Elliptic curve data - 397488.fm1

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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': '397488fm', 'Clabel': '397488fm2', 'Cnumber': 2, 'abc_quality': 1.0242773361136295, 'absD': 25870414972277820672, 'adelic_genus': 5, 'adelic_index': 192, 'adelic_level': 4368, 'ainvs': [0, 1, 0, -46541980, 122196677084], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 397488, 'degree': 43130880, 'elladic_images': ['8.24.0.122'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.9679314266937977821405042167', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 142, 'isogeny_degrees': [1, 2], 'jinv': [34909201168, 81], 'lmfdb_iso': '397488.fm', 'lmfdb_label': '397488.fm1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -5620, 160304], 'min_quad_twist_disc': 364, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.d.1', '8.24.0.bl.2', '26.6.0.b.1', '48.48.1.hj.2', '52.12.0.i.1', '104.48.1.?', '364.24.0.?', '624.96.5.?', '728.96.1.?', '4368.192.5.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 637], [3, 4, 132496], [7, 26, 8112], [13, 62, 2352]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.39083378630330829539710915050', 'prec': 107}, 'szpiro_ratio': 5.009043623262218, '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, -4, 0, 0, 0, 1, 0, 2, 0, 0, 0, -4, 0, -6, 0, 2, 0], 'aplist': [0, 1, -4, 0, 2, 0, -6, 2, 8, 6, -10, 4, 0, -4, 2, -10, 14, 2, -2, -6, -8, 0, -6, 0, 0], 'class_deg': 2, 'class_size': 2, 'conductor': 397488, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '397488.fm', 'trace_hash': 1434182487206303596}
• 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': '0.0026429412995488967586847734232', 'prec': 110}, 'conductor': 397488, 'gens': [], 'heights': [], 'lmfdb_label': '397488.fm1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.18289806390266711415472896218', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4631845112213369132378316974131102961', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[3943, 0, 1]], 'xcoord_integral_points': [3943]}
• lmfdb_label 397488.fm1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 16400501
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '397488.fm1', 'torsion': [2, 2]}
  • id: 16400502
    {'degree': 4, 'field': [29, -22, -24, -1, 1], 'lmfdb_label': '397488.fm1', 'torsion': [2, 4]}
  • id: 16400504
    {'degree': 8, 'field': [-1217307, 0, -2318680, 0, -3822, 0, 0, 0, 1], 'lmfdb_label': '397488.fm1', 'torsion': [6]}
  • id: 16400503
    {'degree': 8, 'field': [531441, 0, -12006, 0, -721, 0, -6, 0, 1], 'lmfdb_label': '397488.fm1', 'torsion': [2, 4]}
  • id: 16400506
    {'degree': 16, 'field': [32761, 0, -4424114, 0, 671089, 0, -53484, 0, 31362, 0, -1662, 0, -140, 0, -20, 0, 1], 'lmfdb_label': '397488.fm1', 'torsion': [2, 8]}
  • id: 16400505
    {'degree': 16, 'field': [7204661, 1253954, -1212256, -48738, -54585, 73704, 8994, -25680, 2392, 2942, -826, 88, 46, -56, 28, -8, 1], 'lmfdb_label': '397488.fm1', 'torsion': [4, 4]}
  • id: 16400508
    {'degree': 16, 'field': [4337056467, 5180736186, 4400738262, 2474439588, 1060539678, 368772258, 94015578, 24135668, 3896649, 569334, 26378, -7404, -2502, -548, -30, 0, 1], 'lmfdb_label': '397488.fm1', 'torsion': [2, 6]}
  • id: 16400507
    {'degree': 16, 'field': [20750978704, 0, -612131616, 0, -1257078832, 0, 106031760, 0, 7868280, 0, 33720, 0, -5932, 0, -12, 0, 1], 'lmfdb_label': '397488.fm1', 'torsion': [2, 8]}
• 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: 9832193
    {'conductor': 397488, 'conductor_valuation': 4, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '397488.fm1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 9832194
    {'conductor': 397488, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '397488.fm1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 9832195
    {'conductor': 397488, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '397488.fm1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 9832196
    {'conductor': 397488, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '397488.fm1', 'prime': 13, '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: 4129744
    {'adelic_gens': [[1457, 3136, 2296, 3249], [3, 2, 4354, 4359], [1, 16, 0, 1], [1336, 609, 4319, 1336], [4353, 16, 4352, 17], [1, 8, 8, 65], [2199, 938, 406, 3767], [1623, 3430, 1232, 601], [1, 0, 16, 1], [3119, 0, 0, 4367]], 'adelic_image': '4368.192.5.?', 'conductor': 397488, 'lmfdb_label': '397488.fm1', 'prime': 0}
  • id: 1352325
    {'conductor': 397488, 'elladic_image': '8.24.0.122', 'lmfdb_label': '397488.fm1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 397488.fm does not appear in ec_padic