180440797100779131475106257', 'prec': 110}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2, 4], 'jinv': [4657463, 3696], 'lmfdb_iso': '1386.k', 'lmfdb_label': '1386.k4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 4, 0], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0-4.c.1.6', '28.12.0-4.c.1.2', '88.12.0.?', '132.12.0.?', '168.24.0.?', '264.24.0.?', '462.6.0.?', '616.24.0.?', '924.24.0.?', '1848.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.62748658513115562482909772472', 'prec': 107}, 'szpiro_ratio': 3.0336076410583277, '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, 2, 0, 1, 1, 0, 2, -1, 0, 2, 1, 0, 1, 6, 0, -4, 2], 'aplist': [1, 0, 2, 1, -1, 2, 6, -4, 4, -2, -4, -2, 6, 0, 8, 14, -12, -14, 4, -12, 6, 0, 0, 6, -14], 'class_deg': 4, 'class_size': 4, 'conductor': 1386, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '1386.k', 'trace_hash': 1032736223719530696}
• 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': '1.1692480870738883765664513150', 'prec': 100}, 'conductor': 1386, 'gens': [], 'heights': [], 'lmfdb_label': '1386.k4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.6456304289591871305477427958', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.2912608579183742610954855915993148720', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-1, 0, 1]], 'xcoord_integral_points': [-1]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '3': 'a', '7': [1, 0], '11': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '1386.k4'}
• ec_torsion_growth •

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

  
  
  • id: 69702
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '1386.k4', 'torsion': [4]}
  • id: 69703
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '1386.k4', 'torsion': [4]}
  • id: 69701
    {'degree': 2, 'field': [58, -1, 1], 'lmfdb_label': '1386.k4', 'torsion': [2, 2]}
  • id: 69704
    {'degree': 4, 'field': [100, 0, -13, 0, 1], 'lmfdb_label': '1386.k4', 'torsion': [2, 4]}
  • id: 69706
    {'degree': 8, 'field': [-536, 712, -66, 12, 13, -96, 0, -4, 1], 'lmfdb_label': '1386.k4', 'torsion': [8]}
  • id: 69708
    {'degree': 8, 'field': [-432, 0, 0, 0, 72, 0, -5, 0, 1], 'lmfdb_label': '1386.k4', 'torsion': [6]}
  • id: 69707
    {'degree': 8, 'field': [576, 0, 4896, 0, 276, 0, -36, 0, 1], 'lmfdb_label': '1386.k4', 'torsion': [8]}
  • id: 69705
    {'degree': 8, 'field': [135972, -153144, 54648, -8592, 1789, -386, 66, -2, 1], 'lmfdb_label': '1386.k4', 'torsion': [2, 4]}
  • id: 69711
    {'degree': 16, 'field': [12868, -47176, 180112, -81820, -512901, 16616, 587332, 353784, -9041, -56472, -1480, 8292, 1745, -200, -76, 0, 1], 'lmfdb_label': '1386.k4', 'torsion': [2, 8]}
  • id: 69714
    {'degree': 16, 'field': [292544, -985824, 754384, 407840, -72752, -138712, 13224, 31466, -10549, -254, 2198, -1322, 372, -98, 34, -8, 1], 'lmfdb_label': '1386.k4', 'torsion': [12]}
  • id: 69710
    {'degree': 16, 'field': [798372, -2024424, 2437704, -2039988, 1455031, -709584, 66536, 163464, -107433, 25944, 2440, -3348, 909, -96, 8, 0, 1], 'lmfdb_label': '1386.k4', 'torsion': [2, 8]}
  • id: 69713
    {'degree': 16, 'field': [5645376, 0, -5645376, 0, 470448, 0, 131868, 0, -1188, 0, -2376, 0, -35, 0, 5, 0, 1], 'lmfdb_label': '1386.k4', 'torsion': [12]}
  • id: 69712
    {'degree': 16, 'field': [504631296, 0, 244021248, 0, -52556544, 0, 3264192, 0, 108000, 0, -1860, 0, -720, 0, 0, 0, 1], 'lmfdb_label': '1386.k4', 'torsion': [2, 6]}
  • id: 69709
    {'degree': 16, 'field': [1800814096, 0, 0, 0, 62531368, 0, 0, 0, -159567, 0, 0, 0, -362, 0, 0, 0, 1], 'lmfdb_label': '1386.k4', 'torsion': [4, 4]}
• 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: 21196
    {'conductor': 1386, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '1386.k4', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 21197
    {'conductor': 1386, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '1386.k4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 21198
    {'conductor': 1386, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '1386.k4', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 21199
    {'conductor': 1386, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '1386.k4', 'prime': 11, 'reduction_type': -1, '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: 1673285
    {'adelic_gens': [[1163, 1158, 698, 1619], [1, 0, 8, 1], [1688, 3, 1517, 2], [1, 8, 0, 1], [1841, 8, 1840, 9], [1, 4, 4, 17], [7, 6, 1842, 1843], [796, 1, 1343, 6], [697, 696, 1630, 703], [1228, 1847, 593, 1842]], 'adelic_image': '1848.48.0.?', 'conductor': 1386, 'lmfdb_label': '1386.k4', 'prime': 0}
  • id: 6749
    {'conductor': 1386, 'elladic_image': '4.6.0.1', 'lmfdb_label': '1386.k4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 1386.k does not appear in ec_padic