Elliptic curve data - 13200.bi4

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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': '13200bm', 'Clabel': '13200bm4', 'Cnumber': 4, 'abc_quality': 1.0376318384434067, 'absD': 374134464000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1320, 'ainvs': [0, -1, 0, 17392, -300288], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 13200, 'degree': 49152, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4852340696603068984751656679', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 34, 'isogeny_degrees': [1, 2, 4], 'jinv': [9090072503, 5845851], 'lmfdb_iso': '13200.bi', 'lmfdb_label': '13200.bi4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 44, 55], 'min_quad_twist_disc': -20, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '20.12.0-4.c.1.2', '22.6.0.a.1', '24.12.0.ba.1', '44.12.0.g.1', '120.24.0.?', '220.24.0.?', '264.24.0.?', '1320.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.012632067116688598242446120171', 'prec': 110}, 'szpiro_ratio': 4.3112313036406436, '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, 0, 0, 4, 0, 1, 0, -1, 0, 2, 0, 0, 0, 2, 0, 0, 0], 'aplist': [0, -1, 0, 4, -1, 2, 2, 0, 8, -6, 8, -6, -2, 0, 8, -6, 4, 6, -4, 0, 14, 4, 12, -6, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 13200, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '13200.bi', 'trace_hash': 1152176485011244649}
• 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': '0.051279298855871657371704796255', 'prec': 107}, 'conductor': 13200, 'gens': [], 'heights': [], 'lmfdb_label': '13200.bi4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.30685933803036095734409279722', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.4548747042428876587527423777442748440', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[17, 0, 1]], 'xcoord_integral_points': [17]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '5': 'a', '11': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '13200.bi4'}
• ec_torsion_growth •

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

  
  
  • id: 679893
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '13200.bi4', 'torsion': [4]}
  • id: 679892
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '13200.bi4', 'torsion': [2, 2]}
  • id: 679894
    {'degree': 2, 'field': [14, -1, 1], 'lmfdb_label': '13200.bi4', 'torsion': [4]}
  • id: 679895
    {'degree': 4, 'field': [16, 0, 3, 0, 1], 'lmfdb_label': '13200.bi4', 'torsion': [2, 4]}
  • id: 679899
    {'degree': 8, 'field': [-1875, 0, -2375, 0, -150, 0, 0, 0, 1], 'lmfdb_label': '13200.bi4', 'torsion': [6]}
  • id: 679897
    {'degree': 8, 'field': [349, 100, -44, -92, -3, 56, -14, -4, 1], 'lmfdb_label': '13200.bi4', 'torsion': [8]}
  • id: 679896
    {'degree': 8, 'field': [729, -162, -270, 198, 27, -22, 12, -4, 1], 'lmfdb_label': '13200.bi4', 'torsion': [2, 4]}
  • id: 679898
    {'degree': 8, 'field': [60624, -3600, 4026, -912, 607, -184, 66, -4, 1], 'lmfdb_label': '13200.bi4', 'torsion': [8]}
  • id: 679904
    {'degree': 16, 'field': [9, 0, 171, 0, 487, 0, 342, 0, -105, 0, -342, 0, -42, 0, 0, 0, 1], 'lmfdb_label': '13200.bi4', 'torsion': [12]}
  • id: 679900
    {'degree': 16, 'field': [196, 0, 1024, 0, 2068, 0, -804, 0, 813, 0, -108, 0, 22, 0, -8, 0, 1], 'lmfdb_label': '13200.bi4', 'torsion': [4, 4]}
  • id: 679902
    {'degree': 16, 'field': [9124, 824, 13780, -26104, 5210, 9032, -462, -6316, 7409, -4928, 2046, -620, 164, -56, 28, -8, 1], 'lmfdb_label': '13200.bi4', 'torsion': [2, 8]}
  • id: 679905
    {'degree': 16, 'field': [45369, 0, -16275, 0, 11944, 0, -3270, 0, 2790, 0, -15, 0, -48, 0, 0, 0, 1], 'lmfdb_label': '13200.bi4', 'torsion': [12]}
  • id: 679903
    {'degree': 16, 'field': [31640625, 0, -14765625, 0, 4359375, 0, -731250, 0, 76875, 0, -4250, 0, 150, 0, 0, 0, 1], 'lmfdb_label': '13200.bi4', 'torsion': [2, 6]}
  • id: 679901
    {'degree': 16, 'field': [518194711, 78774964, -270915884, -47779664, 64963115, 12218260, -9308946, -1780052, 883814, 160412, -58056, -8920, 2615, 284, -74, -4, 1], 'lmfdb_label': '13200.bi4', 'torsion': [2, 8]}
• 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: 287120
    {'conductor': 13200, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '13200.bi4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 287121
    {'conductor': 13200, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '13200.bi4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 287122
    {'conductor': 13200, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '13200.bi4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 287123
    {'conductor': 13200, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '13200.bi4', 'prime': 11, '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: 1751477
    {'adelic_gens': [[881, 800, 620, 561], [1, 0, 8, 1], [316, 265, 695, 6], [1, 8, 0, 1], [1, 4, 4, 17], [263, 0, 0, 1319], [1291, 1290, 970, 571], [1313, 8, 1312, 9], [29, 560, 670, 819], [7, 6, 1314, 1315]], 'adelic_image': '1320.48.0.?', 'conductor': 13200, 'lmfdb_label': '13200.bi4', 'prime': 0}
  • id: 62528
    {'conductor': 13200, 'elladic_image': '4.6.0.1', 'lmfdb_label': '13200.bi4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 13200.bi does not appear in ec_padic