Elliptic curve data - 6720.bp5

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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': '6720u', 'Clabel': '6720u2', 'Cnumber': 2, 'abc_quality': 0.9591619974980434, 'absD': 2265867878400, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 840, 'ainvs': [0, 1, 0, -4481, -91425], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 6720, 'degree': 12288, 'elladic_images': ['8.48.0.80'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0833310197541046081700431088', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 41, 'isogeny_degrees': [1, 2, 4], 'jinv': [37966934881, 8643600], 'lmfdb_iso': '6720.bp', 'lmfdb_label': '6720.bp5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -70, -205], 'min_quad_twist_disc': 8, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.48.0-8.e.1.3', '56.96.0-56.r.1.3', '60.24.0.c.1', '120.96.0.?', '840.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 9, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.9659127093275937559214099552', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.043610248914186644044194926614', 'prec': 107}, 'szpiro_ratio': 4.1798803089087535, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, -8, -6, -8, 2, 2, 12, -8, -6, -4, 2, -12, 8, -14, 0, -12, 2, 10], 'class_deg': 8, 'class_size': 6, 'conductor': 6720, 'isogeny_matrix': [[1, 2, 4, 8, 4, 8], [2, 1, 2, 4, 2, 4], [4, 2, 1, 8, 4, 8], [8, 4, 8, 1, 2, 4], [4, 2, 4, 2, 1, 2], [8, 4, 8, 4, 2, 1]], 'lmfdb_iso': '6720.bp', 'trace_hash': 1225520396839139982}
• 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': '0.11455937407583796423773590337', 'prec': 103}, 'conductor': 6720, 'gens': [[-51, 84, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.9659127093275937559214099552', 'prec': 100}], 'lmfdb_label': '6720.bp5', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.59304424724246094818336579137', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.6634928913902790994064492896598964304', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[-23, 0, 1], [75, 0, 1]], 'xcoord_integral_points': [-53, -51, -23, 75, 82, 1867]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [1, 0], '7': [2, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '6720.bp5'}
• ec_torsion_growth •

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

  
  
