Elliptic curve data - 11616.k4

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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': '11616e', 'Clabel': '11616e4', 'Cnumber': 4, 'abc_quality': 1.059886267720316, 'absD': 73470177792, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 264, 'ainvs': [0, -1, 0, 928, 6888], 'analytic_rank': 0, 'bad_primes': [2, 3, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 11616, 'degree': 10240, 'elladic_images': ['8.12.0.16'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.77272726589601912364535702719', 'prec': 103}, 'faltings_index': 3, 'faltings_ratio': 2, 'intrinsic_torsion': 2, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2, 4], 'jinv': [97336, 81], 'lmfdb_iso': '11616.k', 'lmfdb_label': '11616.k4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 8, -8], 'min_quad_twist_disc': -11, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.d.1', '24.24.0.n.1', '44.12.0-4.c.1.1', '88.24.0.?', '264.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 121], [3, 4, 3872], [11, 62, 96]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.94608075592312513044853885289', 'prec': 107}, 'szpiro_ratio': 3.4306778300347616, '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, 2, 0, -4, 0, 1, 0, 0, 0, 2, 0, -2, 0, 6, 0, -4, 0], 'aplist': [0, -1, 2, -4, 0, 2, 6, -4, 0, -2, -4, -2, -2, 4, -8, 10, 4, -6, -4, 16, 6, 4, 12, 10, -14], 'class_deg': 4, 'class_size': 4, 'conductor': 11616, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '11616.k', 'trace_hash': 1314023199578884489}
• 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': '0.21321493622751271114277222675', 'prec': 103}, 'conductor': 11616, 'gens': [], 'heights': [], 'lmfdb_label': '11616.k4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.70639288927297916976288221483', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4127857785459583395257644296558189598', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-7, 0, 1]], 'xcoord_integral_points': [-7]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '11': 'a'}, 'iwp0': 3, 'lmfdb_label': '11616.k4'}
• ec_torsion_growth •

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

  
  
  • id: 601005
    {'degree': 2, 'field': [-11, 0, 1], 'lmfdb_label': '11616.k4', 'torsion': [4]}
  • id: 601004
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '11616.k4', 'torsion': [2, 2]}
  • id: 601006
    {'degree': 2, 'field': [22, 0, 1], 'lmfdb_label': '11616.k4', 'torsion': [4]}
  • id: 601007
    {'degree': 4, 'field': [25, 0, 12, 0, 1], 'lmfdb_label': '11616.k4', 'torsion': [2, 4]}
  • id: 601011
    {'degree': 8, 'field': [-2526, -3876, 4820, -864, 24, -68, 6, 0, 1], 'lmfdb_label': '11616.k4', 'torsion': [6]}
  • id: 601009
    {'degree': 8, 'field': [-74, 192, -138, -24, 71, -12, -18, 0, 1], 'lmfdb_label': '11616.k4', 'torsion': [8]}
  • id: 601008
    {'degree': 8, 'field': [324, 0, 0, 0, 14, 0, 0, 0, 1], 'lmfdb_label': '11616.k4', 'torsion': [2, 4]}
  • id: 601010
    {'degree': 8, 'field': [841, 0, 96, 0, 152, 0, 24, 0, 1], 'lmfdb_label': '11616.k4', 'torsion': [8]}
  • id: 601012
    {'degree': 16, 'field': [6561, 0, -14580, 0, 16200, 0, -12600, 0, 6079, 0, -1400, 0, 200, 0, -20, 0, 1], 'lmfdb_label': '11616.k4', 'torsion': [4, 4]}
  • id: 601016
    {'degree': 16, 'field': [17513, -3624, -2366, 2792, -14674, 1432, 5574, -952, 2091, 8, -1626, 40, 340, -4, -28, 0, 1], 'lmfdb_label': '11616.k4', 'torsion': [12]}
  • id: 601013
    {'degree': 16, 'field': [20758, 24008, -3020, -31048, -8302, 19472, 6816, -7924, -1729, 1564, 444, -236, -82, 28, 16, -8, 1], 'lmfdb_label': '11616.k4', 'torsion': [2, 8]}
  • id: 601017
    {'degree': 16, 'field': [708964, 0, 1371056, 0, 844576, 0, 291672, 0, 64884, 0, 9360, 0, 844, 0, 44, 0, 1], 'lmfdb_label': '11616.k4', 'torsion': [12]}
  • id: 601015
    {'degree': 16, 'field': [1542418, -3077208, 3003172, -1407416, 144688, 225256, -64036, -58928, 57548, -23356, 5684, -904, 262, -124, 16, 0, 1], 'lmfdb_label': '11616.k4', 'torsion': [2, 6]}
  • id: 601014
    {'degree': 16, 'field': [3418801, 0, 1420032, 0, 205232, 0, 70992, 0, 22983, 0, 3456, 0, 368, 0, 24, 0, 1], 'lmfdb_label': '11616.k4', '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: 249720
    {'conductor': 11616, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '11616.k4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 249721
    {'conductor': 11616, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '11616.k4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 249722
    {'conductor': 11616, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '11616.k4', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 1741038
    {'adelic_gens': [[89, 176, 44, 177], [119, 0, 0, 263], [1, 8, 0, 1], [7, 6, 258, 259], [257, 8, 256, 9], [1, 0, 8, 1], [144, 209, 187, 78], [120, 55, 143, 252], [1, 4, 4, 17]], 'adelic_image': '264.48.0.?', 'conductor': 11616, 'lmfdb_label': '11616.k4', 'prime': 0}
  • id: 55727
    {'conductor': 11616, 'elladic_image': '8.12.0.16', 'lmfdb_label': '11616.k4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 11616.k does not appear in ec_padic