Elliptic curve data - 12240.bp1

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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': '12240bv', 'Clabel': '12240bv1', 'Cnumber': 1, 'abc_quality': 1.0709291492942772, 'absD': 666847516691250000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 2040, 'ainvs': [0, 0, 0, -3964692, 3038267351], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 12240, 'degree': 215040, 'elladic_images': ['4.6.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4560993208958102613775893850', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 41, 'isogeny_degrees': [1, 2], 'jinv': [590887175978458660864, 57171426328125], 'lmfdb_iso': '12240.bp', 'lmfdb_label': '12240.bp1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -440521, 112381580], 'min_quad_twist_disc': 12, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.b.1', '24.12.0-4.b.1.4', '170.6.0.?', '340.24.0.?', '2040.48.0.?'], '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, 'serre_invariants': [[2, 2, 765], [3, 8, 1360], [5, 6, 2448], [7, 2, 2448], [17, 18, 720]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.6757441163751069792075560594', 'prec': 100}, 'szpiro_ratio': 6.076242718690801, '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, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, -1, 0, -8, 0], 'aplist': [0, 0, 1, 0, -2, 2, -1, -8, 4, -2, -2, 6, -2, 2, 6, 6, -8, 10, 2, 2, -2, -10, -2, 2, 2], 'class_deg': 2, 'class_size': 2, 'conductor': 12240, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '12240.bp', 'trace_hash': 663901715299488789}
• 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': '0.0073562966767612516067052731108', 'prec': 110}, 'conductor': 12240, 'gens': [], 'heights': [], 'lmfdb_label': '12240.bp1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.27502331640033054601654479876', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.9251632148023138221158135913376771784', 'prec': 130}, 'tamagawa_product': 28, 'torsion_generators': [[1141, 0, 1]], 'xcoord_integral_points': [1141]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [2, 2, 0], '17': [0, 0]}, 'iwp0': 11, 'lmfdb_label': '12240.bp1'}
• ec_torsion_growth •

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

  
  
  • id: 632255
    {'degree': 2, 'field': [-21, -1, 1], 'lmfdb_label': '12240.bp1', 'torsion': [2, 2]}
  • id: 632256
    {'degree': 4, 'field': [205, -22, -4, -2, 1], 'lmfdb_label': '12240.bp1', 'torsion': [4]}
  • id: 632259
    {'degree': 8, 'field': [-432, 0, 0, 0, 72, 0, 1, 0, 1], 'lmfdb_label': '12240.bp1', 'torsion': [6]}
  • id: 632258
    {'degree': 8, 'field': [34225, -1850, 50, -770, 379, 2, 8, -4, 1], 'lmfdb_label': '12240.bp1', 'torsion': [2, 4]}
  • id: 632257
    {'degree': 8, 'field': [251001, 0, -67344, 0, 6406, 0, -224, 0, 1], 'lmfdb_label': '12240.bp1', 'torsion': [2, 4]}
  • id: 632261
    {'degree': 16, 'field': [86936337, 73231344, -6810840, -47840856, 3690760, 11508608, -937088, -2189352, 342498, 188752, -28152, -11512, 1752, 288, -32, -8, 1], 'lmfdb_label': '12240.bp1', 'torsion': [8]}
  • id: 632260
    {'degree': 16, 'field': [1497063465, 3309536070, 2775368610, 1059054750, 157469346, -3783024, 2715930, 5090850, 925776, -454680, -142326, 5310, 6571, 140, -120, -4, 1], 'lmfdb_label': '12240.bp1', 'torsion': [4, 4]}
  • id: 632262
    {'degree': 16, 'field': [2372177025, 0, 99618300, 0, -74258550, 0, -975120, 0, 484755, 0, 4080, 0, -1526, 0, -4, 0, 1], 'lmfdb_label': '12240.bp1', 'torsion': [2, 6]}
• 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: 264556
    {'conductor': 12240, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '12240.bp1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 264557
    {'conductor': 12240, 'conductor_valuation': 2, 'discriminant_valuation': 22, 'j_denominator_valuation': 16, 'kodaira_symbol': -20, 'lmfdb_label': '12240.bp1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 264558
    {'conductor': 12240, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '12240.bp1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 7}
  • id: 264559
    {'conductor': 12240, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '12240.bp1', 'prime': 17, '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: 1745177
    {'adelic_gens': [[1096, 3, 1365, 682], [1021, 1368, 0, 1], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [3, 8, 28, 75], [503, 2034, 1338, 2021], [5, 8, 48, 77], [679, 0, 0, 2039], [2033, 8, 2032, 9], [766, 681, 783, 4]], 'adelic_image': '2040.48.0.?', 'conductor': 12240, 'lmfdb_label': '12240.bp1', 'prime': 0}
  • id: 58339
    {'conductor': 12240, 'elladic_image': '4.6.0.3', 'lmfdb_label': '12240.bp1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 12240.bp does not appear in ec_padic