Elliptic curve data - 54450.ef1

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '54450gf', 'Clabel': '54450gf7', 'Cnumber': 7, 'abc_quality': 1.0818126452233845, 'absD': 1634514148265625000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 1320, 'ainvs': [1, -1, 1, -145205105, -673437860103], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 11], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 54450, 'degree': 6635520, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.1171387221666419853182163956', 'prec': 100}, 'faltings_index': 6, 'faltings_ratio': 12, 'intrinsic_torsion': 2, 'iso_nlabel': 109, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [16778985534208729, 81000], 'lmfdb_iso': '54450.ef', 'lmfdb_label': '54450.ef1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -5334, -150368], 'min_quad_twist_disc': 165, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '12.24.0.g.1', '24.96.1.dj.3', '40.12.0.v.1', '60.48.0.c.3', '88.12.0.?', '120.192.5.?', '132.48.0.?', '165.8.0.?', '264.192.1.?', '330.24.0.?', '440.24.0.?', '660.96.0.?', '1320.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 27225], [3, 8, 3025], [5, 18, 2178], [11, 62, 450]], 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.56416598521635168028924232154', 'prec': 103}, 'szpiro_ratio': 6.235152567128478, '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, 0, 1, 0, 0, -4, 1, 0, 0, 0, 0, 2, -4, 0, 1, -6, 0, 4, 0], 'aplist': [1, 0, 0, -4, 0, 2, -6, 4, 0, -6, 8, -2, -6, -4, 0, -6, 0, 10, 4, 0, 2, -8, -12, -18, -2], 'class_deg': 12, 'class_size': 8, 'conductor': 54450, 'isogeny_matrix': [[1, 4, 2, 12, 3, 6, 4, 12], [4, 1, 2, 3, 12, 6, 4, 12], [2, 2, 1, 6, 6, 3, 2, 6], [12, 3, 6, 1, 4, 2, 12, 4], [3, 12, 6, 4, 1, 2, 12, 4], [6, 6, 3, 2, 2, 1, 6, 2], [4, 4, 2, 12, 12, 6, 1, 3], [12, 12, 6, 4, 4, 2, 3, 1]], 'lmfdb_iso': '54450.ef', 'trace_hash': 1090374075137280173}
• 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': '0.0019610456671910703994906566497', 'prec': 110}, 'conductor': 54450, 'gens': [], 'heights': [], 'lmfdb_label': '54450.ef1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.043491469678392664467753081087', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.0875905445628478944521478921645901573', 'prec': 130}, 'tamagawa_product': 48, 'torsion_generators': [[-27829, 27825, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 1], '3': 'a', '5': 'a', '11': 'a'}, 'iwp0': 5, 'lmfdb_label': '54450.ef1'}
• ec_torsion_growth •

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

  
  
