Elliptic curve data - 28665.a1

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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': '28665bh', 'Clabel': '28665bh1', 'Cnumber': 1, 'abc_quality': 0.963721504609575, 'absD': 2351867849296875, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 390, 'ainvs': [0, 0, 1, -29253, -3025346], 'analytic_rank': 0, 'bad_primes': [3, 5, 7, 13], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 28665, 'degree': 254016, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6471135596713752557938073056', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1], 'jinv': [-32278933504, 27421875], 'lmfdb_iso': '28665.a', 'lmfdb_label': '28665.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -66, -349], 'min_quad_twist_disc': 21, 'modell_images': [], 'modm_images': ['390.2.0.?'], '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, 'serre_invariants': [[3, 6, 3185], [5, 6, 5733], [7, 26, 117], [13, 14, 2205]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.12485234080966375754350831542', 'prec': 103}, 'szpiro_ratio': 4.2255082709501846, '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, -2, 0, 2, -1, 0, 0, 0, 0, 2, -5, 0, 1, 0, 0, -4, -7, 0, 6, -2], 'aplist': [-2, 0, -1, 0, -5, 1, -7, 6, -3, -2, -2, 7, 9, -8, 10, -5, 0, -5, -4, -9, 6, -3, -4, 11, 11], 'class_deg': 1, 'class_size': 1, 'conductor': 28665, 'isogeny_matrix': [[1]], 'lmfdb_iso': '28665.a', 'trace_hash': 217804569727061449}
• 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': '0.037096705296267933760347473684', 'prec': 107}, 'conductor': 28665, 'gens': [], 'heights': [], 'lmfdb_label': '28665.a1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.17621710865740433941661598286', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.35243421731480867883323196571072205877', 'prec': 133}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 2, 0], '3': 'a', '5': [0, 0], '7': 'a', '11': [0, 0], '13': [3, 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': '28665.a1'}
• ec_torsion_growth •

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

  
  
  • id: 1437807
    {'degree': 3, 'field': [-5, -1, -1, 1], 'lmfdb_label': '28665.a1', 'torsion': [2]}
  • id: 1437808
    {'degree': 6, 'field': [780, 0, 16, 0, -8, 0, 1], 'lmfdb_label': '28665.a1', 'torsion': [2, 2]}
  • id: 1437809
    {'degree': 8, 'field': [-895, 1817, -1403, 484, -56, 38, 2, -1, 1], 'lmfdb_label': '28665.a1', 'torsion': [3]}
  • id: 1437810
    {'degree': 12, 'field': [-3120717, -12933456, -24813864, -11264214, -5381411, -1246892, -257376, -20344, -1439, -364, 0, -2, 1], 'lmfdb_label': '28665.a1', '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: 665805
    {'conductor': 28665, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '28665.a1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 665806
    {'conductor': 28665, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '28665.a1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 665807
    {'conductor': 28665, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '28665.a1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 665808
    {'conductor': 28665, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '28665.a1', 'prime': 13, '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

  
  {'adelic_gens': [[301, 2, 301, 3], [389, 2, 388, 3], [131, 2, 131, 3], [157, 2, 157, 3], [1, 0, 2, 1], [1, 2, 0, 1], [1, 1, 389, 0]], 'adelic_image': '390.2.0.?', 'conductor': 28665, 'lmfdb_label': '28665.a1', 'prime': 0}
• lmfdb_iso 28665.a does not appear in ec_padic