Elliptic curve data - 48960.ds1

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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': '48960cu', 'Clabel': '48960cu1', 'Cnumber': 1, 'abc_quality': 0.9777568001303636, 'absD': 69625856880000000, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 510, 'ainvs': [0, 0, 0, -102252, -17876104], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 17], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 48960, 'degree': 430080, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.9343591048255230993955774010', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 96, 'isogeny_degrees': [1], 'jinv': [-158384129218816, 93270234375], 'lmfdb_iso': '48960.ds', 'lmfdb_label': '48960.ds1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -2840, 81813], 'min_quad_twist_disc': -24, 'modell_images': [], 'modm_images': ['510.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.6218368601012879876520166616', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 765], [3, 8, 320], [5, 6, 9792], [7, 2, 9792], [17, 18, 2880]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.80743031002484716251692801466', 'prec': 103}, 'szpiro_ratio': 4.3450452696636335, '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, 0, 0, 1, 0, -3, 0, 0, 0, -1, 0, 6, 0, 0, 0, -1, 0, 1, 0], 'aplist': [0, 0, 1, -3, -1, 6, -1, 1, -6, -5, -2, 11, 9, 0, -5, -3, -12, 10, -4, 4, 3, -2, 12, -4, 14], 'class_deg': 1, 'class_size': 1, 'conductor': 48960, 'isogeny_matrix': [[1]], 'lmfdb_iso': '48960.ds', 'trace_hash': 2292562614695511444}
• 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': '0.020885122624172057914399933358', 'prec': 107}, 'conductor': 48960, 'gens': [[397, 2025, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.6218368601012879876520166616', 'prec': 100}], 'lmfdb_label': '48960.ds1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.12997734022869747583677730780', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.9024571581031711013287896751440329111', 'prec': 130}, 'tamagawa_product': 28, 'torsion_generators': [], 'xcoord_integral_points': [397]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [4, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [3, 0], '41': [1, 0], '43': [1, 1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '48960.ds1'}
• ec_torsion_growth •

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

  
  
  • id: 2383531
    {'degree': 3, 'field': [-3, 0, -1, 1], 'lmfdb_label': '48960.ds1', 'torsion': [2]}
  • id: 2383532
    {'degree': 6, 'field': [81, -27, 48, 21, -2, -2, 1], 'lmfdb_label': '48960.ds1', 'torsion': [2, 2]}
  • id: 2383533
    {'degree': 8, 'field': [-3, 0, 132, 0, 54, 0, 10, 0, 1], 'lmfdb_label': '48960.ds1', 'torsion': [3]}
  • id: 2383534
    {'degree': 12, 'field': [-6375, 0, -16264, 0, 7710, 0, -1070, 0, 5, 0, 0, 0, 1], 'lmfdb_label': '48960.ds1', '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: 1170649
    {'conductor': 48960, 'conductor_valuation': 6, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '48960.ds1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1170650
    {'conductor': 48960, 'conductor_valuation': 2, 'discriminant_valuation': 11, 'j_denominator_valuation': 5, 'kodaira_symbol': -9, 'lmfdb_label': '48960.ds1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1170651
    {'conductor': 48960, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '48960.ds1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 7}
  • id: 1170652
    {'conductor': 48960, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '48960.ds1', 'prime': 17, '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': [[307, 2, 307, 3], [509, 2, 508, 3], [1, 1, 509, 0], [241, 2, 241, 3], [341, 2, 341, 3], [1, 0, 2, 1], [1, 2, 0, 1]], 'adelic_image': '510.2.0.?', 'conductor': 48960, 'lmfdb_label': '48960.ds1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 2459031
    {'lmfdb_iso': '48960.ds', 'p': 7, 'prec': 20, 'unit': 15594489486381999, 'val': 0}
  • id: 2459033
    {'lmfdb_iso': '48960.ds', 'p': 11, 'prec': 20, 'unit': 3412669272623478200, 'val': 1}
  • id: 2459035
    {'lmfdb_iso': '48960.ds', 'p': 13, 'prec': 20, 'unit': 1279914651523677208536, 'val': 1}
  • id: 2459038
    {'lmfdb_iso': '48960.ds', 'p': 19, 'prec': 20, 'unit': 21638349651664185333484773, 'val': -1}
  • id: 2459041
    {'lmfdb_iso': '48960.ds', 'p': 23, 'prec': 20, 'unit': 30355488822935796599036430, 'val': 1}
  • id: 2459034
    {'lmfdb_iso': '48960.ds', 'p': 29, 'prec': 20, 'unit': 1041540766298844618194770893, 'val': 1}
  • id: 2459046
    {'lmfdb_iso': '48960.ds', 'p': 31, 'prec': 20, 'unit': 18385842662536333656560423375, 'val': 1}
  • id: 2459030
    {'lmfdb_iso': '48960.ds', 'p': 37, 'prec': 20, 'unit': 498470367959949103527281895, 'val': 2}
  • id: 2459032
    {'lmfdb_iso': '48960.ds', 'p': 41, 'prec': 20, 'unit': 55439939969907049100886688460, 'val': 1}
  • id: 2459044
    {'lmfdb_iso': '48960.ds', 'p': 47, 'prec': 20, 'unit': 22307242133803485955834930143015, 'val': 1}
  • id: 2459039
    {'lmfdb_iso': '48960.ds', 'p': 53, 'prec': 20, 'unit': 315395898848874753169401422773711, 'val': 1}
  • id: 2459037
    {'lmfdb_iso': '48960.ds', 'p': 59, 'prec': 20, 'unit': 3840032800832558460458198798284762, 'val': 1}
  • id: 2459045
    {'lmfdb_iso': '48960.ds', 'p': 61, 'prec': 20, 'unit': 7304326099785598253773536961082250, 'val': 1}
  • id: 2459029
    {'lmfdb_iso': '48960.ds', 'p': 67, 'prec': 20, 'unit': 47007539388680512997625375317996627, 'val': 1}
  • id: 2459043
    {'lmfdb_iso': '48960.ds', 'p': 71, 'prec': 20, 'unit': 95096778302487758256523640448753320, 'val': 1}
  • id: 2459040
    {'lmfdb_iso': '48960.ds', 'p': 73, 'prec': 20, 'unit': 7277031223963006604105208591622542, 'val': 1}
  • id: 2459036
    {'lmfdb_iso': '48960.ds', 'p': 79, 'prec': 20, 'unit': 816568921506427886594566665743217413, 'val': 1}
  • id: 2459028
    {'lmfdb_iso': '48960.ds', 'p': 83, 'prec': 20, 'unit': 2612802180715145262289647542189187001, 'val': 1}
  • id: 2459042
    {'lmfdb_iso': '48960.ds', 'p': 89, 'prec': 20, 'unit': 2903242880646603934313702315784485466, 'val': 1}
  • id: 2459027
    {'lmfdb_iso': '48960.ds', 'p': 97, 'prec': 20, 'unit': 33787660798367203606328515259262886889, 'val': 1}