  • id: 2634308
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '54450.ef1', 'torsion': [2, 2]}
  • id: 2634311
    {'degree': 2, 'field': [14, -1, 1], 'lmfdb_label': '54450.ef1', 'torsion': [6]}
  • id: 2634309
    {'degree': 2, 'field': [33, 0, 1], 'lmfdb_label': '54450.ef1', 'torsion': [4]}
  • id: 2634310
    {'degree': 2, 'field': [330, 0, 1], 'lmfdb_label': '54450.ef1', 'torsion': [4]}
  • id: 2634313
    {'degree': 4, 'field': [64, 0, 6, 0, 1], 'lmfdb_label': '54450.ef1', 'torsion': [2, 6]}
  • id: 2634314
    {'degree': 4, 'field': [144, 0, 9, 0, 1], 'lmfdb_label': '54450.ef1', 'torsion': [12]}
  • id: 2634315
    {'degree': 4, 'field': [394, -16, 17, -2, 1], 'lmfdb_label': '54450.ef1', 'torsion': [12]}
  • id: 2634312
    {'degree': 4, 'field': [1849, 0, 46, 0, 1], 'lmfdb_label': '54450.ef1', 'torsion': [2, 4]}
  • id: 2634316
    {'degree': 6, 'field': [-6591, 0, 0, -126, 0, 0, 1], 'lmfdb_label': '54450.ef1', 'torsion': [6]}
  • id: 2634317
    {'degree': 8, 'field': [-744, 6048, -5744, -576, 209, 92, -26, -4, 1], 'lmfdb_label': '54450.ef1', 'torsion': [2, 4]}
  • id: 2634320
    {'degree': 8, 'field': [18496, 0, 3648, 0, 308, 0, -12, 0, 1], 'lmfdb_label': '54450.ef1', 'torsion': [2, 12]}
  • id: 2634318
    {'degree': 8, 'field': [37266, -9240, 2548, -1320, 69, -110, 27, 0, 1], 'lmfdb_label': '54450.ef1', 'torsion': [8]}
  • id: 2634319
    {'degree': 8, 'field': [98926, -13880, 14908, -2096, 1149, -124, 46, -4, 1], 'lmfdb_label': '54450.ef1', 'torsion': [24]}
  • id: 2634323
    {'degree': 12, 'field': [9, 0, 0, 0, 0, 0, 6474, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '54450.ef1', 'torsion': [12]}
  • id: 2634322
    {'degree': 12, 'field': [576, 0, 0, 0, 0, 0, -51792, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '54450.ef1', 'torsion': [2, 6]}
  • id: 2634321
    {'degree': 12, 'field': [7518124, -3243342, 3818349, -1204900, 742605, -176502, 72947, -12606, 3795, -440, 99, -6, 1], 'lmfdb_label': '54450.ef1', 'torsion': [3, 6]}
  • id: 2634324
    {'degree': 12, 'field': [43673809, -9953496, -600216, 1677060, 490956, 6048, 2854, 0, 60, -252, 12, 0, 1], 'lmfdb_label': '54450.ef1', 'torsion': [12]}
  • id: 2634327
    {'degree': 16, 'field': [5503716, 0, -2897016, 0, 747760, 0, -157524, 0, 39309, 0, -6944, 0, 690, 0, -36, 0, 1], 'lmfdb_label': '54450.ef1', 'torsion': [2, 8]}
  • id: 2634329
    {'degree': 16, 'field': [6584356, 0, -1279324, 0, 58745, 0, -37896, 0, 9284, 0, -426, 0, -40, 0, -4, 0, 1], 'lmfdb_label': '54450.ef1', 'torsion': [24]}
  • id: 2634328
    {'degree': 16, 'field': [20322856, 31521152, 14948264, -1493448, -745007, 2711092, 442026, -550084, 303063, -66328, 9204, -1904, 463, -156, 26, -4, 1], 'lmfdb_label': '54450.ef1', 'torsion': [2, 12]}
  • id: 2634325
    {'degree': 16, 'field': [33709636, 0, 8576432, 0, 5629340, 0, 1494912, 0, 291749, 0, 32028, 0, 2030, 0, 68, 0, 1], 'lmfdb_label': '54450.ef1', 'torsion': [4, 4]}
  • id: 2634326
    {'degree': 16, 'field': [131729284, -338592, 52966432, 5784096, 9114296, 1514160, 1233072, 134208, 113816, 12576, 5568, 432, 404, -24, -8, 0, 1], 'lmfdb_label': '54450.ef1', 'torsion': [2, 24]}
  • id: 2634330
    {'degree': 18, 'field': [8742287920, -7765984800, -107726400, 1546098220, -53820300, -209061780, 11458164, 21350724, -1315548, -1967965, 143265, 148374, -14976, -7788, 1170, 250, -48, -3, 1], 'lmfdb_label': '54450.ef1', '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: 1308295
    {'conductor': 54450, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '54450.ef1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 1308296
    {'conductor': 54450, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '54450.ef1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1308297
    {'conductor': 54450, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '54450.ef1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1308298
    {'conductor': 54450, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '54450.ef1', 'prime': 11, '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: 2026035
    {'adelic_gens': [[1, 12, 12, 145], [219, 1276, 352, 747], [1297, 24, 1296, 25], [1088, 957, 363, 1286], [1002, 319, 77, 452], [15, 106, 14, 11], [1, 24, 0, 1], [991, 264, 990, 1], [1, 0, 24, 1], [119, 0, 0, 1319]], 'adelic_image': '1320.384.5.?', 'conductor': 54450, 'lmfdb_label': '54450.ef1', 'prime': 0}
  • id: 232336
    {'conductor': 54450, 'elladic_image': '4.6.0.1', 'lmfdb_label': '54450.ef1', 'modell_image': '2B', 'prime': 2}
  • id: 232337
    {'conductor': 54450, 'elladic_image': '3.4.0.1', 'lmfdb_label': '54450.ef1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 54450.ef does not appear in ec_padic