Elliptic curve data - 6720.bw6

Formats: - HTML - YAML - JSON - 2024-05-03T05:48:55.514134

• 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': '6720ca', 'Clabel': '6720ca6', 'Cnumber': 6, 'abc_quality': 1.1006655403587287, 'absD': 56670299750400, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 1680, 'ainvs': [0, 1, 0, 9599, -9601], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 6720, 'degree': 16384, 'elladic_images': ['8.24.0.97'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3284832049844247154748340214', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 48, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [746185003198, 432360075], 'lmfdb_iso': '6720.bw', 'lmfdb_label': '6720.bw6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, 2400, 2400], 'min_quad_twist_disc': -8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0-8.n.1.11', '12.12.0-4.c.1.2', '24.48.0-24.bn.1.3', '40.48.0-40.ca.2.1', '112.48.0.?', '120.96.0.?', '336.96.0.?', '560.96.0.?', '1680.192.1.?'], '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, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.34652469919116886046708851600', 'prec': 103}, 'szpiro_ratio': 4.4391735499008504, '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, 1, 0, 1, 0, 4, 0, 2, 0, -1, 0, 2, 0, 4, 0], 'aplist': [0, 1, -1, 1, 4, 2, 2, 4, 0, 2, -8, 2, 2, 4, 0, 10, -12, -6, 12, 0, -6, 8, 4, 2, -14], 'class_deg': 8, 'class_size': 6, 'conductor': 6720, 'isogeny_matrix': [[1, 8, 4, 2, 4, 8], [8, 1, 2, 4, 8, 4], [4, 2, 1, 2, 4, 2], [2, 4, 2, 1, 2, 4], [4, 8, 4, 2, 1, 8], [8, 4, 2, 4, 8, 1]], 'lmfdb_iso': '6720.bw', 'trace_hash': 901733934894741258}
• 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': '0.070160738153690131040085801785', 'prec': 107}, 'conductor': 6720, 'gens': [], 'heights': [], 'lmfdb_label': '6720.bw6', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.37285232311100548266982857589', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.9828185848880438613586286071001279746', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[1, 0, 1]], 'xcoord_integral_points': [1]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [0, 0], '7': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '6720.bw6'}
• ec_torsion_growth •

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

  
  
  • id: 353370
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '6720.bw6', 'torsion': [4]}
  • id: 353371
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '6720.bw6', 'torsion': [4]}
  • id: 353369
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '6720.bw6', 'torsion': [2, 2]}
  • id: 353372
    {'degree': 4, 'field': [4, 0, 2, 0, 1], 'lmfdb_label': '6720.bw6', 'torsion': [2, 4]}
  • id: 353374
    {'degree': 4, 'field': [9, 0, 4, 0, 1], 'lmfdb_label': '6720.bw6', 'torsion': [8]}
  • id: 353373
    {'degree': 4, 'field': [49, 0, -16, 0, 1], 'lmfdb_label': '6720.bw6', 'torsion': [8]}
  • id: 353378
    {'degree': 8, 'field': [-243, 0, 666, 0, -54, 0, 0, 0, 1], 'lmfdb_label': '6720.bw6', 'torsion': [6]}
  • id: 353376
    {'degree': 8, 'field': [36, 0, 0, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '6720.bw6', 'torsion': [8]}
  • id: 353377
    {'degree': 8, 'field': [81, 0, -36, 0, 7, 0, -4, 0, 1], 'lmfdb_label': '6720.bw6', 'torsion': [2, 8]}
  • id: 353375
    {'degree': 8, 'field': [24601, -18360, 3608, -240, 318, -120, 8, 0, 1], 'lmfdb_label': '6720.bw6', 'torsion': [2, 4]}
  • id: 353380
    {'degree': 16, 'field': [81, 0, -324, 0, 648, 0, -864, 0, 711, 0, -288, 0, 72, 0, -12, 0, 1], 'lmfdb_label': '6720.bw6', 'torsion': [2, 8]}
  • id: 353384
    {'degree': 16, 'field': [1225, 0, -4900, 0, 4900, 0, -732, 0, 942, 0, 132, 0, 4, 0, -4, 0, 1], 'lmfdb_label': '6720.bw6', 'torsion': [12]}
  • id: 353383
    {'degree': 16, 'field': [11025, 0, 25164, 0, 11980, 0, -3948, 0, -2298, 0, 340, 0, 60, 0, 12, 0, 1], 'lmfdb_label': '6720.bw6', 'torsion': [2, 6]}
  • id: 353385
    {'degree': 16, 'field': [59049, 0, 161838, 0, 430434, 0, 35964, 0, 3159, 0, 1332, 0, 54, 0, 0, 0, 1], 'lmfdb_label': '6720.bw6', 'torsion': [12]}
  • id: 353379
    {'degree': 16, 'field': [31640625, 0, -25312500, 0, 10125000, 0, -2700000, 0, 444375, 0, -36000, 0, 1800, 0, -60, 0, 1], 'lmfdb_label': '6720.bw6', 'torsion': [4, 4]}
  • id: 353382
    {'degree': 16, 'field': [65610000, 0, 38880000, 0, 16974000, 0, 3012000, 0, 503500, 0, 35600, 0, 1940, 0, 40, 0, 1], 'lmfdb_label': '6720.bw6', 'torsion': [16]}
  • id: 353381
    {'degree': 16, 'field': [133800625, -203962500, -86621500, 238945000, -59179900, -42627900, 25321460, -8489820, 3166411, -874884, 159940, -23116, 3804, -616, 40, -4, 1], 'lmfdb_label': '6720.bw6', 'torsion': [16]}
• 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: 136874
    {'conductor': 6720, 'conductor_valuation': 6, 'discriminant_valuation': 17, 'j_denominator_valuation': 0, 'kodaira_symbol': -11, 'lmfdb_label': '6720.bw6', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 136875
    {'conductor': 6720, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '6720.bw6', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 136876
    {'conductor': 6720, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '6720.bw6', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 136877
    {'conductor': 6720, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '6720.bw6', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1708286
    {'adelic_gens': [[5, 4, 1676, 1677], [1021, 16, 1088, 1365], [1, 16, 0, 1], [1469, 1664, 1050, 1259], [1665, 16, 1664, 17], [1136, 5, 1635, 1666], [15, 2, 1582, 1667], [1244, 1259, 681, 830], [241, 16, 248, 129], [1, 0, 16, 1]], 'adelic_image': '1680.192.1.?', 'conductor': 6720, 'lmfdb_label': '6720.bw6', 'prime': 0}
  • id: 33154
    {'conductor': 6720, 'elladic_image': '8.24.0.97', 'lmfdb_label': '6720.bw6', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 6720.bw does not appear in ec_padic