Elliptic curve data - 9702.cc1

Formats: - HTML - YAML - JSON - 2024-04-30T07:44:00.854229

• 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': '9702bk', 'Clabel': '9702bk1', 'Cnumber': 1, 'abc_quality': 0.9672157377550301, 'absD': 109577337408, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 264, 'ainvs': [1, -1, 1, -1259, -6149], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 11], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 9702, 'degree': 9216, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.81128991226909222665444882438', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 54, 'isogeny_degrees': [1, 2], 'jinv': [69426531, 34496], 'lmfdb_iso': '9702.cc', 'lmfdb_label': '9702.cc1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -231, -451], 'min_quad_twist_disc': 21, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '24.6.0.c.1', '66.6.0.a.1', '88.6.0.?', '264.12.0.?'], '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': '-0.43631823442559184874703885657', 'prec': 107}, 'szpiro_ratio': 3.597686625506597, '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, 0, 1, 0, 2, 1, 0, 4, 0, 0, 1, 2, 0, 6, 2], 'aplist': [1, 0, 2, 0, 1, 4, 2, 6, 2, 2, 8, -2, -2, -2, 2, -6, 0, -4, 0, -10, 2, -12, -12, 12, 2], 'class_deg': 2, 'class_size': 2, 'conductor': 9702, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '9702.cc', 'trace_hash': 1704940862566475887}
• 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': '0.19738881315455494580803398524', 'prec': 103}, 'conductor': 9702, 'gens': [], 'heights': [], 'lmfdb_label': '9702.cc1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.84367936974564380165761621262', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.0620762184738628099456972756954689659', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [[-5, 2, 1]], 'xcoord_integral_points': [-5]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [7, 0], '3': 'a', '7': 'a', '11': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '9702.cc1'}
• ec_torsion_growth •

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

  
  
  • id: 504173
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '9702.cc1', 'torsion': [2, 2]}
  • id: 504174
    {'degree': 4, 'field': [70, 28, 15, -2, 1], 'lmfdb_label': '9702.cc1', 'torsion': [4]}
  • id: 504177
    {'degree': 8, 'field': [-14, -203, 70, 91, 91, 7, 1, -2, 1], 'lmfdb_label': '9702.cc1', 'torsion': [6]}
  • id: 504175
    {'degree': 8, 'field': [3424, 32, 1436, -88, 160, -56, 11, -2, 1], 'lmfdb_label': '9702.cc1', 'torsion': [2, 4]}
  • id: 504176
    {'degree': 8, 'field': [9216, 0, 17892, 0, -1599, 0, -42, 0, 1], 'lmfdb_label': '9702.cc1', 'torsion': [2, 4]}
  • id: 504179
    {'degree': 16, 'field': [-4688, -3056, 121233, 476252, 620789, 302094, 16318, -52508, -24468, -4826, 1546, 306, 146, -52, 3, -2, 1], 'lmfdb_label': '9702.cc1', 'torsion': [2, 6]}
  • id: 504178
    {'degree': 16, 'field': [1434736, -5273920, 8663344, -6293024, 4202564, -2756560, 1106360, -322160, 169924, -42416, 25316, -8056, 2585, -524, 106, -4, 1], 'lmfdb_label': '9702.cc1', 'torsion': [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: 204651
    {'conductor': 9702, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '9702.cc1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 204652
    {'conductor': 9702, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '9702.cc1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 204653
    {'conductor': 9702, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '9702.cc1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 204654
    {'conductor': 9702, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '9702.cc1', '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: 1728136
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [92, 1, 175, 0], [261, 4, 260, 5], [26, 1, 119, 0], [133, 4, 2, 9], [233, 34, 32, 231]], 'adelic_image': '264.12.0.?', 'conductor': 9702, 'lmfdb_label': '9702.cc1', 'prime': 0}
  • id: 46963
    {'conductor': 9702, 'elladic_image': '2.3.0.1', 'lmfdb_label': '9702.cc1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 9702.cc does not appear in ec_padic