Elliptic curve data - 678.e1

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '678d', 'Clabel': '678d2', 'Cnumber': 2, 'abc_quality': 1.055383581120981, 'absD': 2823126576537804, 'adelic_genus': 2, 'adelic_index': 96, 'adelic_level': 4746, 'ainvs': [1, 0, 0, -7121, -2567403], 'analytic_rank': 0, 'bad_primes': [2, 3, 113], 'class_deg': 7, 'class_size': 2, 'cm': 0, 'conductor': 678, 'degree': 3528, 'elladic_images': ['7.48.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6444472771688781770540215721', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 7, 'intrinsic_torsion': 1, 'iso_nlabel': 4, 'isogeny_degrees': [1, 7], 'jinv': [-39934705050538129, 2823126576537804], 'lmfdb_iso': '678.e', 'lmfdb_label': '678.e1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -7121, -2567403], 'min_quad_twist_disc': 1, 'modell_images': ['7B.1.3'], 'modm_images': ['7.48.0-7.a.2.2', '678.2.0.?', '4746.96.2.?'], 'nonmax_primes': [7], 'nonmax_rad': 7, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 339], [3, 4, 226], [7, 2, 6], [113, 114, 6]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.6444472771688781770540215721', 'prec': 100}, 'szpiro_ratio': 6.602012838883326, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 1, 1, -1, 1, 1, 1, 1, -1, -2, 1, 7, 1, -1, 1, -3, 1, 6, -1], 'aplist': [1, 1, -1, 1, -2, 7, -3, 6, 3, 2, -3, -4, 0, 2, -8, -2, -3, -1, -2, -5, 4, -4, 0, 6, -14], 'class_deg': 7, 'class_size': 2, 'conductor': 678, 'isogeny_matrix': [[1, 7], [7, 1]], 'lmfdb_iso': '678.e', 'trace_hash': 1172314809173008301}
• 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': '0.037295054273112882871435868934', 'prec': 107}, 'conductor': 678, 'gens': [], 'heights': [], 'lmfdb_label': '678.e1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.19957796163276756937006926630', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.7940914628587459711809697282689482811', 'prec': 130}, 'tamagawa_product': 14, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 0], '3': [1, 0], '5': [0, 0], '7': [2, 1], '113': [1, 0]}, 'iwp0': 11, 'lmfdb_label': '678.e1'}
• ec_torsion_growth •

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

  
  
  • id: 31417
    {'degree': 3, 'field': [4, -1, -1, 1], 'lmfdb_label': '678.e1', 'torsion': [2]}
  • id: 31419
    {'degree': 6, 'field': [1, -1, 1, -1, 1, -1, 1], 'lmfdb_label': '678.e1', 'torsion': [7]}
  • id: 31418
    {'degree': 6, 'field': [241, -182, 110, -26, 2, -2, 1], 'lmfdb_label': '678.e1', 'torsion': [2, 2]}
  • id: 31420
    {'degree': 7, 'field': [-18, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '678.e1', 'torsion': [7]}
  • id: 31421
    {'degree': 8, 'field': [-192, 336, -372, 71, -32, -7, 7, -4, 1], 'lmfdb_label': '678.e1', 'torsion': [3]}
  • id: 31422
    {'degree': 12, 'field': [34344, 93420, 65421, 49278, 37168, 1960, 7825, -536, 823, -80, 34, -2, 1], 'lmfdb_label': '678.e1', 'torsion': [4]}
  • id: 31423
    {'degree': 18, 'field': [4096, -1024, 1280, 448, -48, 444, -11, -87, 130, -57, 25, 12, -11, 12, -3, 1, 2, -1, 1], 'lmfdb_label': '678.e1', 'torsion': [14]}
  • id: 31424
    {'degree': 21, 'field': [-15552, 0, 0, 0, 0, 0, 0, 28320, 0, 0, 0, 0, 0, 0, -336, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '678.e1', 'torsion': [14]}
• 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: 8334
    {'conductor': 678, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '678.e1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 8335
    {'conductor': 678, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '678.e1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 8336
    {'conductor': 678, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '678.e1', 'prime': 113, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 7}
• ec_galrep •

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

  
  
  • id: 1668997
    {'adelic_gens': [[2941, 14, 1603, 99], [1, 14, 0, 1], [3, 3398, 4732, 2675], [1, 0, 14, 1], [1583, 14, 1589, 99], [8, 5, 91, 57], [4733, 14, 4732, 15]], 'adelic_image': '4746.96.2.?', 'conductor': 678, 'lmfdb_label': '678.e1', 'prime': 0}
  • id: 3088
    {'conductor': 678, 'elladic_image': '7.48.0.5', 'lmfdb_label': '678.e1', 'modell_image': '7B.1.3', 'prime': 7}
• lmfdb_iso 678.e does not appear in ec_padic