Elliptic curve data - 48960.ea2

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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': '48960cr', 'Clabel': '48960cr2', 'Cnumber': 2, 'abc_quality': 0.9103514678397865, 'absD': 138071900160000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 2040, 'ainvs': [0, 0, 0, 7188, -514384], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 48960, 'degree': 147456, 'elladic_images': ['4.6.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3963096170198921867810484718', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 104, 'isogeny_degrees': [1, 2], 'jinv': [214921799, 722500], 'lmfdb_iso': '48960.ea', 'lmfdb_label': '48960.ea2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 12, 38], 'min_quad_twist_disc': -24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.a.1', '24.12.0-4.a.1.1', '68.12.0.d.1', '408.24.0.?', '680.24.0.?', '2040.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 7, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.4073484319804115383979046901', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 9], [3, 6, 5440], [5, 6, 9792], [17, 18, 2880]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.19271729815408062304242232885', 'prec': 107}, 'szpiro_ratio': 3.6878864078234765, '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, 0, 0, 1, 0, -2, 0, 0, 0, -2, 0, 6, 0, 0, 0, -1, 0, 8, 0], 'aplist': [0, 0, 1, -2, -2, 6, -1, 8, 2, 6, -2, -6, -2, 4, -4, -10, 0, 10, -8, -14, 10, -14, -4, -6, -14], 'class_deg': 2, 'class_size': 2, 'conductor': 48960, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '48960.ea', 'trace_hash': 269208398244990779}
• 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': '0.061260547883570946040264256135', 'prec': 107}, 'conductor': 48960, 'gens': [[70, 576, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.4073484319804115383979046901', 'prec': 100}], 'lmfdb_label': '48960.ea2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.29707442015592104472138864686', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.6893955102068071509161472105644576908', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[52, 0, 1]], 'xcoord_integral_points': [52, 70, 221, 902]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [2, 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': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '48960.ea2'}
• ec_torsion_growth •

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

  
  
  • id: 2383505
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '48960.ea2', 'torsion': [2, 2]}
  • id: 2383506
    {'degree': 4, 'field': [-144, 0, -6, 0, 1], 'lmfdb_label': '48960.ea2', 'torsion': [4]}
  • id: 2383509
    {'degree': 8, 'field': [-1200, 0, 0, 0, 120, 0, -8, 0, 1], 'lmfdb_label': '48960.ea2', 'torsion': [6]}
  • id: 2383508
    {'degree': 8, 'field': [81, 0, -108, 0, 63, 0, -12, 0, 1], 'lmfdb_label': '48960.ea2', 'torsion': [2, 4]}
  • id: 2383507
    {'degree': 8, 'field': [1296, 0, 0, 0, 81, 0, 0, 0, 1], 'lmfdb_label': '48960.ea2', 'torsion': [2, 4]}
  • id: 2383511
    {'degree': 16, 'field': [4096, 0, -31616, 0, -80832, 0, -36760, 0, -7444, 0, -250, 0, -243, 0, -2, 0, 1], 'lmfdb_label': '48960.ea2', 'torsion': [8]}
  • id: 2383512
    {'degree': 16, 'field': [5625, 0, 0, 0, 4500, 0, 0, 0, 750, 0, 0, 0, -44, 0, 0, 0, 1], 'lmfdb_label': '48960.ea2', 'torsion': [2, 6]}
  • id: 2383510
    {'degree': 16, 'field': [16516, 14352, -7208, -16416, 19500, 768, -2596, 1104, 437, 204, 32, 120, 69, -12, 10, 0, 1], 'lmfdb_label': '48960.ea2', 'torsion': [4, 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: 1170633
    {'conductor': 48960, 'conductor_valuation': 6, 'discriminant_valuation': 20, 'j_denominator_valuation': 2, 'kodaira_symbol': -14, 'lmfdb_label': '48960.ea2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 1170634
    {'conductor': 48960, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '48960.ea2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1170635
    {'conductor': 48960, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '48960.ea2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1170636
    {'conductor': 48960, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '48960.ea2', 'prime': 17, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
• ec_galrep •

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

  
  
