Elliptic curve data - 6800.c1

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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': '6800n', 'Clabel': '6800n1', 'Cnumber': 1, 'abc_quality': 0.9887036529951482, 'absD': 435200000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 680, 'ainvs': [0, 1, 0, -3008, -56012], 'analytic_rank': 0, 'bad_primes': [2, 5, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 6800, 'degree': 9216, 'elladic_images': ['4.6.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.95857524834294221896657339852', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 2, 'isogeny_degrees': [1, 2], 'jinv': [47045881, 6800], 'lmfdb_iso': '6800.c', 'lmfdb_label': '6800.c1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -8, 6], 'min_quad_twist_disc': -20, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.b.1', '34.6.0.a.1', '40.12.0-4.b.1.3', '68.12.0.e.1', '136.24.0.?', '340.24.0.?', '680.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 425], [5, 18, 272], [17, 18, 400]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.53929088843405327775103838955', 'prec': 107}, 'szpiro_ratio': 4.038790758811553, '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, 0, -2, 0, 0, 0, -2, 0, 1, 0, 2, 0, 6, 0, 0, 0, -1, 0, 8, 0], 'aplist': [0, -2, 0, -2, 2, 6, -1, 8, -2, 6, 2, -6, 2, -4, 4, 10, 0, -10, 8, -14, -10, 14, -4, 6, 14], 'class_deg': 2, 'class_size': 2, 'conductor': 6800, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '6800.c', 'trace_hash': 326921376587346473}
• 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': '0.14702531492057027049663421472', 'prec': 103}, 'conductor': 6800, 'gens': [], 'heights': [], 'lmfdb_label': '6800.c1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.65085744470866137417023945441', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.3017148894173227483404789088177453221', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-22, 0, 1]], 'xcoord_integral_points': [-22]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '5': 'a', '17': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '6800.c1'}
• ec_torsion_growth •

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

  
  
  • id: 357481
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '6800.c1', 'torsion': [2, 2]}
  • id: 357482
    {'degree': 4, 'field': [26, 2, -1, -2, 1], 'lmfdb_label': '6800.c1', 'torsion': [4]}
  • id: 357485
    {'degree': 8, 'field': [-675, 0, 180, 0, -90, 0, 0, 0, 1], 'lmfdb_label': '6800.c1', 'torsion': [6]}
  • id: 357483
    {'degree': 8, 'field': [-64, -24, 68, 70, -5, -28, 0, -2, 1], 'lmfdb_label': '6800.c1', 'torsion': [2, 4]}
  • id: 357484
    {'degree': 8, 'field': [16, 0, 57, 0, -17, 0, 7, 0, 1], 'lmfdb_label': '6800.c1', 'torsion': [2, 4]}
  • id: 357487
    {'degree': 16, 'field': [1, -6, 27, -94, 177, -180, 102, 24, -50, 0, 50, -28, -11, 6, 3, -2, 1], 'lmfdb_label': '6800.c1', 'torsion': [8]}
  • id: 357486
    {'degree': 16, 'field': [4096, 0, 9280, 0, 8624, 0, 6924, 0, 3721, 0, 368, 0, -122, 0, 4, 0, 1], 'lmfdb_label': '6800.c1', 'torsion': [4, 4]}
  • id: 357488
    {'degree': 16, 'field': [1114936, 1436792, -1824124, 1559568, -2643844, 1966936, -220556, -344136, 51757, 20424, -2096, -544, -334, 168, -4, -8, 1], 'lmfdb_label': '6800.c1', 'torsion': [2, 6]}
• 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: 138624
    {'conductor': 6800, 'conductor_valuation': 4, 'discriminant_valuation': 16, 'j_denominator_valuation': 4, 'kodaira_symbol': -12, 'lmfdb_label': '6800.c1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 138625
    {'conductor': 6800, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '6800.c1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 138626
    {'conductor': 6800, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '6800.c1', 'prime': 17, '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: 1708895
    {'adelic_gens': [[1, 0, 8, 1], [673, 8, 672, 9], [1, 8, 0, 1], [1, 4, 4, 17], [3, 8, 28, 75], [401, 674, 142, 5], [341, 8, 4, 33], [86, 1, 103, 4], [5, 8, 48, 77], [169, 672, 336, 647]], 'adelic_image': '680.48.0.?', 'conductor': 6800, 'lmfdb_label': '6800.c1', 'prime': 0}
  • id: 33615
    {'conductor': 6800, 'elladic_image': '4.6.0.3', 'lmfdb_label': '6800.c1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 6800.c does not appear in ec_padic