Elliptic curve data - 4800.cl1

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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': '4800be', 'Clabel': '4800be1', 'Cnumber': 1, 'abc_quality': 1.1506287661298975, 'absD': 6075000000, 'adelic_genus': 3, 'adelic_index': 60, 'adelic_level': 60, 'ainvs': [0, 1, 0, -4583, 117963], 'analytic_rank': 1, 'bad_primes': [2, 3, 5], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 4800, 'degree': 4800, 'elladic_images': ['5.15.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.82362219268068716548020177694', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 63, 'isogeny_degrees': [1], 'jinv': [-425920000, 243], 'lmfdb_iso': '4800.cl', 'lmfdb_label': '4800.cl1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -733, -7403], 'min_quad_twist_disc': -40, 'modell_images': ['5Ns'], 'modm_images': ['5.15.0.a.1', '6.2.0.a.1', '20.30.0.b.1', '30.30.2.b.1', '60.60.3.j.1'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 3, 'num_int_pts': 4, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.23730025548654069992156175255', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 75], [3, 4, 1600], [5, 10, 64]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.59591000588868573896225383927', 'prec': 107}, 'szpiro_ratio': 4.353883638218193, '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, 0, 0, 3, 0, 1, 0, 0, 0, -5, 0, 0, 0, 0, 0, -5, 0], 'aplist': [0, 1, 0, 3, 0, -5, 0, -5, -4, -4, -5, -10, -10, 1, 2, -10, 10, 5, -3, -10, 10, 0, -14, 16, 5], 'class_deg': 1, 'class_size': 1, 'conductor': 4800, 'isogeny_matrix': [[1]], 'lmfdb_iso': '4800.cl', 'trace_hash': 375103375342645684}
• 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': '0.19257985398756032305305337187', 'prec': 103}, 'conductor': 4800, 'gens': [[58, 225, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.23730025548654069992156175255', 'prec': 103}], 'lmfdb_label': '4800.cl1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.3276436172671621535118576417', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.7257525435885895541940812976517805322', 'prec': 130}, 'tamagawa_product': 15, 'torsion_generators': [], 'xcoord_integral_points': [34, 58]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': 'a', '7': [1, 0], '11': [1, 1, 0], '13': [1, 0], '17': [1, 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': '4800.cl1'}
• ec_torsion_growth •

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

  
  
  • id: 249705
    {'degree': 3, 'field': [-3, -3, -1, 1], 'lmfdb_label': '4800.cl1', 'torsion': [2]}
  • id: 249706
    {'degree': 6, 'field': [3, 3, -2, -3, 4, -3, 1], 'lmfdb_label': '4800.cl1', 'torsion': [2, 2]}
  • id: 249707
    {'degree': 8, 'field': [-243, 0, -144, 0, -54, 0, 0, 0, 1], 'lmfdb_label': '4800.cl1', 'torsion': [3]}
  • id: 249708
    {'degree': 8, 'field': [20, 0, 40, 0, 20, 0, 0, 0, 1], 'lmfdb_label': '4800.cl1', 'torsion': [5]}
  • id: 249709
    {'degree': 12, 'field': [-66, 24, 120, -264, 392, -388, 304, -188, 94, -40, 14, -4, 1], 'lmfdb_label': '4800.cl1', 'torsion': [4]}
  • id: 249710
    {'degree': 16, 'field': [25, 0, 0, 0, 100, 0, 0, 0, -210, 0, 0, 0, 20, 0, 0, 0, 1], 'lmfdb_label': '4800.cl1', 'torsion': [5]}
• 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: 92062
    {'conductor': 4800, 'conductor_valuation': 6, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '4800.cl1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 92063
    {'conductor': 4800, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '4800.cl1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 5}
  • id: 92064
    {'conductor': 4800, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '4800.cl1', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
• ec_galrep •

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

  
  
  • id: 1695216
    {'adelic_gens': [[1, 0, 10, 1], [37, 4, 26, 33], [1, 10, 0, 1], [51, 10, 50, 11], [41, 10, 25, 51], [2, 7, 35, 33], [37, 10, 26, 3]], 'adelic_image': '60.60.3.?', 'conductor': 4800, 'lmfdb_label': '4800.cl1', 'prime': 0}
  • id: 23737
    {'conductor': 4800, 'elladic_image': '5.15.0.1', 'lmfdb_label': '4800.cl1', 'modell_image': '5Ns', 'prime': 5}
• ec_padic •

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

  
  
  • id: 174644
    {'lmfdb_iso': '4800.cl', 'p': 7, 'prec': 20, 'unit': 4237608861305213, 'val': 1}
  • id: 174648
    {'lmfdb_iso': '4800.cl', 'p': 13, 'prec': 20, 'unit': 1259854721621888475763, 'val': 1}
  • id: 174650
    {'lmfdb_iso': '4800.cl', 'p': 19, 'prec': 20, 'unit': 144176634134827148791044, 'val': 1}
  • id: 174653
    {'lmfdb_iso': '4800.cl', 'p': 23, 'prec': 20, 'unit': 69872535447727547769741375, 'val': 1}
  • id: 174647
    {'lmfdb_iso': '4800.cl', 'p': 29, 'prec': 20, 'unit': 3148913325099516532871026669, 'val': 1}
  • id: 174658
    {'lmfdb_iso': '4800.cl', 'p': 31, 'prec': 20, 'unit': 16777410101276348790185999451, 'val': 1}
  • id: 174643
    {'lmfdb_iso': '4800.cl', 'p': 37, 'prec': 20, 'unit': 469075698525589383210892304653, 'val': 1}
  • id: 174645
    {'lmfdb_iso': '4800.cl', 'p': 41, 'prec': 20, 'unit': 1282192992200000913553800992926, 'val': 1}
  • id: 174646
    {'lmfdb_iso': '4800.cl', 'p': 43, 'prec': 20, 'unit': 83087447089196285329014691498238, 'val': -1}
  • id: 174649
    {'lmfdb_iso': '4800.cl', 'p': 47, 'prec': 20, 'unit': 22266777803218608282238699376995, 'val': 1}
  • id: 174651
    {'lmfdb_iso': '4800.cl', 'p': 53, 'prec': 20, 'unit': 127640740499942358192653093034966, 'val': 1}
  • id: 174656
    {'lmfdb_iso': '4800.cl', 'p': 59, 'prec': 20, 'unit': 2105291945970533458024479156949339, 'val': 1}
  • id: 174657
    {'lmfdb_iso': '4800.cl', 'p': 61, 'prec': 20, 'unit': 780136752922972755705204647390911, 'val': 1}
  • id: 174642
    {'lmfdb_iso': '4800.cl', 'p': 67, 'prec': 20, 'unit': 5974478274778353042998090900017304, 'val': 1}
  • id: 174655
    {'lmfdb_iso': '4800.cl', 'p': 71, 'prec': 20, 'unit': 143926313360175722976253507243866115, 'val': 1}
  • id: 174652
    {'lmfdb_iso': '4800.cl', 'p': 73, 'prec': 20, 'unit': 126278893205137721207549180980905393, 'val': 1}
  • id: 174641
    {'lmfdb_iso': '4800.cl', 'p': 83, 'prec': 20, 'unit': 2810206168581432896668065225148532870, 'val': 1}
  • id: 174654
    {'lmfdb_iso': '4800.cl', 'p': 89, 'prec': 20, 'unit': 1752842185851006190359310295064483872, 'val': 1}
  • id: 174640
    {'lmfdb_iso': '4800.cl', 'p': 97, 'prec': 20, 'unit': 19525391564864832045498055905173022836, 'val': 1}