Elliptic curve data - 31680.m2

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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': '31680l', 'Clabel': '31680l1', 'Cnumber': 1, 'abc_quality': 0.9501666666067821, 'absD': 88209000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1320, 'ainvs': [0, 0, 0, 1077, 4372], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 11], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 31680, 'degree': 18432, 'elladic_images': ['4.6.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.78921492684761297006188830017', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 12, 'isogeny_degrees': [1, 2], 'jinv': [2961169856, 1890625], 'lmfdb_iso': '31680.m', 'lmfdb_label': '31680.m2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, 479, 1455], 'min_quad_twist_disc': 24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.a.1', '20.12.0.d.1', '40.24.0.t.1', '132.12.0.?', '660.24.0.?', '1320.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.10666480776641453034435037902', 'prec': 107}, 'szpiro_ratio': 3.1417564444327324, '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, 0, 0, -1, 0, -2, 0, 0, 0, -1, 0, 2, 0, 0, 0, 2, 0, 0, 0], 'aplist': [0, 0, -1, -2, -1, 2, 2, 0, 2, -2, -4, 6, -6, -6, 6, -6, 0, 6, 2, 4, -10, 8, 14, -10, -14], 'class_deg': 2, 'class_size': 2, 'conductor': 31680, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '31680.m', 'trace_hash': 1826282119404302141}
• 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': '0.20629876327846908272469910978', 'prec': 103}, 'conductor': 31680, 'gens': [], 'heights': [], 'lmfdb_label': '31680.m2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.66937235774488099617091939790', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.3387447154897619923418387958035658119', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-4, 0, 1]], 'xcoord_integral_points': [-4]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [0, 0], '11': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '31680.m2'}
• ec_torsion_growth •

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

  
  
  • id: 1576539
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '31680.m2', 'torsion': [2, 2]}
  • id: 1576540
    {'degree': 4, 'field': [-36, 0, -6, 0, 1], 'lmfdb_label': '31680.m2', 'torsion': [4]}
  • id: 1576543
    {'degree': 8, 'field': [-363, 0, 0, 0, 66, 0, -16, 0, 1], 'lmfdb_label': '31680.m2', 'torsion': [6]}
  • id: 1576542
    {'degree': 8, 'field': [81, 0, 0, 0, 27, 0, 0, 0, 1], 'lmfdb_label': '31680.m2', 'torsion': [2, 4]}
  • id: 1576541
    {'degree': 8, 'field': [400, 0, -560, 0, 269, 0, -28, 0, 1], 'lmfdb_label': '31680.m2', 'torsion': [2, 4]}
  • id: 1576544
    {'degree': 16, 'field': [256, 0, 0, 0, 1968, 0, 0, 0, 1793, 0, 0, 0, 123, 0, 0, 0, 1], 'lmfdb_label': '31680.m2', 'torsion': [4, 4]}
  • id: 1576546
    {'degree': 16, 'field': [14400, 0, 10368, 0, 1008, 0, -4008, 0, 1965, 0, -384, 0, 58, 0, -8, 0, 1], 'lmfdb_label': '31680.m2', 'torsion': [2, 6]}
  • id: 1576545
    {'degree': 16, 'field': [331441, 345920, 641328, 3067440, 3911650, 2386440, 517488, -237920, -172501, -26120, 7552, 3680, 490, -120, -48, 0, 1], 'lmfdb_label': '31680.m2', 'torsion': [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: 739035
    {'conductor': 31680, 'conductor_valuation': 6, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '31680.m2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 739036
    {'conductor': 31680, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '31680.m2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 739037
    {'conductor': 31680, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '31680.m2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 739038
    {'conductor': 31680, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '31680.m2', 'prime': 11, '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: 1875767
    {'adelic_gens': [[3, 8, 10, 27], [1, 0, 8, 1], [1, 8, 0, 1], [1057, 882, 0, 1], [1313, 8, 1312, 9], [439, 0, 0, 1319], [5, 8, 48, 77], [1201, 888, 642, 457], [989, 876, 495, 1319], [659, 876, 438, 431]], 'adelic_image': '1320.48.0.?', 'conductor': 31680, 'lmfdb_label': '31680.m2', 'prime': 0}
  • id: 141750
    {'conductor': 31680, 'elladic_image': '4.6.0.5', 'lmfdb_label': '31680.m2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 31680.m does not appear in ec_padic