Elliptic curve data - 1776.a1

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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': '1776a', 'Clabel': '1776a3', 'Cnumber': 3, 'abc_quality': 0.9861762476903563, 'absD': 340992, 'adelic_genus': 3, 'adelic_index': 192, 'adelic_level': 1776, 'ainvs': [0, -1, 0, -7104, 232848], 'analytic_rank': 0, 'bad_primes': [2, 3, 37], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 1776, 'degree': 1024, 'elladic_images': ['8.24.0.47'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.64704223062772207156547247601', 'prec': 103}, 'faltings_index': 2, 'faltings_ratio': 4, 'intrinsic_torsion': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [38725206845188, 333], 'lmfdb_iso': '1776.a', 'lmfdb_label': '1776.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -7104, -232848], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '8.24.0-8.o.1.1', '48.48.0-48.i.1.4', '74.6.0.?', '148.24.0.?', '296.96.0.?', '1776.192.3.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 37], [3, 4, 592], [37, 38, 48]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.069419580161100980384445708128', 'prec': 107}, 'szpiro_ratio': 5.10804279371955, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
• 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, 0, 0, 1, 0, 4, 0, -2, 0, 2, 0, -6, 0, 0, 0], 'aplist': [0, -1, -2, 0, 4, -2, -6, 0, 4, 6, -4, 1, -6, 8, 8, 6, 0, 14, -4, 16, -6, 4, 4, 18, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 1776, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '1776.a', 'trace_hash': 2162911691296224502}
• 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': '0.27414874326546012109674251875', 'prec': 103}, 'conductor': 1776, 'gens': [], 'heights': [], 'lmfdb_label': '1776.a1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '2.1087618124100925918450850703', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0543809062050462959225425351297652639', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[48, 12, 1]], 'xcoord_integral_points': [48, 49]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '37': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '1776.a1'}
• ec_torsion_growth •

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

  
  
  • id: 90039
    {'degree': 2, 'field': [-9, -1, 1], 'lmfdb_label': '1776.a1', 'torsion': [2, 4]}
  • id: 90040
    {'degree': 4, 'field': [85, 14, -16, -2, 1], 'lmfdb_label': '1776.a1', 'torsion': [8]}
  • id: 90041
    {'degree': 4, 'field': [1332, 0, -74, 0, 1], 'lmfdb_label': '1776.a1', 'torsion': [2, 8]}
  • id: 90044
    {'degree': 8, 'field': [-3, 0, -584, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '1776.a1', 'torsion': [12]}
  • id: 90043
    {'degree': 8, 'field': [441, -1008, 1152, 378, 7, 62, 2, -2, 1], 'lmfdb_label': '1776.a1', 'torsion': [2, 8]}
  • id: 90042
    {'degree': 8, 'field': [111556, 0, -3992, 0, 672, 0, 4, 0, 1], 'lmfdb_label': '1776.a1', 'torsion': [4, 4]}
  • id: 90048
    {'degree': 16, 'field': [-2997, 11988, -35964, 47286, -47286, -1998, 1888, -3778, 3669, -5038, 5152, 210, 46, -154, 6, -4, 1], 'lmfdb_label': '1776.a1', 'torsion': [2, 12]}
  • id: 90047
    {'degree': 16, 'field': [8982009, 0, -3992004, 0, -7762230, 0, 443556, 0, 1768230, 0, -195804, 0, 8066, 0, -148, 0, 1], 'lmfdb_label': '1776.a1', 'torsion': [2, 16]}
  • id: 90045
    {'degree': 16, 'field': [40332532, -149402416, 79864968, 145773136, 81677400, 42209304, 14502928, 3456544, 583812, 20360, -11252, -7104, 0, -28, 24, -8, 1], 'lmfdb_label': '1776.a1', 'torsion': [4, 8]}
  • id: 90046
    {'degree': 16, 'field': [12296370321, 0, 886224888, 0, 155688156, 0, 2661336, 0, 714618, 0, -7992, 0, 1404, 0, -24, 0, 1], 'lmfdb_label': '1776.a1', '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: 28477
    {'conductor': 1776, 'conductor_valuation': 4, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -6, 'lmfdb_label': '1776.a1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 28478
    {'conductor': 1776, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '1776.a1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 28479
    {'conductor': 1776, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '1776.a1', 'prime': 37, '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: 1675621
    {'adelic_gens': [[593, 16, 1192, 129], [1761, 16, 1760, 17], [1496, 9, 1415, 26], [1, 16, 0, 1], [1, 8, 8, 65], [443, 1326, 1552, 653], [1, 0, 16, 1], [895, 898, 586, 647], [15, 166, 1490, 387]], 'adelic_image': '1776.192.3.?', 'conductor': 1776, 'lmfdb_label': '1776.a1', 'prime': 0}
  • id: 8697
    {'conductor': 1776, 'elladic_image': '8.24.0.47', 'lmfdb_label': '1776.a1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 1776.a does not appear in ec_padic