Elliptic curve data - 7098.bc1

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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': '7098y', 'Clabel': '7098y3', 'Cnumber': 3, 'abc_quality': 1.0121377482115463, 'absD': 113433535488, 'adelic_genus': 5, 'adelic_index': 288, 'adelic_level': 10920, 'ainvs': [1, 0, 0, -13517, 603537], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 13], 'class_deg': 10, 'class_size': 4, 'cm': 0, 'conductor': 7098, 'degree': 12000, 'elladic_images': ['2.3.0.1', '5.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0830459330521300522587451908', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 5, 'iso_nlabel': 28, 'isogeny_degrees': [1, 2, 5, 10], 'jinv': [124318741396429, 51631104], 'lmfdb_iso': '7098.bc', 'lmfdb_label': '7098.bc1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -13517, 603537], 'min_quad_twist_disc': 1, 'modell_images': ['2B', '5B'], 'modm_images': ['2.3.0.a.1', '5.6.0.a.1', '10.18.0.a.1', '40.36.0.c.1', '65.24.0-65.a.1.3', '104.6.0.?', '130.72.0.?', '168.6.0.?', '210.36.0.?', '520.144.1.?', '546.6.0.?', '840.72.1.?', '2184.12.0.?', '2730.144.1.?', '10920.288.5.?'], 'nonmax_primes': [2, 5], 'nonmax_rad': 10, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.44180859368674586824537333041', 'prec': 103}, 'szpiro_ratio': 4.527590478286306, '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, 1, 1, 2, 1, -1, 1, 1, 2, 0, 1, 0, -1, 2, 1, 2, 1, 4, 2], 'aplist': [1, 1, 2, -1, 0, 0, 2, 4, 6, 0, 0, 2, 0, -4, -8, 4, 6, 12, -2, 0, 14, 0, -14, -4, -2], 'class_deg': 10, 'class_size': 4, 'conductor': 7098, 'isogeny_matrix': [[1, 2, 5, 10], [2, 1, 10, 5], [5, 10, 1, 2], [10, 5, 2, 1]], 'lmfdb_iso': '7098.bc', 'trace_hash': 908481420297379413}
• 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': '0.11462471140914384761301777462', 'prec': 103}, 'conductor': 7098, 'gens': [], 'heights': [], 'lmfdb_label': '7098.bc1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.0354952541232427161523397505', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.1774762706162135807616987524909796268', 'prec': 130}, 'tamagawa_product': 20, 'torsion_generators': [[66, -33, 1]], 'xcoord_integral_points': [66]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 0], '3': [3, 0], '5': [2, 0], '7': [0, 0], '13': 'a'}, 'iwp0': 7, 'lmfdb_label': '7098.bc1'}
• ec_torsion_growth •

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

  
  
  • id: 373757
    {'degree': 2, 'field': [-68, -1, 1], 'lmfdb_label': '7098.bc1', 'torsion': [2, 2]}
  • id: 373759
    {'degree': 4, 'field': [16, 4, -24, -1, 1], 'lmfdb_label': '7098.bc1', 'torsion': [10]}
  • id: 373758
    {'degree': 4, 'field': [360, -72, -5, -2, 1], 'lmfdb_label': '7098.bc1', 'torsion': [4]}
  • id: 373760
    {'degree': 8, 'field': [-96704, 137120, -52904, -1576, 3250, -118, -47, -4, 1], 'lmfdb_label': '7098.bc1', 'torsion': [2, 4]}
  • id: 373762
    {'degree': 8, 'field': [11274, 20022, 7764, -787, -856, 167, -17, -2, 1], 'lmfdb_label': '7098.bc1', 'torsion': [6]}
  • id: 373763
    {'degree': 8, 'field': [27556, 0, -26693, 0, 3359, 0, -127, 0, 1], 'lmfdb_label': '7098.bc1', 'torsion': [2, 10]}
  • id: 373761
    {'degree': 8, 'field': [217504, 7952, -7010, -1888, 955, -16, 10, -4, 1], 'lmfdb_label': '7098.bc1', 'torsion': [2, 4]}
  • id: 373765
    {'degree': 16, 'field': [-9982860996, 12345149868, -1857351492, -1034103468, 137412690, -17529174, 4241125, 7659976, -1284246, -580302, 38421, -6246, 4263, -192, -54, -2, 1], 'lmfdb_label': '7098.bc1', 'torsion': [2, 6]}
  • id: 373766
    {'degree': 16, 'field': [50536196, 85758912, 43582828, -32671032, -7861483, 24296348, 65894, -5138964, 2446987, -363448, 107376, -10416, 3547, -164, 62, -4, 1], 'lmfdb_label': '7098.bc1', 'torsion': [20]}
  • id: 373764
    {'degree': 16, 'field': [559910568, -154005984, 165462264, -22348320, 9814870, 1484904, -243848, -228896, 71739, -5592, -3176, 2592, -614, 56, 12, -8, 1], 'lmfdb_label': '7098.bc1', 'torsion': [8]}
  • id: 373767
    {'degree': 20, 'field': [14348907, 0, 0, 0, 0, -905418, 0, 0, 0, 0, 14580, 0, 0, 0, 0, -6, 0, 0, 0, 0, 1], 'lmfdb_label': '7098.bc1', 'torsion': [10]}
• 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: 145756
    {'conductor': 7098, 'conductor_valuation': 1, 'discriminant_valuation': 10, 'j_denominator_valuation': 10, 'kodaira_symbol': 14, 'lmfdb_label': '7098.bc1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 10}
  • id: 145757
    {'conductor': 7098, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '7098.bc1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 145758
    {'conductor': 7098, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '7098.bc1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 145759
    {'conductor': 7098, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '7098.bc1', 'prime': 13, 'reduction_type': 0, '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: 1710958
    {'adelic_gens': [[10901, 20, 10900, 21], [4696, 5, 9315, 10906], [8737, 20, 0, 1], [8191, 20, 0, 1], [5461, 20, 10, 201], [1, 10, 10, 101], [3656, 5, 10875, 10906], [1, 0, 20, 1], [11, 16, 10680, 10571], [10098, 5, 5335, 82], [1, 20, 0, 1]], 'adelic_image': '10920.288.5.?', 'conductor': 7098, 'lmfdb_label': '7098.bc1', 'prime': 0}
  • id: 35073
    {'conductor': 7098, 'elladic_image': '2.3.0.1', 'lmfdb_label': '7098.bc1', 'modell_image': '2B', 'prime': 2}
  • id: 35074
    {'conductor': 7098, 'elladic_image': '5.6.0.1', 'lmfdb_label': '7098.bc1', 'modell_image': '5B', 'prime': 5}
• lmfdb_iso 7098.bc does not appear in ec_padic