Elliptic curve data - 1872.c4

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '1872r', 'Clabel': '1872r1', 'Cnumber': 1, 'abc_quality': 1.085841646160488, 'absD': 618182964412416, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 312, 'ainvs': [0, 0, 0, -2811, 1197610], 'analytic_rank': 0, 'bad_primes': [2, 3, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 1872, 'degree': 7680, 'elladic_images': ['4.12.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5173837966515958269710662128', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 2, 'iso_nlabel': 2, 'isogeny_degrees': [1, 2, 4], 'jinv': [-822656953, 207028224], 'lmfdb_iso': '1872.c', 'lmfdb_label': '1872.c4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -19, 685], 'min_quad_twist_disc': 12, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '24.24.0-24.ba.1.16', '78.6.0.?', '104.24.0.?', '156.24.0.?', '312.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 117], [3, 8, 208], [13, 14, 144]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.27493047175759567185621147288', 'prec': 103}, 'szpiro_ratio': 5.5097717541248725, '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, -2, 0, -4, 0, 0, 0, -4, 0, 1, 0, 0, 0, -2, 0, 8, 0], 'aplist': [0, 0, -2, -4, -4, 1, -2, 8, 0, -6, 4, -2, 10, -4, 8, 10, 4, -2, 16, -8, 2, -8, 12, -14, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 1872, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '1872.c', 'trace_hash': 1574266268976004840}
• 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': '0.048085837047620184643103404691', 'prec': 107}, 'conductor': 1872, 'gens': [], 'heights': [], 'lmfdb_label': '1872.c4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.41870478621018002153846112818', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.83740957242036004307692225635067938358', 'prec': 133}, 'tamagawa_product': 8, 'torsion_generators': [[-115, 0, 1]], 'xcoord_integral_points': [-115]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '13': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '1872.c4'}
• ec_torsion_growth •

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

  
  
  • id: 95090
    {'degree': 2, 'field': [-39, 0, 1], 'lmfdb_label': '1872.c4', 'torsion': [4]}
  • id: 95091
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '1872.c4', 'torsion': [4]}
  • id: 95089
    {'degree': 2, 'field': [10, -1, 1], 'lmfdb_label': '1872.c4', 'torsion': [2, 2]}
  • id: 95092
    {'degree': 4, 'field': [16, 17, 15, -1, 1], 'lmfdb_label': '1872.c4', 'torsion': [2, 4]}
  • id: 95093
    {'degree': 4, 'field': [100, 0, -19, 0, 1], 'lmfdb_label': '1872.c4', 'torsion': [2, 4]}
  • id: 95097
    {'degree': 8, 'field': [-27, 0, -60, 0, -18, 0, 0, 0, 1], 'lmfdb_label': '1872.c4', 'torsion': [6]}
  • id: 95096
    {'degree': 8, 'field': [4, 4, 10, -14, 7, -2, 1, -2, 1], 'lmfdb_label': '1872.c4', 'torsion': [8]}
  • id: 95095
    {'degree': 8, 'field': [9, 0, -126, 0, 31, 0, 10, 0, 1], 'lmfdb_label': '1872.c4', 'torsion': [8]}
  • id: 95094
    {'degree': 8, 'field': [256, 0, -191, 0, 291, 0, -29, 0, 1], 'lmfdb_label': '1872.c4', 'torsion': [4, 4]}
  • id: 95100
    {'degree': 16, 'field': [1, 0, -9, 0, 49, 0, -270, 0, 942, 0, -270, 0, 49, 0, -9, 0, 1], 'lmfdb_label': '1872.c4', 'torsion': [2, 8]}
  • id: 95099
    {'degree': 16, 'field': [1, 0, -1, 0, -11, 0, -10, 0, 142, 0, -10, 0, -11, 0, -1, 0, 1], 'lmfdb_label': '1872.c4', 'torsion': [2, 8]}
  • id: 95102
    {'degree': 16, 'field': [42, -96, 22, -446, 784, 1448, -2707, -442, 2432, -598, -811, 466, -17, -56, 28, -8, 1], 'lmfdb_label': '1872.c4', 'torsion': [12]}
  • id: 95103
    {'degree': 16, 'field': [144, 0, 0, 0, 900, 0, 0, 0, 1440, 0, 0, 0, 76, 0, 0, 0, 1], 'lmfdb_label': '1872.c4', 'torsion': [12]}
  • id: 95101
    {'degree': 16, 'field': [43264, 0, -23660, 0, 33124, 0, -14300, 0, 5005, 0, -1040, 0, 178, 0, -20, 0, 1], 'lmfdb_label': '1872.c4', 'torsion': [2, 6]}
  • id: 95098
    {'degree': 16, 'field': [125316, 0, -28836, 0, 2277, 0, 12672, 0, 7971, 0, 1980, 0, 291, 0, 24, 0, 1], 'lmfdb_label': '1872.c4', '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: 30372
    {'conductor': 1872, 'conductor_valuation': 4, 'discriminant_valuation': 28, 'j_denominator_valuation': 16, 'kodaira_symbol': -24, 'lmfdb_label': '1872.c4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 30373
    {'conductor': 1872, 'conductor_valuation': 2, 'discriminant_valuation': 11, 'j_denominator_valuation': 5, 'kodaira_symbol': -9, 'lmfdb_label': '1872.c4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 30374
    {'conductor': 1872, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '1872.c4', 'prime': 13, '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: 1676200
    {'adelic_gens': [[7, 6, 306, 307], [1, 0, 8, 1], [200, 309, 203, 310], [1, 8, 0, 1], [1, 4, 4, 17], [43, 42, 130, 283], [305, 8, 304, 9], [191, 192, 26, 185], [268, 1, 215, 6]], 'adelic_image': '312.48.0.?', 'conductor': 1872, 'lmfdb_label': '1872.c4', 'prime': 0}
  • id: 9138
    {'conductor': 1872, 'elladic_image': '4.12.0.8', 'lmfdb_label': '1872.c4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 1872.c does not appear in ec_padic