Elliptic curve data - 27735.j2

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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': '27735f', 'Clabel': '27735f1', 'Cnumber': 1, 'abc_quality': 1.0526811717862732, 'absD': 14671277634375, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 2580, 'ainvs': [1, 0, 1, -684, 184357], 'analytic_rank': 0, 'bad_primes': [3, 5, 43], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 27735, 'degree': 83600, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.2055404935471765801849878517', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 9, 'isogeny_degrees': [1, 2], 'jinv': [-444194947, 184528125], 'lmfdb_iso': '27735.j', 'lmfdb_label': '27735.j2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -684, 184357], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '60.6.0.d.1', '430.6.0.?', '516.6.0.?', '2580.12.0.?'], '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, 215], [3, 4, 9245], [5, 6, 1849], [43, 506, 15]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.26524046462378597431677722336', 'prec': 103}, 'szpiro_ratio': 3.6922152232783185, '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, -1, 1, -4, -3, 1, -1, 4, -1, 2, -4, -1, -1, 8, 1, 2, 1], 'aplist': [1, 1, -1, -4, 4, 2, 8, 2, 6, -6, -8, -2, 10, 0, -10, 4, 0, 8, 4, 12, 10, -16, 6, -2, 6], 'class_deg': 2, 'class_size': 2, 'conductor': 27735, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '27735.j', 'trace_hash': 825003602061876785}
• 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': '0.089718257855108185837696042770', 'prec': 107}, 'conductor': 27735, 'gens': [], 'heights': [], 'lmfdb_label': '27735.j2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.56968093911366774979881840591', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.8484046955683387489940920295272412191', 'prec': 130}, 'tamagawa_product': 20, 'torsion_generators': [[-61, 30, 1]], 'xcoord_integral_points': [-61]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': [1, 0], '5': [2, 0], '43': 'a'}, 'iwp0': 7, 'lmfdb_label': '27735.j2'}
• ec_torsion_growth •

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

  
  
  • id: 1387970
    {'degree': 2, 'field': [54, -1, 1], 'lmfdb_label': '27735.j2', 'torsion': [2, 2]}
  • id: 1387971
    {'degree': 4, 'field': [-108, 180, -5, -1, 1], 'lmfdb_label': '27735.j2', 'torsion': [4]}
  • id: 1387974
    {'degree': 8, 'field': [-6735, -29127, -132789, -47024, -5525, 181, 31, -2, 1], 'lmfdb_label': '27735.j2', 'torsion': [6]}
  • id: 1387972
    {'degree': 8, 'field': [1356, -2334, 4309, -2853, 753, 46, 21, -3, 1], 'lmfdb_label': '27735.j2', 'torsion': [2, 4]}
  • id: 1387973
    {'degree': 8, 'field': [240100, 0, -8000, 0, -715, 0, 10, 0, 1], 'lmfdb_label': '27735.j2', 'torsion': [2, 4]}
  • id: 1387975
    {'degree': 16, 'field': [61504, 0, -461984, 0, 246793, 0, -12992, 0, -10820, 0, 1858, 0, -308, 0, 16, 0, 1], 'lmfdb_label': '27735.j2', 'torsion': [8]}
  • id: 1387976
    {'degree': 16, 'field': [9152355915, 13994781210, 6134167611, 755042259, 124281492, 6673932, 14888702, 8478520, 2665305, 351490, -31030, -19980, -842, 137, -9, -4, 1], 'lmfdb_label': '27735.j2', '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: 640617
    {'conductor': 27735, 'conductor_valuation': 1, 'discriminant_valuation': 10, 'j_denominator_valuation': 10, 'kodaira_symbol': 14, 'lmfdb_label': '27735.j2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 10}
  • id: 640618
    {'conductor': 27735, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '27735.j2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 640619
    {'conductor': 27735, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '27735.j2', 'prime': 43, '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: 1848955
    {'adelic_gens': [[1, 2, 2, 5], [1, 4, 0, 1], [1721, 4, 862, 9], [1034, 1, 2063, 0], [2577, 4, 2576, 5], [1, 0, 4, 1], [184, 1, 599, 0], [1937, 646, 644, 1935], [3, 4, 8, 11]], 'adelic_image': '2580.12.0.?', 'conductor': 27735, 'lmfdb_label': '27735.j2', 'prime': 0}
  • id: 125371
    {'conductor': 27735, 'elladic_image': '2.3.0.1', 'lmfdb_label': '27735.j2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 27735.j does not appear in ec_padic