Elliptic curve data - 51520.bv1

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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': '51520h', 'Clabel': '51520h1', 'Cnumber': 1, 'abc_quality': 0.8556046575596292, 'absD': 18032000000, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 46, 'ainvs': [0, 1, 0, 639, -1561], 'analytic_rank': 2, 'bad_primes': [2, 5, 7, 23], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 51520, 'degree': 30720, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.65701784558033654638994498445', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 47, 'isogeny_degrees': [1], 'jinv': [28134973184, 17609375], 'lmfdb_iso': '51520.bv', 'lmfdb_label': '51520.bv1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 160, -275], 'min_quad_twist_disc': 8, 'modell_images': [], 'modm_images': ['46.2.0.a.1'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 4, 'num_int_pts': 6, 'optimality': 1, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '3.6101878133404047981080370249', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.079395195113715455208918216568', 'prec': 107}, 'szpiro_ratio': 2.8564548881897935, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, -2, 0, 2, 0, -3, 0, -1, 0, -6, 0, -6, 0], 'aplist': [0, 1, -1, -1, 2, -3, -6, -6, 1, -5, -7, 4, -3, -10, 7, 4, 4, -12, 4, 3, -11, -14, -14, -10, -14], 'class_deg': 1, 'class_size': 1, 'conductor': 51520, 'isogeny_matrix': [[1]], 'lmfdb_iso': '51520.bv', 'trace_hash': 892390979811301304}
• 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': '0.26873334026840240408895598119', 'prec': 103}, 'conductor': 51520, 'gens': [[61, 875, 2], [10, 77, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.5333608867356437924539790414', 'prec': 100}, {'__RealLiteral__': 0, 'data': '2.4430094941219508098750389505', 'prec': 100}], 'lmfdb_label': '51520.bv1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.70660486256669124985567026284', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '10.203905054741361342187402301746800184', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': [10, 1234, 3202]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [2, 0], '7': [2, 0], '11': [2, 0], '13': [2, 0], '17': [2, 0], '19': [2, 0], '23': [3, 0], '29': [2, 0], '31': [2, 0], '37': [2, 0], '41': [2, 0], '43': [2, 0], '47': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '51520.bv1'}
• ec_torsion_growth •

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

  
  
  • id: 2496104
    {'degree': 3, 'field': [1, 0, -1, 1], 'lmfdb_label': '51520.bv1', 'torsion': [2]}
  • id: 2496105
    {'degree': 6, 'field': [1, -3, 5, -5, 5, -3, 1], 'lmfdb_label': '51520.bv1', 'torsion': [2, 2]}
  • id: 2496106
    {'degree': 8, 'field': [-15552, 0, -4768, 0, -432, 0, 0, 0, 1], 'lmfdb_label': '51520.bv1', 'torsion': [3]}
  • id: 2496107
    {'degree': 12, 'field': [-80063, 0, 47120, 0, 19613, 0, 3140, 0, 266, 0, 22, 0, 1], 'lmfdb_label': '51520.bv1', 'torsion': [4]}
• 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: 1232955
    {'conductor': 51520, 'conductor_valuation': 6, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '51520.bv1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1232956
    {'conductor': 51520, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '51520.bv1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1232957
    {'conductor': 51520, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '51520.bv1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1232958
    {'conductor': 51520, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '51520.bv1', 'prime': 23, '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

  
  {'adelic_gens': [[5, 2, 5, 3], [1, 1, 45, 0], [1, 2, 0, 1], [45, 2, 44, 3], [1, 0, 2, 1]], 'adelic_image': '46.2.0.?', 'conductor': 51520, 'lmfdb_label': '51520.bv1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 2591804
    {'lmfdb_iso': '51520.bv', 'p': 11, 'prec': 20, 'unit': 33311580688892270423, 'val': 2}
  • id: 2591810
    {'lmfdb_iso': '51520.bv', 'p': 13, 'prec': 20, 'unit': 1290621530618089803388, 'val': 2}
  • id: 2591812
    {'lmfdb_iso': '51520.bv', 'p': 17, 'prec': 20, 'unit': 78869018517449294837868, 'val': 2}
  • id: 2591813
    {'lmfdb_iso': '51520.bv', 'p': 19, 'prec': 20, 'unit': 1022549304756766148303376, 'val': 2}
  • id: 2591809
    {'lmfdb_iso': '51520.bv', 'p': 29, 'prec': 20, 'unit': 3553132543663493106977363975, 'val': 2}
  • id: 2591821
    {'lmfdb_iso': '51520.bv', 'p': 31, 'prec': 20, 'unit': 16549010264652005086841319953, 'val': 2}
  • id: 2591805
    {'lmfdb_iso': '51520.bv', 'p': 37, 'prec': 20, 'unit': 170178092070422518782016525632, 'val': 2}
  • id: 2591807
    {'lmfdb_iso': '51520.bv', 'p': 41, 'prec': 20, 'unit': 1065633784383039418560201520201, 'val': 2}
  • id: 2591808
    {'lmfdb_iso': '51520.bv', 'p': 43, 'prec': 20, 'unit': 10212380543033083570951285941821, 'val': 2}
  • id: 2591819
    {'lmfdb_iso': '51520.bv', 'p': 47, 'prec': 20, 'unit': 55799566937979058311617154614128, 'val': 2}
  • id: 2591814
    {'lmfdb_iso': '51520.bv', 'p': 53, 'prec': 20, 'unit': 49577866326304985620264175770694, 'val': 2}
  • id: 2591815
    {'lmfdb_iso': '51520.bv', 'p': 59, 'prec': 20, 'unit': 2936177973943751558201062824593089, 'val': 2}
  • id: 2591820
    {'lmfdb_iso': '51520.bv', 'p': 61, 'prec': 20, 'unit': 1092275387989788149052009251167393, 'val': 2}
  • id: 2591803
    {'lmfdb_iso': '51520.bv', 'p': 67, 'prec': 20, 'unit': 48089418145147665802571044930658054, 'val': 2}
  • id: 2591806
    {'lmfdb_iso': '51520.bv', 'p': 71, 'prec': 20, 'unit': 58018871979880393862648933033170406, 'val': 2}
  • id: 2591816
    {'lmfdb_iso': '51520.bv', 'p': 73, 'prec': 20, 'unit': 134705329366842210676972315813615505, 'val': 2}
  • id: 2591811
    {'lmfdb_iso': '51520.bv', 'p': 79, 'prec': 20, 'unit': 486280392002476301541084212325191470, 'val': 2}
  • id: 2591817
    {'lmfdb_iso': '51520.bv', 'p': 83, 'prec': 20, 'unit': 618279351559093400700630770165386242, 'val': 2}
  • id: 2591818
    {'lmfdb_iso': '51520.bv', 'p': 89, 'prec': 20, 'unit': 7684489486694062136118751935686437875, 'val': 2}
  • id: 2591802
    {'lmfdb_iso': '51520.bv', 'p': 97, 'prec': 20, 'unit': 21248036428541157285584491016518350416, 'val': 2}