Elliptic curve data - 221760.hy2

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '221760cy', 'Clabel': '221760cy1', 'Cnumber': 1, 'abc_quality': 0.9884660970305377, 'absD': 792559823239800000, 'adelic_genus': 1, 'adelic_index': 48, 'adelic_level': 9240, 'ainvs': [0, 0, 0, -321852, 82303846], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 5, 'class_size': 2, 'cm': 0, 'conductor': 221760, 'degree': 3840000, 'elladic_images': ['5.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1556448102891121919111814840', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 206, 'isogeny_degrees': [1, 5], 'jinv': [-79028701534867456, 16987307596875], 'lmfdb_iso': '221760.hy', 'lmfdb_label': '221760.hy2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -8940, 378056], 'min_quad_twist_disc': 24, 'modell_images': ['5B.4.1'], 'modm_images': ['5.12.0.a.1', '120.24.0.?', '2310.24.1.?', '3080.24.0.?', '9240.48.1.?'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.2597650756750846915049428048', 'prec': 100}, 'szpiro_ratio': 4.059921790354771, '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, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 6, 0, 0, 0, 7, 0, -5, 0], 'aplist': [0, 0, 1, -1, -1, 6, 7, -5, -1, -5, 8, 2, -12, -11, 8, -11, 5, -7, -2, 12, 4, 10, 1, -15, 3], 'class_deg': 5, 'class_size': 2, 'conductor': 221760, 'isogeny_matrix': [[1, 5], [5, 1]], 'lmfdb_iso': '221760.hy', 'trace_hash': 1392827428620845888}
• 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': '0.013416236578260284841240831612', 'prec': 107}, 'conductor': 221760, 'gens': [], 'heights': [], 'lmfdb_label': '221760.hy2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.27081339671744287487995578443', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.7081339671744287487995578443096813991', 'prec': 130}, 'tamagawa_product': 10, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 221760.hy2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9644680
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '221760.hy2', 'torsion': [5]}
  • id: 9644681
    {'degree': 3, 'field': [-26, 18, 0, 1], 'lmfdb_label': '221760.hy2', 'torsion': [2]}
  • id: 9644683
    {'degree': 6, 'field': [-600, 0, 76, 0, 22, 0, 1], 'lmfdb_label': '221760.hy2', 'torsion': [10]}
  • id: 9644682
    {'degree': 6, 'field': [2055, 2190, 1099, 64, -3, -2, 1], 'lmfdb_label': '221760.hy2', 'torsion': [2, 2]}
  • id: 9644684
    {'degree': 8, 'field': [-432, 0, 0, 0, 72, 0, 26, 0, 1], 'lmfdb_label': '221760.hy2', 'torsion': [3]}
  • id: 9644686
    {'degree': 12, 'field': [5926320, 4201920, 7299744, -819552, 1505152, -120960, 115136, -4464, 4908, -96, 116, 0, 1], 'lmfdb_label': '221760.hy2', 'torsion': [2, 10]}
  • id: 9644685
    {'degree': 12, 'field': [347429803, 232745672, 144178942, 26688300, 7356455, 1265848, -28778, 14332, -2065, -660, 4, -4, 1], 'lmfdb_label': '221760.hy2', 'torsion': [4]}
  • id: 9644687
    {'degree': 16, 'field': [998001, 0, -2937822, 0, 1641301, 0, -496644, 0, 96066, 0, -12266, 0, 996, 0, -48, 0, 1], 'lmfdb_label': '221760.hy2', 'torsion': [15]}
  • id: 9644688
    {'degree': 20, 'field': [98883223561, -154558399184, 158371733384, -124865409584, 82609701944, -42901596132, 21417883616, -8105117976, 3236096726, -924308376, 304794134, -66156328, 18298888, -2983988, 693968, -82028, 15908, -1248, 198, -8, 1], 'lmfdb_label': '221760.hy2', 'torsion': [5]}
• 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: 5497110
    {'conductor': 221760, 'conductor_valuation': 6, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '221760.hy2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 5497111
    {'conductor': 221760, 'conductor_valuation': 2, 'discriminant_valuation': 11, 'j_denominator_valuation': 5, 'kodaira_symbol': -9, 'lmfdb_label': '221760.hy2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5497112
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '221760.hy2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 5}
  • id: 5497113
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '221760.hy2', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 5497114
    {'conductor': 221760, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '221760.hy2', 'prime': 11, '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

  
  
  • id: 3079854
    {'adelic_gens': [[9234, 9235, 7705, 6934], [6929, 0, 0, 9239], [1, 0, 10, 1], [6, 13, 9185, 9121], [6939, 9230, 6940, 9229], [1266, 5, 1255, 2306], [9234, 9227, 6985, 7049], [9234, 9235, 6935, 7858], [1656, 5, 1315, 2306], [9231, 10, 9230, 11], [1, 10, 0, 1], [4619, 0, 0, 9239]], 'adelic_image': '9240.48.1.?', 'conductor': 221760, 'lmfdb_label': '221760.hy2', 'prime': 0}
  • id: 812758
    {'conductor': 221760, 'elladic_image': '5.12.0.1', 'lmfdb_label': '221760.hy2', 'modell_image': '5B.4.1', 'prime': 5}
• lmfdb_iso 221760.hy does not appear in ec_padic