Elliptic curve data - 270480.fx4

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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': '270480fx', 'Clabel': '270480fx2', 'Cnumber': 2, 'abc_quality': 0.9093994819073755, 'absD': 1451848896288000, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 9660, 'ainvs': [0, 1, 0, 22524, -1283976], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 23], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 270480, 'degree': 1161216, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5956703092880991496041354385', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 153, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [41957807024, 48205125], 'lmfdb_iso': '270480.fx', 'lmfdb_label': '270480.fx4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, 460, -3612], 'min_quad_twist_disc': 28, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '20.6.0.a.1', '60.24.0.o.1', '84.24.0.?', '210.24.0.?', '276.24.0.?', '420.48.0.?', '1380.48.1.?', '1932.48.0.?', '9660.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.6225435521333934178729211964', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 245], [3, 4, 18032], [5, 6, 54096], [7, 26, 5520], [23, 24, 11760]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.16061711438714562410663765247', 'prec': 103}, 'szpiro_ratio': 3.3323252203564273, '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, 0, 1, 0, -1, 0, 0, 0, 1, 0, 0, 0, -2, 0, -1, 0, -6, 0, 2, 0], 'aplist': [0, 1, -1, 0, 0, -2, -6, 2, 1, 6, -4, 8, -6, -8, 12, -6, -6, 10, -8, 6, -2, 10, -12, -6, -8], 'class_deg': 6, 'class_size': 4, 'conductor': 270480, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '270480.fx', 'trace_hash': 1556820592792056993}
• 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': '0.041116712145782657482642628711', 'prec': 107}, 'conductor': 270480, 'gens': [[135, 2058, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.6225435521333934178729211964', 'prec': 100}], 'lmfdb_label': '270480.fx4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.25772751856754321124911970696', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.1108197043197985566926092151423227880', 'prec': 130}, 'tamagawa_product': 48, 'torsion_generators': [[51, 0, 1]], 'xcoord_integral_points': [51, 135]}
• lmfdb_label 270480.fx4 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11555053
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '270480.fx4', 'torsion': [6]}
  • id: 11555052
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '270480.fx4', 'torsion': [2, 2]}
  • id: 11555054
    {'degree': 4, 'field': [-245, 0, 112, 0, 1], 'lmfdb_label': '270480.fx4', 'torsion': [4]}
  • id: 11555055
    {'degree': 4, 'field': [9, 0, -1, 0, 1], 'lmfdb_label': '270480.fx4', 'torsion': [2, 6]}
  • id: 11555056
    {'degree': 6, 'field': [25725, 0, 1519, 0, 7, 0, 1], 'lmfdb_label': '270480.fx4', 'torsion': [6]}
  • id: 11555059
    {'degree': 8, 'field': [24336, 0, -7104, 0, 316, 0, 4, 0, 1], 'lmfdb_label': '270480.fx4', 'torsion': [12]}
  • id: 11555057
    {'degree': 8, 'field': [688900, 0, -10600, 0, 1020, 0, 80, 0, 1], 'lmfdb_label': '270480.fx4', 'torsion': [2, 4]}
  • id: 11555058
    {'degree': 8, 'field': [4319841, 78750, 79498, -6510, 4743, -70, 48, 0, 1], 'lmfdb_label': '270480.fx4', 'torsion': [2, 4]}
  • id: 11555060
    {'degree': 12, 'field': [102393, 195534, 88782, 51714, 40375, -17676, 8588, -2220, 447, -114, 38, -6, 1], 'lmfdb_label': '270480.fx4', 'torsion': [3, 6]}
  • id: 11555061
    {'degree': 12, 'field': [7810020, 8197200, 2098476, -361836, -238692, -11316, 16141, 0, 555, -184, 39, 0, 1], 'lmfdb_label': '270480.fx4', 'torsion': [2, 6]}
  • id: 11555063
    {'degree': 16, 'field': [271161, -344916, 492816, -208404, -82594, 141688, 72208, -68892, -19073, 15896, 4512, -3436, -34, 252, -16, -8, 1], 'lmfdb_label': '270480.fx4', 'torsion': [2, 12]}
  • id: 11555064
    {'degree': 16, 'field': [6548481, 0, 2481504, 0, 2068366, 0, 79764, 0, 65679, 0, 12316, 0, 1398, 0, 60, 0, 1], 'lmfdb_label': '270480.fx4', 'torsion': [2, 12]}
  • id: 11555062
    {'degree': 16, 'field': [124316182225, 0, -140683580600, 0, 11514398860, 0, 3255228760, 0, 316131574, 0, 9701944, 0, 75820, 0, 424, 0, 1], 'lmfdb_label': '270480.fx4', 'torsion': [8]}
  • id: 11555065
    {'degree': 18, 'field': [-5649891264, -5886618624, -7292960064, -406271232, 3386971584, 315655488, -427104864, 26425152, 11439648, -7442800, 591792, 194112, 2972, 816, 48, 316, -18, -6, 1], 'lmfdb_label': '270480.fx4', 'torsion': [18]}
• 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: 6701698
    {'conductor': 270480, 'conductor_valuation': 4, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '270480.fx4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 6701699
    {'conductor': 270480, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '270480.fx4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 6701700
    {'conductor': 270480, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '270480.fx4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 6701701
    {'conductor': 270480, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '270480.fx4', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 6701702
    {'conductor': 270480, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '270480.fx4', 'prime': 23, 'reduction_type': 1, '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: 3373810
    {'adelic_gens': [[6721, 2772, 3066, 6973], [6899, 0, 0, 9659], [5634, 6083, 5635, 8854], [1, 0, 12, 1], [9649, 12, 9648, 13], [1, 6, 6, 37], [11, 2, 9610, 9651], [5069, 6902, 924, 1], [1, 12, 0, 1], [6910, 5523, 6321, 2752]], 'adelic_image': '9660.96.1.?', 'conductor': 270480, 'lmfdb_label': '270480.fx4', 'prime': 0}
  • id: 966686
    {'conductor': 270480, 'elladic_image': '2.3.0.1', 'lmfdb_label': '270480.fx4', 'modell_image': '2B', 'prime': 2}
  • id: 966687
    {'conductor': 270480, 'elladic_image': '3.4.0.1', 'lmfdb_label': '270480.fx4', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 270480.fx does not appear in ec_padic