Elliptic curve data - 6240.p1

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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': '6240z', 'Clabel': '6240z2', 'Cnumber': 2, 'abc_quality': 1.0847562556631796, 'absD': 465593334336000, 'adelic_genus': 3, 'adelic_index': 192, 'adelic_level': 1040, 'ainvs': [0, -1, 0, -227520, -41682600], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 6240, 'degree': 49152, 'elladic_images': ['8.24.0.57'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7837915225525824771364455964', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 15, 'isogeny_degrees': [1, 2, 4], 'jinv': [2543984126301795848, 909361981125], 'lmfdb_iso': '6240.p', 'lmfdb_label': '6240.p1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -227520, -41682600], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '8.24.0-8.o.1.3', '40.48.0-40.by.1.7', '80.96.0.?', '208.48.0.?', '1040.192.3.?'], '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, 4, 5], [3, 4, 416], [5, 6, 1248], [13, 14, 480]], 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.2639311371326234950735215053', 'prec': 100}, 'szpiro_ratio': 5.5635724321541264, '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, 4, 0, 1, 0, 0, 0, 1, 0, -1, 0, 2, 0, 8, 0], 'aplist': [0, -1, 1, 4, 0, 1, 2, 8, 4, 6, -8, 6, -6, -4, 4, 6, 8, -10, 4, 8, -14, 0, 12, -6, -6], 'class_deg': 4, 'class_size': 4, 'conductor': 6240, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '6240.p', 'trace_hash': 1890080444446588596}
• 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': '0.028223987413583143300726769587', 'prec': 107}, 'conductor': 6240, 'gens': [], 'heights': [], 'lmfdb_label': '6240.p1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.21860184215428118432619676701', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.6232221058513742119143612041483218774', 'prec': 130}, 'tamagawa_product': 12, 'torsion_generators': [[-279, 0, 1]], 'xcoord_integral_points': [-279]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [1, 0], '13': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '6240.p1'}
• ec_torsion_growth •

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

  
  
  • id: 325239
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '6240.p1', 'torsion': [2, 2]}
  • id: 325240
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '6240.p1', 'torsion': [4]}
  • id: 325241
    {'degree': 2, 'field': [10, 0, 1], 'lmfdb_label': '6240.p1', 'torsion': [4]}
  • id: 325243
    {'degree': 4, 'field': [-6760, 0, 0, 0, 1], 'lmfdb_label': '6240.p1', 'torsion': [2, 4]}
  • id: 325242
    {'degree': 4, 'field': [25, 0, 0, 0, 1], 'lmfdb_label': '6240.p1', 'torsion': [2, 4]}
  • id: 325244
    {'degree': 4, 'field': [1690, 0, -78, 0, 1], 'lmfdb_label': '6240.p1', 'torsion': [8]}
  • id: 325248
    {'degree': 8, 'field': [521, -140, -346, -124, -116, -40, -2, -4, 1], 'lmfdb_label': '6240.p1', 'torsion': [6]}
  • id: 325246
    {'degree': 8, 'field': [625, 0, 0, 0, -40, 0, 0, 0, 1], 'lmfdb_label': '6240.p1', 'torsion': [2, 8]}
  • id: 325247
    {'degree': 8, 'field': [227786, -7904, -21388, -760, 1126, -40, -8, -4, 1], 'lmfdb_label': '6240.p1', 'torsion': [2, 8]}
  • id: 325245
    {'degree': 8, 'field': [2859481, 0, -20276, 0, 3386, 0, 4, 0, 1], 'lmfdb_label': '6240.p1', 'torsion': [4, 4]}
  • id: 325253
    {'degree': 16, 'field': [6500, -11600, 201280, -186288, 22528, 64328, -1184, -20240, 8028, -200, -760, 32, 140, -84, 32, -8, 1], 'lmfdb_label': '6240.p1', 'torsion': [12]}
  • id: 325252
    {'degree': 16, 'field': [27501201, -131895036, 212706104, -129516764, 27239498, -4624880, -1009108, 1116196, -159276, 28716, -10536, 1804, -694, 136, -8, -4, 1], 'lmfdb_label': '6240.p1', 'torsion': [2, 6]}
  • id: 325254
    {'degree': 16, 'field': [325056446, -311964376, 133972924, -33247184, 22161008, -17890560, 8683732, -2307824, 317684, 636, -6076, 2144, -354, -4, 32, -4, 1], 'lmfdb_label': '6240.p1', 'torsion': [12]}
  • id: 325250
    {'degree': 16, 'field': [427844106, 369708192, 734670000, 514448736, 332023948, 145733456, 52660984, 10409784, 646950, -385592, -80952, 2816, 3672, 456, -68, -8, 1], 'lmfdb_label': '6240.p1', 'torsion': [4, 8]}
  • id: 325251
    {'degree': 16, 'field': [1785062500, 0, 0, 0, -68107000, 0, 0, 0, 6428760, 0, 0, 0, -1612, 0, 0, 0, 1], 'lmfdb_label': '6240.p1', 'torsion': [16]}
  • id: 325249
    {'degree': 16, 'field': [3417571600, 0, -7993769600, 0, -1493215200, 0, -55576000, 0, 840280, 0, -95200, 0, 2760, 0, -80, 0, 1], 'lmfdb_label': '6240.p1', '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: 124757
    {'conductor': 6240, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '6240.p1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 124758
    {'conductor': 6240, 'conductor_valuation': 1, 'discriminant_valuation': 16, 'j_denominator_valuation': 16, 'kodaira_symbol': 20, 'lmfdb_label': '6240.p1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 124759
    {'conductor': 6240, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '6240.p1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 124760
    {'conductor': 6240, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '6240.p1', 'prime': 13, '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: 1704879
    {'adelic_gens': [[794, 783, 93, 20], [15, 166, 754, 995], [253, 770, 768, 187], [1, 16, 0, 1], [1025, 16, 1024, 17], [1, 8, 8, 65], [561, 16, 328, 129], [638, 3, 301, 20], [1, 0, 16, 1]], 'adelic_image': '1040.192.3.?', 'conductor': 6240, 'lmfdb_label': '6240.p1', 'prime': 0}
  • id: 30641
    {'conductor': 6240, 'elladic_image': '8.24.0.57', 'lmfdb_label': '6240.p1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 6240.p does not appear in ec_padic