  • id: 1990108
    {'adelic_gens': [[241, 1362, 0, 1], [817, 684, 0, 1], [1019, 672, 0, 2039], [1, 0, 8, 1], [5, 8, 48, 77], [2033, 8, 2032, 9], [3, 8, 10, 27], [679, 0, 0, 2039], [511, 1368, 87, 697], [1, 8, 0, 1]], 'adelic_image': '2040.48.0.?', 'conductor': 48960, 'lmfdb_label': '48960.ea2', 'prime': 0}
  • id: 211013
    {'conductor': 48960, 'elladic_image': '4.6.0.5', 'lmfdb_label': '48960.ea2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 2458991
    {'lmfdb_iso': '48960.ea', 'p': 7, 'prec': 20, 'unit': 6631973464757874, 'val': 1}
  • id: 2458989
    {'lmfdb_iso': '48960.ea', 'p': 11, 'prec': 20, 'unit': 15917615957288782302, 'val': 1}
  • id: 2458995
    {'lmfdb_iso': '48960.ea', 'p': 13, 'prec': 20, 'unit': 1095820788197400318165, 'val': 1}
  • id: 2458997
    {'lmfdb_iso': '48960.ea', 'p': 19, 'prec': 20, 'unit': 1955051392704357335215819, 'val': 1}
  • id: 2459000
    {'lmfdb_iso': '48960.ea', 'p': 23, 'prec': 20, 'unit': 47082911935235201050967036, 'val': 1}
  • id: 2458994
    {'lmfdb_iso': '48960.ea', 'p': 29, 'prec': 20, 'unit': 1880692628628512860914120901, 'val': 1}
  • id: 2459006
    {'lmfdb_iso': '48960.ea', 'p': 31, 'prec': 20, 'unit': 15736256711955640643577513507, 'val': 1}
  • id: 2458990
    {'lmfdb_iso': '48960.ea', 'p': 37, 'prec': 20, 'unit': 327565117697732188024013657317, 'val': 1}
  • id: 2458992
    {'lmfdb_iso': '48960.ea', 'p': 41, 'prec': 20, 'unit': 326700054182111457261178225746, 'val': 1}
  • id: 2458993
    {'lmfdb_iso': '48960.ea', 'p': 43, 'prec': 20, 'unit': 896750096105231137402330061209, 'val': 1}
  • id: 2458996
    {'lmfdb_iso': '48960.ea', 'p': 47, 'prec': 20, 'unit': 24938164582632408023938961923944, 'val': 1}
  • id: 2458998
    {'lmfdb_iso': '48960.ea', 'p': 53, 'prec': 20, 'unit': 445357715254935584550191767793552, 'val': 1}
  • id: 2459004
    {'lmfdb_iso': '48960.ea', 'p': 61, 'prec': 20, 'unit': 8323022953146275752773982835301498, 'val': 1}
  • id: 2458988
    {'lmfdb_iso': '48960.ea', 'p': 67, 'prec': 20, 'unit': 2473756113109099502909413080984458, 'val': 1}
  • id: 2459002
    {'lmfdb_iso': '48960.ea', 'p': 71, 'prec': 20, 'unit': 63668060783438906965627694059573023, 'val': 1}
  • id: 2458999
    {'lmfdb_iso': '48960.ea', 'p': 73, 'prec': 20, 'unit': 120679733796280500766819564902992629, 'val': 1}
  • id: 2459003
    {'lmfdb_iso': '48960.ea', 'p': 79, 'prec': 20, 'unit': 97493566439498964691684533815850167, 'val': 1}
  • id: 2459005
    {'lmfdb_iso': '48960.ea', 'p': 83, 'prec': 20, 'unit': 347388855476147315245155572694507989, 'val': 1}
  • id: 2459001
    {'lmfdb_iso': '48960.ea', 'p': 89, 'prec': 20, 'unit': 9226651034067588328728100107502131682, 'val': 1}
  • id: 2458987
    {'lmfdb_iso': '48960.ea', 'p': 97, 'prec': 20, 'unit': 16413710134025429847297107478454760837, 'val': 1}