Elliptic curve data - 5160.i3

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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': '5160e', 'Clabel': '5160e1', 'Cnumber': 1, 'abc_quality': 0.8109604537281869, 'absD': 20640000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 5160, 'ainvs': [0, 1, 0, -76, -160], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 43], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 5160, 'degree': 1536, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.10053199847939611865702463758', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 8, 'isogeny_degrees': [1, 2, 4], 'jinv': [192143824, 80625], 'lmfdb_iso': '5160.i', 'lmfdb_label': '5160.i3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -76, -160], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '12.12.0-4.c.1.2', '40.12.0-4.c.1.4', '120.24.0.?', '172.12.0.?', '258.6.0.?', '516.24.0.?', '1720.24.0.?', '5160.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 129], [3, 4, 1720], [5, 6, 1032], [43, 44, 120]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.36156612189390075428779677673', 'prec': 107}, 'szpiro_ratio': 2.8798478860802077, '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, 1, 0, -1, 0, -4, 0, 1, 0, 4, 0, -2, 0, -1, 0, 6, 0, -8, 0], 'aplist': [0, 1, -1, -4, 4, -2, 6, -8, 0, 2, -8, -2, 2, -1, 8, 6, 12, 10, 4, 0, -2, 0, 0, -10, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 5160, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '5160.i', 'trace_hash': 653600390306882082}
• 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': '0.81786008932057132415275754180', 'prec': 103}, 'conductor': 5160, 'gens': [], 'heights': [], 'lmfdb_label': '5160.i3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.6766667245330456752382593659', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.6766667245330456752382593659456231602', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[-8, 0, 1]], 'xcoord_integral_points': [-8]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [0, 0], '43': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '5160.i3'}
• ec_torsion_growth •

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

  
  
  • id: 269268
    {'degree': 2, 'field': [-32, -1, 1], 'lmfdb_label': '5160.i3', 'torsion': [2, 2]}
  • id: 269269
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '5160.i3', 'torsion': [4]}
  • id: 269270
    {'degree': 2, 'field': [11, -1, 1], 'lmfdb_label': '5160.i3', 'torsion': [4]}
  • id: 269271
    {'degree': 4, 'field': [121, -11, -10, -1, 1], 'lmfdb_label': '5160.i3', 'torsion': [2, 4]}
  • id: 269275
    {'degree': 8, 'field': [-243, 0, -5976, 0, -54, 0, 0, 0, 1], 'lmfdb_label': '5160.i3', 'torsion': [6]}
  • id: 269272
    {'degree': 8, 'field': [1024, -64, -386, -646, -455, 2, 4, -4, 1], 'lmfdb_label': '5160.i3', 'torsion': [2, 4]}
  • id: 269273
    {'degree': 8, 'field': [16641, 0, -774, 0, -93, 0, -6, 0, 1], 'lmfdb_label': '5160.i3', 'torsion': [8]}
  • id: 269274
    {'degree': 8, 'field': [2013561, 0, 99846, 0, -473, 0, -86, 0, 1], 'lmfdb_label': '5160.i3', 'torsion': [8]}
  • id: 269280
    {'degree': 16, 'field': [59049, 0, -1452168, 0, 35699454, 0, -322704, 0, 3159, 0, -11952, 0, 54, 0, 0, 0, 1], 'lmfdb_label': '5160.i3', 'torsion': [12]}
  • id: 269276
    {'degree': 16, 'field': [1048576, 65536, 2048, 274560, -66172, -19852, 34834, -13326, 2437, 1470, -1016, 370, -49, -12, 8, -4, 1], 'lmfdb_label': '5160.i3', 'torsion': [4, 4]}
  • id: 269277
    {'degree': 16, 'field': [2313441, 0, 1998594, 0, 1046709, 0, 569106, 0, 190404, 0, 54, 0, -411, 0, 6, 0, 1], 'lmfdb_label': '5160.i3', 'torsion': [2, 8]}
  • id: 269278
    {'degree': 16, 'field': [100000000, 0, -177600000, 0, 273727600, 0, -71521440, 0, 15132801, 0, -489774, 0, 11707, 0, -126, 0, 1], 'lmfdb_label': '5160.i3', 'torsion': [2, 8]}
  • id: 269279
    {'degree': 16, 'field': [900000000, 0, -1976160000, 0, -41900000, 0, -11040000, 0, 95277, 0, -5336, 0, -1974, 0, 0, 0, 1], 'lmfdb_label': '5160.i3', 'torsion': [2, 6]}
  • id: 269281
    {'degree': 16, 'field': [4755049213, 1228921832, -1303189264, 113626536, 33355178, -116380232, 52621084, -12257712, 3594883, -391176, 117052, -22816, 5198, -672, 116, -8, 1], 'lmfdb_label': '5160.i3', 'torsion': [12]}
• 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: 100184
    {'conductor': 5160, 'conductor_valuation': 3, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -5, 'lmfdb_label': '5160.i3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 100185
    {'conductor': 5160, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '5160.i3', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 100186
    {'conductor': 5160, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '5160.i3', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 100187
    {'conductor': 5160, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '5160.i3', 'prime': 43, '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

  
  
  • id: 1697616
    {'adelic_gens': [[3097, 8, 2068, 33], [4523, 4518, 650, 3227], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [5153, 8, 5152, 9], [7, 6, 5154, 5155], [649, 648, 3238, 655], [368, 3, 2165, 2], [1724, 1, 3463, 6]], 'adelic_image': '5160.48.0.?', 'conductor': 5160, 'lmfdb_label': '5160.i3', 'prime': 0}
  • id: 25556
    {'conductor': 5160, 'elladic_image': '4.6.0.1', 'lmfdb_label': '5160.i3', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 5160.i does not appear in ec_padic