Elliptic curve data - 61200.ek7

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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': '61200ff', 'Clabel': '61200ff5', 'Cnumber': 5, 'abc_quality': 1.0137929987603158, 'absD': 292914845250566400000000, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 8160, 'ainvs': [0, 0, 0, 11015925, 21908920250], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 17], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 61200, 'degree': 4718592, 'elladic_images': ['8.96.0.98'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.1873385677442143325982733550', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 114, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [3168685387909439, 6278181696900], 'lmfdb_iso': '61200.ek', 'lmfdb_label': '61200.ek7', 'lmfdb_number': 7, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, 3060, 102705], 'min_quad_twist_disc': 60, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.24.0-4.d.1.2', '8.96.0-8.n.1.2', '60.48.0-60.h.1.1', '120.192.1.?', '272.192.1.?', '1632.384.5.?', '2720.384.5.?', '4080.384.5.?', '8160.768.13.?'], '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': '1.1401662866331639901830389485', 'prec': 100}, 'szpiro_ratio': 5.547451098277184, '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, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 1, 0, -4, 0], 'aplist': [0, 0, 0, 0, 4, 2, 1, -4, 0, 2, -8, -6, 6, -4, 0, -10, -4, -2, 4, 0, 6, -8, 12, 6, 14], 'class_deg': 16, 'class_size': 8, 'conductor': 61200, 'isogeny_matrix': [[1, 16, 2, 4, 8, 16, 8, 4], [16, 1, 8, 4, 2, 4, 8, 16], [2, 8, 1, 2, 4, 8, 4, 2], [4, 4, 2, 1, 2, 4, 2, 4], [8, 2, 4, 2, 1, 2, 4, 8], [16, 4, 8, 4, 2, 1, 8, 16], [8, 8, 4, 2, 4, 8, 1, 8], [4, 16, 2, 4, 8, 16, 8, 1]], 'lmfdb_iso': '61200.ek', 'trace_hash': 476957594898869070}
• 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': '0.0017041699229793413161870646577', 'prec': 110}, 'conductor': 61200, 'gens': [], 'heights': [], 'lmfdb_label': '61200.ek7', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.067163572557632226236436986853', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.1492343218442312395659835792830433282', 'prec': 130}, 'tamagawa_product': 128, 'torsion_generators': [[-1610, 0, 1]], 'xcoord_integral_points': [-1610]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': 'a', '17': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '61200.ek7'}
• ec_torsion_growth •

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

  
  
  • id: 2934196
    {'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '61200.ek7', 'torsion': [4]}
  • id: 2934195
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '61200.ek7', 'torsion': [2, 2]}
  • id: 2934197
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '61200.ek7', 'torsion': [4]}
  • id: 2934202
    {'degree': 4, 'field': [6, -12, 13, -2, 1], 'lmfdb_label': '61200.ek7', 'torsion': [8]}
  • id: 2934198
    {'degree': 4, 'field': [16, 0, -7, 0, 1], 'lmfdb_label': '61200.ek7', 'torsion': [4, 4]}
  • id: 2934201
    {'degree': 4, 'field': [34, -4, 5, -2, 1], 'lmfdb_label': '61200.ek7', 'torsion': [8]}
  • id: 2934199
    {'degree': 4, 'field': [49, 0, -16, 0, 1], 'lmfdb_label': '61200.ek7', 'torsion': [8]}
  • id: 2934200
    {'degree': 4, 'field': [49, 0, 16, 0, 1], 'lmfdb_label': '61200.ek7', 'torsion': [8]}
  • id: 2934205
    {'degree': 8, 'field': [-151875, 0, 42360, 0, -1350, 0, 0, 0, 1], 'lmfdb_label': '61200.ek7', 'torsion': [6]}
  • id: 2934203
    {'degree': 8, 'field': [256, 0, 0, 0, 17, 0, 0, 0, 1], 'lmfdb_label': '61200.ek7', 'torsion': [4, 8]}
  • id: 2934204
    {'degree': 8, 'field': [900, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '61200.ek7', 'torsion': [4, 8]}
  • id: 2934206
    {'degree': 16, 'field': [1156, 4080, 848, -6256, 12512, -8736, 1496, 2592, -2240, 1032, -272, -8, 72, -56, 28, -8, 1], 'lmfdb_label': '61200.ek7', 'torsion': [8, 8]}
  • id: 2934211
    {'degree': 16, 'field': [583696, 0, -708448, 0, 508048, 0, -97351, 0, 1810, 0, 1409, 0, -167, 0, 2, 0, 1], 'lmfdb_label': '61200.ek7', 'torsion': [2, 6]}
  • id: 2934213
    {'degree': 16, 'field': [589824, 0, -1649712, 0, 1070800, 0, 447096, 0, 95565, 0, 6064, 0, -102, 0, 0, 0, 1], 'lmfdb_label': '61200.ek7', 'torsion': [12]}
  • id: 2934207
    {'degree': 16, 'field': [614656, 0, -112896, 0, -365184, 0, 7536, 0, 43553, 0, -1452, 0, -936, 0, -12, 0, 1], 'lmfdb_label': '61200.ek7', 'torsion': [16]}
  • id: 2934212
    {'degree': 16, 'field': [810000, 0, -432000, 0, 57600, 0, -894375, 0, 124650, 0, -2895, 0, 225, 0, -30, 0, 1], 'lmfdb_label': '61200.ek7', 'torsion': [12]}
  • id: 2934208
    {'degree': 16, 'field': [21381376, 0, -665856, 0, 1581696, 0, 203376, 0, 55313, 0, 2388, 0, -216, 0, -12, 0, 1], 'lmfdb_label': '61200.ek7', 'torsion': [16]}
  • id: 2934209
    {'degree': 16, 'field': [53084160000, 0, 6635520000, 0, -891648000, 0, -89856000, 0, 7056000, 0, 187200, 0, -3870, 0, -60, 0, 1], 'lmfdb_label': '61200.ek7', 'torsion': [16]}
  • id: 2934210
    {'degree': 16, 'field': [85030560000, 0, -33592320000, 0, 5988384000, 0, -605448000, 0, 36252225, 0, -1238400, 0, 23760, 0, -240, 0, 1], 'lmfdb_label': '61200.ek7', 'torsion': [16]}
• 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: 1475065
    {'conductor': 61200, 'conductor_valuation': 4, 'discriminant_valuation': 14, 'j_denominator_valuation': 2, 'kodaira_symbol': -10, 'lmfdb_label': '61200.ek7', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1475066
    {'conductor': 61200, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '61200.ek7', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1475067
    {'conductor': 61200, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '61200.ek7', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 1475068
    {'conductor': 61200, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '61200.ek7', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
• ec_galrep •

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

  
  
  • id: 2069672
    {'adelic_gens': [[1, 0, 32, 1], [1, 32, 0, 1], [4321, 8, 0, 1], [8129, 32, 8128, 33], [6093, 4072, 107, 2355], [1, 8, 0, 7141], [2695, 8128, 7498, 3831], [1, 32, 4, 129], [8135, 8144, 6282, 887], [25, 16, 6424, 7049]], 'adelic_image': '8160.768.13.?', 'conductor': 61200, 'lmfdb_label': '61200.ek7', 'prime': 0}
  • id: 258032
    {'conductor': 61200, 'elladic_image': '8.96.0.98', 'lmfdb_label': '61200.ek7', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 61200.ek does not appear in ec_padic