  • id: 351709
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '6720.bp5', 'torsion': [2, 4]}
  • id: 351711
    {'degree': 4, 'field': [6, -12, 13, -2, 1], 'lmfdb_label': '6720.bp5', 'torsion': [2, 4]}
  • id: 351712
    {'degree': 4, 'field': [16, 0, 6, 0, 1], 'lmfdb_label': '6720.bp5', 'torsion': [2, 8]}
  • id: 351710
    {'degree': 4, 'field': [49, 0, 16, 0, 1], 'lmfdb_label': '6720.bp5', 'torsion': [2, 4]}
  • id: 351716
    {'degree': 8, 'field': [-48, 0, -34, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '6720.bp5', 'torsion': [2, 6]}
  • id: 351714
    {'degree': 8, 'field': [16, 0, 32, 0, 9, 0, 8, 0, 1], 'lmfdb_label': '6720.bp5', 'torsion': [2, 8]}
  • id: 351715
    {'degree': 8, 'field': [196, 0, -420, 0, 197, 0, -30, 0, 1], 'lmfdb_label': '6720.bp5', 'torsion': [2, 8]}
  • id: 351713
    {'degree': 8, 'field': [256, 0, 0, 0, 17, 0, 0, 0, 1], 'lmfdb_label': '6720.bp5', 'torsion': [4, 4]}
  • id: 351719
    {'degree': 16, 'field': [2116, -4784, 5408, -5992, 4808, -1672, -24, 924, -1307, 732, -216, -4, 98, -76, 32, -8, 1], 'lmfdb_label': '6720.bp5', 'torsion': [4, 8]}
  • id: 351721
    {'degree': 16, 'field': [17948, -4856, -7220, 28532, -21454, -1716, 17317, -13624, 3020, -454, 621, -76, -139, 42, 14, -8, 1], 'lmfdb_label': '6720.bp5', 'torsion': [2, 12]}
  • id: 351720
    {'degree': 16, 'field': [50176, 0, -50176, 0, 19040, 0, -1792, 0, -1692, 0, 528, 0, 52, 0, -8, 0, 1], 'lmfdb_label': '6720.bp5', 'torsion': [2, 16]}
  • id: 351717
    {'degree': 16, 'field': [65536, 0, 90112, 0, 77968, 0, -2816, 0, -6215, 0, -776, 0, 298, 0, -8, 0, 1], 'lmfdb_label': '6720.bp5', 'torsion': [2, 8]}
  • id: 351718
    {'degree': 16, 'field': [67104, 169920, 51360, -60288, 76402, 48084, -37930, -16152, 13881, 840, -2630, 72, 360, -12, -28, 0, 1], 'lmfdb_label': '6720.bp5', 'torsion': [4, 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: 136354
    {'conductor': 6720, 'conductor_valuation': 6, 'discriminant_valuation': 22, 'j_denominator_valuation': 4, 'kodaira_symbol': -16, 'lmfdb_label': '6720.bp5', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 136355
    {'conductor': 6720, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '6720.bp5', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 136356
    {'conductor': 6720, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '6720.bp5', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 136357
    {'conductor': 6720, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '6720.bp5', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 1708257
    {'adelic_gens': [[415, 624, 656, 451], [5, 636, 814, 179], [833, 8, 832, 9], [679, 2, 654, 835], [1, 0, 8, 1], [287, 2, 822, 835], [241, 4, 0, 1], [5, 4, 836, 837], [1, 8, 0, 1]], 'adelic_image': '840.192.1.?', 'conductor': 6720, 'lmfdb_label': '6720.bp5', 'prime': 0}
  • id: 33125
    {'conductor': 6720, 'elladic_image': '8.48.0.80', 'lmfdb_label': '6720.bp5', 'modell_image': '2Cs', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 267893
    {'lmfdb_iso': '6720.bp', 'p': 11, 'prec': 20, 'unit': 29519961362211707336, 'val': 1}
  • id: 267899
    {'lmfdb_iso': '6720.bp', 'p': 13, 'prec': 20, 'unit': 1054708638696759883222, 'val': 1}
  • id: 267901
    {'lmfdb_iso': '6720.bp', 'p': 17, 'prec': 20, 'unit': 205936319945045246493583, 'val': 1}
  • id: 267902
    {'lmfdb_iso': '6720.bp', 'p': 19, 'prec': 20, 'unit': 264920937517456684304138, 'val': 1}
  • id: 267905
    {'lmfdb_iso': '6720.bp', 'p': 23, 'prec': 20, 'unit': 39750084004430048483588041, 'val': 1}
  • id: 267898
    {'lmfdb_iso': '6720.bp', 'p': 29, 'prec': 20, 'unit': 5539625992520814433961315590, 'val': 1}
  • id: 267910
    {'lmfdb_iso': '6720.bp', 'p': 31, 'prec': 20, 'unit': 11186301246526293542069269374, 'val': 1}
  • id: 267894
    {'lmfdb_iso': '6720.bp', 'p': 37, 'prec': 20, 'unit': 324256495861952536657481705122, 'val': 1}
  • id: 267896
    {'lmfdb_iso': '6720.bp', 'p': 41, 'prec': 20, 'unit': 133424288005730637721444398358, 'val': 1}
  • id: 267897
    {'lmfdb_iso': '6720.bp', 'p': 43, 'prec': 20, 'unit': 7435520802229328639753404167545, 'val': 1}
  • id: 267900
    {'lmfdb_iso': '6720.bp', 'p': 47, 'prec': 20, 'unit': 54924069226688227925062247537455, 'val': 1}
  • id: 267903
    {'lmfdb_iso': '6720.bp', 'p': 53, 'prec': 20, 'unit': 523684378309642073581878278576706, 'val': 1}
  • id: 267907
    {'lmfdb_iso': '6720.bp', 'p': 59, 'prec': 20, 'unit': 4418224427158548171198759469749448, 'val': 1}
  • id: 267908
    {'lmfdb_iso': '6720.bp', 'p': 61, 'prec': 20, 'unit': 5897533547626900673438848313651208, 'val': 1}
  • id: 267892
    {'lmfdb_iso': '6720.bp', 'p': 67, 'prec': 20, 'unit': 29961083461666801585068038435489126, 'val': 1}
  • id: 267895
    {'lmfdb_iso': '6720.bp', 'p': 71, 'prec': 20, 'unit': 54120680906820555154446434563811609, 'val': 1}
  • id: 267904
    {'lmfdb_iso': '6720.bp', 'p': 73, 'prec': 20, 'unit': 400019158325098723961774622442834, 'val': 2}
  • id: 267909
    {'lmfdb_iso': '6720.bp', 'p': 83, 'prec': 20, 'unit': 2610122805261616405403730985926498389, 'val': 1}
  • id: 267906
    {'lmfdb_iso': '6720.bp', 'p': 89, 'prec': 20, 'unit': 1729729188671047186864403130719496872, 'val': 1}
  • id: 267891
    {'lmfdb_iso': '6720.bp', 'p': 97, 'prec': 20, 'unit': 14769176598951173603670969392299406528, 'val': 1}