Elliptic curve data - 12480.j1

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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': '12480h', 'Clabel': '12480h2', 'Cnumber': 2, 'abc_quality': 0.997177538945588, 'absD': 17686356480000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 312, 'ainvs': [0, -1, 0, -42361, 3363865], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 12480, 'degree': 36864, 'elladic_images': ['4.6.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4270659222290096344986777367', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 9, 'isogeny_degrees': [1, 2], 'jinv': [2052450196928704, 4317958125], 'lmfdb_iso': '12480.j', 'lmfdb_label': '12480.j1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -10590, -415188], 'min_quad_twist_disc': -8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.b.1', '24.12.0-4.b.1.1', '26.6.0.b.1', '52.12.0.e.1', '104.24.0.?', '312.48.0.?'], '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, 13], [3, 4, 4160], [5, 6, 2496], [13, 14, 960]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.73391874166906432508144561524', 'prec': 103}, 'szpiro_ratio': 4.620029586182773, '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, -2, 0, 1, 0, 2, 0, 1, 0, 1, 0, -2, 0, 2, 0], 'aplist': [0, -1, -1, -2, 2, 1, -2, 2, 8, 6, 2, -2, -2, 0, -6, 10, -14, 10, 2, 6, 2, 12, 6, -18, -14], 'class_deg': 2, 'class_size': 2, 'conductor': 12480, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '12480.j', 'trace_hash': 1420948974998049219}
• 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': '0.057605810221987268440208044670', 'prec': 107}, 'conductor': 12480, 'gens': [], 'heights': [], 'lmfdb_label': '12480.j1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.69233173281901444908294857384', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.3846634656380288981658971476761830603', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[115, 0, 1]], 'xcoord_integral_points': [115]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '5': [0, 0], '13': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '12480.j1'}
• ec_torsion_growth •

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

  
  
  • id: 642866
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '12480.j1', 'torsion': [2, 2]}
  • id: 642867
    {'degree': 4, 'field': [13, 0, -4, 0, 1], 'lmfdb_label': '12480.j1', 'torsion': [4]}
  • id: 642870
    {'degree': 8, 'field': [-588, 0, 424, 0, -84, 0, 0, 0, 1], 'lmfdb_label': '12480.j1', 'torsion': [6]}
  • id: 642869
    {'degree': 8, 'field': [1, 0, 0, 0, 11, 0, 0, 0, 1], 'lmfdb_label': '12480.j1', 'torsion': [2, 4]}
  • id: 642868
    {'degree': 8, 'field': [9, 0, -22, 0, 31, 0, -16, 0, 1], 'lmfdb_label': '12480.j1', 'torsion': [2, 4]}
  • id: 642873
    {'degree': 16, 'field': [-9087, 97656, -469156, 1241792, -1790794, 1190056, -46256, -288728, 58095, 8856, -1560, 280, -350, 112, 4, -8, 1], 'lmfdb_label': '12480.j1', 'torsion': [2, 6]}
  • id: 642871
    {'degree': 16, 'field': [144, -1344, 6272, -14176, 20320, -22112, 19104, -12816, 6700, -3200, 1632, -664, 196, -72, 32, -8, 1], 'lmfdb_label': '12480.j1', 'torsion': [4, 4]}
  • id: 642872
    {'degree': 16, 'field': [28561, 0, -17576, 0, -2366, 0, -5408, 0, 5083, 0, -416, 0, -14, 0, -8, 0, 1], 'lmfdb_label': '12480.j1', '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: 269771
    {'conductor': 12480, 'conductor_valuation': 6, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -6, 'lmfdb_label': '12480.j1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 269772
    {'conductor': 12480, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '12480.j1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 269773
    {'conductor': 12480, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '12480.j1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 269774
    {'conductor': 12480, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '12480.j1', 'prime': 13, '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: 1746867
    {'adelic_gens': [[149, 306, 6, 5], [224, 3, 101, 2], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [3, 8, 28, 75], [241, 6, 306, 307], [5, 8, 48, 77], [305, 8, 304, 9], [209, 8, 212, 33]], 'adelic_image': '312.48.0.?', 'conductor': 12480, 'lmfdb_label': '12480.j1', 'prime': 0}
  • id: 59493
    {'conductor': 12480, 'elladic_image': '4.6.0.3', 'lmfdb_label': '12480.j1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 12480.j does not appear in ec_padic