Elliptic curve data - 176610.bs4

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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': '176610by', 'Clabel': '176610by3', 'Cnumber': 3, 'abc_quality': 0.9866121641692004, 'absD': 205742284543447260, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 48720, 'ainvs': [1, 0, 1, -311188, 63125798], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 29], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 176610, 'degree': 3096576, 'elladic_images': ['8.24.0.90'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0738317541873963123444470035', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 44, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [5602762882081, 345888060], 'lmfdb_iso': '176610.bs', 'lmfdb_label': '176610.bs4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -370, 2435], 'min_quad_twist_disc': 29, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.bb.2', '60.12.0.h.1', '112.48.0.?', '116.12.0.?', '120.48.0.?', '232.48.0.?', '1680.96.1.?', '1740.24.0.?', '3248.96.0.?', '3480.96.0.?', '48720.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.39018383919415929875281098732', 'prec': 103}, 'szpiro_ratio': 4.101911093921947, '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, -1, 1, 1, 1, -1, 1, -1, 1, -1, -4, 1, -2, -1, 1, 1, -2, -1, 4, 1], 'aplist': [-1, 1, 1, 1, -4, -2, -2, 4, -8, 0, 8, 2, -2, 12, 8, 6, 4, 2, 12, 8, 14, 0, 12, -2, -10], 'class_deg': 8, 'class_size': 6, 'conductor': 176610, 'isogeny_matrix': [[1, 2, 4, 8, 4, 8], [2, 1, 2, 4, 2, 4], [4, 2, 1, 8, 4, 8], [8, 4, 8, 1, 2, 4], [4, 2, 4, 2, 1, 2], [8, 4, 8, 4, 2, 1]], 'lmfdb_iso': '176610.bs', 'trace_hash': 2250398269320246681}
• 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': '0.015801292975977650239687710810', 'prec': 107}, 'conductor': 176610, 'gens': [], 'heights': [], 'lmfdb_label': '176610.bs4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.31148209853354760980305325682', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.4918567882683808784244260545850664385', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[1527, -1531, 2]], 'xcoord_integral_points': []}
• lmfdb_label 176610.bs4 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7826143
    {'degree': 2, 'field': [-435, 0, 1], 'lmfdb_label': '176610.bs4', 'torsion': [4]}
  • id: 7826141
    {'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '176610.bs4', 'torsion': [2, 2]}
  • id: 7826142
    {'degree': 2, 'field': [-7, -1, 1], 'lmfdb_label': '176610.bs4', 'torsion': [4]}
  • id: 7826146
    {'degree': 4, 'field': [23, 18, -17, -2, 1], 'lmfdb_label': '176610.bs4', 'torsion': [8]}
  • id: 7826144
    {'degree': 4, 'field': [49, 44, -43, -2, 1], 'lmfdb_label': '176610.bs4', 'torsion': [2, 4]}
  • id: 7826145
    {'degree': 4, 'field': [499, 74, -73, -2, 1], 'lmfdb_label': '176610.bs4', 'torsion': [8]}
  • id: 7826150
    {'degree': 8, 'field': [-5638080, 1666560, -28560, 6688, -1648, -848, 4, -4, 1], 'lmfdb_label': '176610.bs4', 'torsion': [6]}
  • id: 7826149
    {'degree': 8, 'field': [49, 420, 436, -1652, 677, 176, -54, -4, 1], 'lmfdb_label': '176610.bs4', 'torsion': [2, 8]}
  • id: 7826147
    {'degree': 8, 'field': [2865, -2010, 2340, -690, 421, -94, 36, -4, 1], 'lmfdb_label': '176610.bs4', 'torsion': [2, 4]}
  • id: 7826148
    {'degree': 8, 'field': [811801, 0, 76676, 0, 5166, 0, 116, 0, 1], 'lmfdb_label': '176610.bs4', 'torsion': [8]}
  • id: 7826153
    {'degree': 16, 'field': [519841, 0, 10748040, 0, 8848186, 0, 1591380, 0, 242571, 0, 23220, 0, 1486, 0, 60, 0, 1], 'lmfdb_label': '176610.bs4', 'torsion': [2, 8]}
  • id: 7826151
    {'degree': 16, 'field': [8208225, 0, -9368100, 0, 5114130, 0, -1322580, 0, 205651, 0, -20636, 0, 1386, 0, -56, 0, 1], 'lmfdb_label': '176610.bs4', 'torsion': [4, 4]}
  • id: 7826155
    {'degree': 16, 'field': [9038087, -28526160, 52123268, -48933656, 28922744, -5618616, 2240560, -151896, -151907, 105064, -500, -9920, 622, 448, -44, -8, 1], 'lmfdb_label': '176610.bs4', 'torsion': [16]}
  • id: 7826157
    {'degree': 16, 'field': [9922500, 0, -4465125, 0, 3505950, 0, -1212359, 0, 204647, 0, -21239, 0, 1471, 0, -58, 0, 1], 'lmfdb_label': '176610.bs4', 'torsion': [12]}
  • id: 7826152
    {'degree': 16, 'field': [132419865, -27714900, -85691940, 43417260, 9898890, -20138160, 10913100, -3339900, 776971, -153488, 44308, -11036, 2890, -476, 88, -8, 1], 'lmfdb_label': '176610.bs4', 'torsion': [2, 8]}
  • id: 7826154
    {'degree': 16, 'field': [390493651, 1083689504, -314854252, -1327851912, 163012196, 536132104, -74029760, -82629816, 11986849, 5471208, -789260, -161008, 22406, 2016, -268, -8, 1], 'lmfdb_label': '176610.bs4', 'torsion': [16]}
  • id: 7826158
    {'degree': 16, 'field': [13282101504, 0, 8448139392, 0, 5219822020, 0, 86205504, 0, -160542240, 0, -2676344, 0, -44112, 0, 0, 0, 1], 'lmfdb_label': '176610.bs4', 'torsion': [12]}
  • id: 7826156
    {'degree': 16, 'field': [355267257849, 0, -61469028168, 0, -16661937860, 0, -2507040096, 0, -91919430, 0, -2466584, 0, -29352, 0, -120, 0, 1], 'lmfdb_label': '176610.bs4', 'torsion': [2, 6]}
• 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: 4369636
    {'conductor': 176610, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '176610.bs4', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4369637
    {'conductor': 176610, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '176610.bs4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 4369638
    {'conductor': 176610, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '176610.bs4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 4369639
    {'conductor': 176610, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '176610.bs4', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 4369640
    {'conductor': 176610, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '176610.bs4', 'prime': 29, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
• ec_galrep •

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

  
  
  • id: 2801428
    {'adelic_gens': [[48705, 16, 48704, 17], [5, 4, 48716, 48717], [15, 2, 48622, 48707], [1, 16, 0, 1], [1016, 25201, 3103, 31930], [10093, 13456, 39324, 41065], [11978, 21431, 21547, 726], [25199, 0, 0, 48719], [1, 0, 16, 1], [14008, 25201, 9599, 31930], [6961, 13456, 13688, 10209]], 'adelic_image': '48720.192.1.?', 'conductor': 176610, 'lmfdb_label': '176610.bs4', 'prime': 0}
  • id: 664087
    {'conductor': 176610, 'elladic_image': '8.24.0.90', 'lmfdb_label': '176610.bs4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 176610.bs does not appear in ec_padic