Elliptic curve data - 10164.f1

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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': '10164l', 'Clabel': '10164l1', 'Cnumber': 1, 'abc_quality': 1.0585088593901664, 'absD': 2196586496455645383936, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 42, 'ainvs': [0, -1, 0, -9096941, 10320150249], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 11], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 10164, 'degree': 570240, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.8763420717228023221951630363', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 5, 'isogeny_degrees': [1], 'jinv': [12538427613184, 330812181], 'lmfdb_iso': '10164.f', 'lmfdb_label': '10164.f1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -75181, -7726343], 'min_quad_twist_disc': -11, 'modell_images': [], 'modm_images': ['42.2.0.a.1'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.41599789068419666253205530703', 'prec': 103}, 'szpiro_ratio': 6.4686777271389895, '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, 0, -1, 0, -1, 0, 1, 0, 1, 0, 0, 0, -2, 0, 1, 0, -3, 0, -4, 0], 'aplist': [0, -1, -1, 1, 0, -2, -3, -4, -2, -8, -10, -6, 6, 7, 13, -8, -11, 2, 11, 14, 14, -4, -7, 1, 12], 'class_deg': 1, 'class_size': 1, 'conductor': 10164, 'isogeny_matrix': [[1]], 'lmfdb_iso': '10164.f', 'trace_hash': 1939291305692535234}
• 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': '0.0031742492114172619069375904614', 'prec': 110}, 'conductor': 10164, 'gens': [], 'heights': [], 'lmfdb_label': '10164.f1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.14582299855894646911699633958', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.72911499279473234558498169790514526723', 'prec': 133}, 'tamagawa_product': 5, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '5': [6, 0], '7': [1, 0], '11': 'a', '13': [0, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '10164.f1'}
• ec_torsion_growth •

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

  
  
  • id: 527101
    {'degree': 3, 'field': [57, -29, -1, 1], 'lmfdb_label': '10164.f1', 'torsion': [2]}
  • id: 527102
    {'degree': 6, 'field': [-27, -9, 114, -3, -38, -1, 1], 'lmfdb_label': '10164.f1', 'torsion': [2, 2]}
  • id: 527103
    {'degree': 8, 'field': [-238, -20, 74, -109, 58, -7, 7, -4, 1], 'lmfdb_label': '10164.f1', 'torsion': [3]}
  • id: 527104
    {'degree': 12, 'field': [23259, -15510, -26626, 15048, 8979, -6336, -1004, 1056, 155, -66, -30, 0, 1], 'lmfdb_label': '10164.f1', 'torsion': [4]}
• 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: 215385
    {'conductor': 10164, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '10164.f1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 215386
    {'conductor': 10164, 'conductor_valuation': 1, 'discriminant_valuation': 9, 'j_denominator_valuation': 9, 'kodaira_symbol': 13, 'lmfdb_label': '10164.f1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 215387
    {'conductor': 10164, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '10164.f1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 5}
  • id: 215388
    {'conductor': 10164, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '10164.f1', 'prime': 11, 'reduction_type': 0, '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

  
  {'adelic_gens': [[1, 1, 41, 0], [1, 2, 0, 1], [31, 2, 31, 3], [1, 0, 2, 1], [41, 2, 40, 3], [29, 2, 29, 3]], 'adelic_image': '42.2.0.?', 'conductor': 10164, 'lmfdb_label': '10164.f1', 'prime': 0}
• lmfdb_iso 10164.f does not appear in ec_padic