Elliptic curve data - 1386.k1

Formats: - HTML - YAML - JSON - 2025-03-20T14:28:00.535366

• 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': '1386l', 'Clabel': '1386l4', 'Cnumber': 4, 'abc_quality': 0.9493319727776763, 'absD': 448278138, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1848, 'ainvs': [1, -1, 1, -2039, 35925], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 1386, 'degree': 1024, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.61496673976284453028575701520', 'prec': 103}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2, 4], 'jinv': [1285429208617, 614922], 'lmfdb_iso': '1386.k', 'lmfdb_label': '1386.k1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -226, -1406], '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.1.1', '28.12.0-4.c.1.1', '88.12.0.?', '168.24.0.?', '264.24.0.?', '616.24.0.?', '1848.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 63], [3, 8, 154], [7, 8, 198], [11, 12, 126]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.065660595428789684588134396739', 'prec': 107}, 'szpiro_ratio': 4.765405472995891, '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': '0.29231202176847209414161282876', 'prec': 103}, 'conductor': 1386, 'gens': [], 'heights': [], 'lmfdb_label': '1386.k1', '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': [[107, -111, 2]], 'xcoord_integral_points': []}
• 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.k1'}
• ec_torsion_growth •

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

  
  
  • id: 69737
    {'degree': 2, 'field': [-42, 0, 1], 'lmfdb_label': '1386.k1', 'torsion': [2, 2]}
  • id: 69739
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '1386.k1', 'torsion': [4]}
  • id: 69738
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '1386.k1', 'torsion': [4]}
  • id: 69740
    {'degree': 4, 'field': [81, 0, -24, 0, 1], 'lmfdb_label': '1386.k1', 'torsion': [2, 4]}
  • id: 69744
    {'degree': 8, 'field': [-432, 0, 0, 0, 72, 0, -5, 0, 1], 'lmfdb_label': '1386.k1', 'torsion': [6]}
  • id: 69742
    {'degree': 8, 'field': [196, 0, -3248, 0, 900, 0, -56, 0, 1], 'lmfdb_label': '1386.k1', 'torsion': [8]}
  • id: 69743
    {'degree': 8, 'field': [4900, 0, 1568, 0, 1365, 0, -70, 0, 1], 'lmfdb_label': '1386.k1', 'torsion': [8]}
  • id: 69741
    {'degree': 8, 'field': [28072, -3392, 3080, 616, -287, -28, 14, -4, 1], 'lmfdb_label': '1386.k1', 'torsion': [2, 4]}
  • id: 69746
    {'degree': 16, 'field': [236196, 0, -10252656, 0, 10379340, 0, -3999888, 0, 751653, 0, -74100, 0, 3868, 0, -100, 0, 1], 'lmfdb_label': '1386.k1', 'torsion': [2, 8]}
  • id: 69745
    {'degree': 16, 'field': [3319684, 0, 3203664, 0, 1336636, 0, 140112, 0, -4347, 0, 252, 0, 238, 0, -12, 0, 1], 'lmfdb_label': '1386.k1', 'torsion': [4, 4]}
  • id: 69749
    {'degree': 16, 'field': [5645376, 0, -5645376, 0, -3122064, 0, 75168, 0, 44172, 0, -15228, 0, 1477, 0, -58, 0, 1], 'lmfdb_label': '1386.k1', 'torsion': [12]}
  • id: 69750
    {'degree': 16, 'field': [14303524, 0, -8048208, 0, -4737683, 0, 9598, 0, 103083, 0, -23372, 0, 1891, 0, -66, 0, 1], 'lmfdb_label': '1386.k1', 'torsion': [12]}
  • id: 69748
    {'degree': 16, 'field': [18249984, 0, -170714880, 0, 105781824, 0, -28176672, 0, 3318960, 0, -201648, 0, 6553, 0, -94, 0, 1], 'lmfdb_label': '1386.k1', 'torsion': [2, 6]}
  • id: 69747
    {'degree': 16, 'field': [134031913, -19883368, 36742832, -35181768, 21433850, -5141048, 2623684, -836064, 281371, -51720, 13732, -1744, 230, 0, 20, -8, 1], 'lmfdb_label': '1386.k1', 'torsion': [2, 8]}
• 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: 21208
    {'conductor': 1386, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '1386.k1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 21209
    {'conductor': 1386, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '1386.k1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 21210
    {'conductor': 1386, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '1386.k1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 21211
    {'conductor': 1386, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '1386.k1', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
• ec_galrep •

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

  
  
  • id: 1673282
    {'adelic_gens': [[235, 232, 1178, 237], [1, 0, 8, 1], [1, 8, 0, 1], [1841, 8, 1840, 9], [1, 4, 4, 17], [796, 1, 1343, 6], [7, 6, 1842, 1843], [232, 1163, 697, 726], [1228, 1847, 593, 1842], [673, 8, 844, 33]], 'adelic_image': '1848.48.0.?', 'conductor': 1386, 'lmfdb_label': '1386.k1', 'prime': 0}
  • id: 6746
    {'conductor': 1386, 'elladic_image': '4.6.0.1', 'lmfdb_label': '1386.k1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 1386.k does not appear in ec_padic