Elliptic curve data - 270480.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': '270480a', 'Clabel': '270480a1', 'Cnumber': 1, 'abc_quality': 0.9145689077107393, 'absD': 90936239999673600000, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 2760, 'ainvs': [0, -1, 0, -1863976, -864791024], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 23], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 270480, 'degree': 10725120, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5588533518880736584572596002', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1], 'jinv': [1238039614322, 157190625], 'lmfdb_iso': '270480.a', 'lmfdb_label': '270480.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -38040, -2510388], 'min_quad_twist_disc': 28, 'modell_images': [], 'modm_images': ['2760.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 5, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '10.144574844311571943867224640', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 16905], [3, 4, 90160], [5, 6, 54096], [7, 20, 1840], [23, 24, 11760]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.30187664549536270390366953599', 'prec': 103}, 'szpiro_ratio': 4.391467480273416, '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, 0, 0, 1, 0, -6, 0, 3, 0, 1, 0, 0, 0, -1, 0], 'aplist': [0, -1, -1, 0, -6, 3, 0, -1, 1, -1, 9, -8, 12, 6, 0, -9, 11, 1, 10, 2, 14, -14, 0, 11, -17], 'class_deg': 1, 'class_size': 1, 'conductor': 270480, 'isogeny_matrix': [[1]], 'lmfdb_iso': '270480.a', 'trace_hash': 1370905817805633098}
• 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': '0.0059897434123367562224349249447', 'prec': 110}, 'conductor': 270480, 'gens': [[84840, 24708244, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '10.144574844311571943867224640', 'prec': 100}], 'lmfdb_label': '270480.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.13028710493842535798405851247', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.2868291491861274484930912417896954451', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': [84840]}
• lmfdb_label 270480.a1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11552520
    {'degree': 3, 'field': [15, -51, -1, 1], 'lmfdb_label': '270480.a1', 'torsion': [2]}
  • id: 11552521
    {'degree': 6, 'field': [-540960, 0, 23716, 0, -308, 0, 1], 'lmfdb_label': '270480.a1', 'torsion': [2, 2]}
  • id: 11552522
    {'degree': 8, 'field': [-44467500, 0, 1911700, 0, -23100, 0, 0, 0, 1], 'lmfdb_label': '270480.a1', 'torsion': [3]}
  • id: 11552523
    {'degree': 12, 'field': [-17017524, -49224890, -49521641, -48205420, -33237583, -9870712, -106484, 355800, 10440, -4218, 47, -4, 1], 'lmfdb_label': '270480.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: 6700243
    {'conductor': 270480, 'conductor_valuation': 4, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '270480.a1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 6700244
    {'conductor': 270480, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '270480.a1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 6700245
    {'conductor': 270480, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '270480.a1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 6700246
    {'conductor': 270480, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '270480.a1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 6700247
    {'conductor': 270480, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '270480.a1', 'prime': 23, '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': [[2071, 2, 0, 1], [1657, 2, 1657, 3], [1, 0, 2, 1], [1, 2, 0, 1], [1, 1, 2759, 0], [1201, 2, 1201, 3], [1381, 2, 1381, 3], [2759, 2, 2758, 3], [1841, 2, 1841, 3]], 'adelic_image': '2760.2.0.?', 'conductor': 270480, 'lmfdb_label': '270480.a1', 'prime': 0}
• lmfdb_iso 270480.a does not appear in ec_padic