Elliptic curve data - 1785.a4

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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': '1785c', 'Clabel': '1785c1', 'Cnumber': 1, 'abc_quality': 0.9108309731708967, 'absD': 1581036975, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 2856, 'ainvs': [1, 1, 1, -181, -2206], 'analytic_rank': 0, 'bad_primes': [3, 5, 7, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 1785, 'degree': 768, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.45323309894190965334877567832', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [-656008386769, 1581036975], 'lmfdb_iso': '1785.a', 'lmfdb_label': '1785.a4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -181, -2206], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0-4.c.1.3', '28.12.0-4.c.1.2', '68.12.0-4.c.1.2', '168.24.0.?', '238.6.0.?', '408.24.0.?', '476.24.0.?', '2856.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.45323309894190965334877567832', 'prec': 103}, 'szpiro_ratio': 3.853426400917808, '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, 3, 1, 1, 0, 1, -2, -1, 1, -1, -1, -1, 0, 1], 'aplist': [-1, -1, -1, 1, 0, -2, -1, 0, 4, -6, 0, -2, 6, -12, 8, 6, -12, 2, -4, -12, -2, 0, 12, 14, 14], 'class_deg': 4, 'class_size': 4, 'conductor': 1785, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '1785.a', 'trace_hash': 12982309239163447}
• 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': '0.40394918126390154467832839732', 'prec': 103}, 'conductor': 1785, 'gens': [], 'heights': [], 'lmfdb_label': '1785.a4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.60707155472398560983868478962', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.60707155472398560983868478961902994060', 'prec': 133}, 'tamagawa_product': 4, 'torsion_generators': [[17, -9, 1]], 'xcoord_integral_points': [17]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [6, 0], '3': [0, 0], '5': [0, 0], '7': [1, 0], '17': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '1785.a4'}
• ec_torsion_growth •

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

  
  
  • id: 90451
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '1785.a4', 'torsion': [4]}
  • id: 90452
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '1785.a4', 'torsion': [4]}
  • id: 90450
    {'degree': 2, 'field': [30, -1, 1], 'lmfdb_label': '1785.a4', 'torsion': [2, 2]}
  • id: 90453
    {'degree': 4, 'field': [36, 0, -5, 0, 1], 'lmfdb_label': '1785.a4', 'torsion': [2, 4]}
  • id: 90457
    {'degree': 8, 'field': [-243, 0, -209, 0, -54, 0, 0, 0, 1], 'lmfdb_label': '1785.a4', 'torsion': [6]}
  • id: 90456
    {'degree': 8, 'field': [9, 0, 87, 0, -32, 0, -1, 0, 1], 'lmfdb_label': '1785.a4', 'torsion': [8]}
  • id: 90454
    {'degree': 8, 'field': [51956, 56824, 23936, 3776, 573, 278, 34, -2, 1], 'lmfdb_label': '1785.a4', 'torsion': [2, 4]}
  • id: 90455
    {'degree': 8, 'field': [76249, -74912, -6913, -10668, -3016, -330, -133, -2, 1], 'lmfdb_label': '1785.a4', 'torsion': [8]}
  • id: 90463
    {'degree': 16, 'field': [5159, -41174, 169912, -377698, 507935, -435036, 232642, -76624, 21164, -1654, 894, -640, 410, -168, 44, -8, 1], 'lmfdb_label': '1785.a4', 'torsion': [12]}
  • id: 90459
    {'degree': 16, 'field': [9216, -16128, 41472, -64464, 67804, -45156, 16993, 2908, -6894, 4698, -1307, -96, 289, -154, 42, -8, 1], 'lmfdb_label': '1785.a4', 'torsion': [2, 8]}
  • id: 90462
    {'degree': 16, 'field': [2165651, 3828634, -3144164, -1111954, -57841, 661452, -110174, -65776, -17296, 19274, -1074, -976, -262, 168, -4, -8, 1], 'lmfdb_label': '1785.a4', 'torsion': [12]}
  • id: 90461
    {'degree': 16, 'field': [15116544, 0, 16108800, 0, 3412768, 0, -431520, 0, 47805, 0, 1535, 0, 282, 0, 0, 0, 1], 'lmfdb_label': '1785.a4', 'torsion': [2, 6]}
  • id: 90458
    {'degree': 16, 'field': [146410000, 0, 0, 0, 52724200, 0, 0, 0, 491361, 0, 0, 0, 1702, 0, 0, 0, 1], 'lmfdb_label': '1785.a4', 'torsion': [4, 4]}
  • id: 90460
    {'degree': 16, 'field': [1949698804, 2652836696, 1959387380, 962334856, 579500389, -70501410, -63017155, 13848214, 8819098, 394118, -228895, -12114, 7006, 302, -127, -2, 1], 'lmfdb_label': '1785.a4', '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: 28633
    {'conductor': 1785, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '1785.a4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 28634
    {'conductor': 1785, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '1785.a4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 28635
    {'conductor': 1785, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '1785.a4', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 28636
    {'conductor': 1785, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '1785.a4', 'prime': 17, '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: 1675671
    {'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [2188, 1, 1871, 6], [416, 3, 2045, 2], [7, 6, 2850, 2851], [2849, 8, 2848, 9], [953, 8, 956, 33], [1075, 1074, 370, 1795], [1793, 1788, 1790, 359]], 'adelic_image': '2856.48.0.?', 'conductor': 1785, 'lmfdb_label': '1785.a4', 'prime': 0}
  • id: 8744
    {'conductor': 1785, 'elladic_image': '4.6.0.1', 'lmfdb_label': '1785.a4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 1785.a does not appear in ec_padic