Elliptic curve data - 77616.dq2

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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': '77616ex', 'Clabel': '77616ex4', 'Cnumber': 4, 'abc_quality': 1.0528666156799333, 'absD': 44808904237512425472, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 1848, 'ainvs': [0, 0, 0, -285915, 327394186], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 11], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 77616, 'degree': 1658880, 'elladic_images': ['8.6.0.5', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4519050155463497008132678198', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 6, 'iso_nlabel': 94, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [-7357983625, 127552392], 'lmfdb_iso': '77616.dq', 'lmfdb_label': '77616.dq2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -41, -556], 'min_quad_twist_disc': -84, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '8.6.0.a.1', '24.24.0.p.1', '84.24.0.?', '132.24.0.?', '168.48.0.?', '264.48.1.?', '924.48.0.?', '1848.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, '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': '0.23649661612469289314573670816', 'prec': 103}, 'szpiro_ratio': 4.683721412638079, '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, -1, 0, 4, 0, 0, 0, -6, 0, -4, 0], 'aplist': [0, 0, 0, 0, -1, 4, -6, -4, 6, -6, 8, -10, 6, -8, 6, 0, 0, -8, 4, 6, -2, -14, 12, -6, -14], 'class_deg': 6, 'class_size': 4, 'conductor': 77616, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '77616.dq', 'trace_hash': 152592397638697069}
• 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': '0.0074182653378672654479782739740', 'prec': 110}, 'conductor': 77616, 'gens': [], 'heights': [], 'lmfdb_label': '77616.dq2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.17059403722216071064104955165', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.3647522977772856851283964132049310302', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-826, 0, 1]], 'xcoord_integral_points': [-826]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '7': 'a', '11': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '77616.dq2'}
• ec_torsion_growth •

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

  
  
  • id: 3666454
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '77616.dq2', 'torsion': [6]}
  • id: 3666453
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '77616.dq2', 'torsion': [2, 2]}
  • id: 3666455
    {'degree': 4, 'field': [-24, 30, -2, -1, 1], 'lmfdb_label': '77616.dq2', 'torsion': [4]}
  • id: 3666456
    {'degree': 4, 'field': [9, 0, 8, 0, 1], 'lmfdb_label': '77616.dq2', 'torsion': [2, 6]}
  • id: 3666457
    {'degree': 6, 'field': [1029, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '77616.dq2', 'torsion': [6]}
  • id: 3666458
    {'degree': 8, 'field': [1089, 0, -540, 0, 280, 0, 4, 0, 1], 'lmfdb_label': '77616.dq2', 'torsion': [2, 4]}
  • id: 3666459
    {'degree': 8, 'field': [2304, -2688, 1648, -320, -82, 52, 5, -2, 1], 'lmfdb_label': '77616.dq2', 'torsion': [2, 4]}
  • id: 3666460
    {'degree': 8, 'field': [2304, 0, -2172, 0, 265, 0, -26, 0, 1], 'lmfdb_label': '77616.dq2', 'torsion': [12]}
  • id: 3666461
    {'degree': 12, 'field': [119716, 0, -96432, 0, 36645, 0, -6854, 0, 735, 0, -42, 0, 1], 'lmfdb_label': '77616.dq2', 'torsion': [3, 6]}
  • id: 3666462
    {'degree': 12, 'field': [140625, 0, 0, 0, 0, 0, 708, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '77616.dq2', 'torsion': [2, 6]}
  • id: 3666465
    {'degree': 16, 'field': [89028, -13248, -39000, 31584, 68080, -60576, 11724, 11136, -4611, -2640, 1048, 96, 210, -48, -12, 0, 1], 'lmfdb_label': '77616.dq2', 'torsion': [2, 12]}
  • id: 3666464
    {'degree': 16, 'field': [205713, -597672, 933120, -584784, 509112, -355992, 216064, -64032, 80446, -2936, 14656, -80, 1432, -8, 64, 0, 1], 'lmfdb_label': '77616.dq2', 'torsion': [2, 12]}
  • id: 3666463
    {'degree': 16, 'field': [18386944, 0, 98545408, 0, -36503456, 0, 5249584, 0, -312656, 0, -2336, 0, 1342, 0, -65, 0, 1], 'lmfdb_label': '77616.dq2', 'torsion': [8]}
  • id: 3666466
    {'degree': 18, 'field': [-185313504, -332251488, -7248624, 250533952, 103074840, -18298536, -19499036, -8620896, 640824, 1289404, 152412, -32988, -32015, -672, 2295, -8, -69, 0, 1], 'lmfdb_label': '77616.dq2', 'torsion': [18]}
• 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: 1888802
    {'conductor': 77616, 'conductor_valuation': 4, 'discriminant_valuation': 15, 'j_denominator_valuation': 3, 'kodaira_symbol': -11, 'lmfdb_label': '77616.dq2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1888803
    {'conductor': 77616, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '77616.dq2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1888804
    {'conductor': 77616, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '77616.dq2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1888805
    {'conductor': 77616, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '77616.dq2', 'prime': 11, 'reduction_type': -1, '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: 2176582
    {'adelic_gens': [[274, 1323, 105, 1576], [846, 791, 1771, 1462], [1, 0, 12, 1], [11, 2, 1798, 1839], [1837, 12, 1836, 13], [1, 6, 6, 37], [1, 12, 0, 1], [1231, 252, 1358, 1511], [263, 0, 0, 1847], [673, 1596, 1134, 337]], 'adelic_image': '1848.96.1.?', 'conductor': 77616, 'lmfdb_label': '77616.dq2', 'prime': 0}
  • id: 320143
    {'conductor': 77616, 'elladic_image': '8.6.0.5', 'lmfdb_label': '77616.dq2', 'modell_image': '2B', 'prime': 2}
  • id: 320144
    {'conductor': 77616, 'elladic_image': '3.4.0.1', 'lmfdb_label': '77616.dq2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 77616.dq does not appear in ec_padic