Elliptic curve data - 51600.dq3

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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': '51600di', 'Clabel': '51600di2', 'Cnumber': 2, 'abc_quality': 0.9535732176190836, 'absD': 21566736000000000, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 5160, 'ainvs': [0, 1, 0, -543008, -154032012], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 43], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 51600, 'degree': 552960, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0443341030956074806417868977', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 94, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [276670733768281, 336980250], 'lmfdb_iso': '51600.dq', 'lmfdb_label': '51600.dq3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -1358, 19118], 'min_quad_twist_disc': -20, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '24.24.0-6.a.1.12', '40.6.0.b.1', '60.24.0-6.a.1.4', '120.48.0.?', '516.24.0.?', '1032.48.0.?', '2580.48.0.?', '5160.96.1.?'], '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': '0.54646796631861198392417510963', 'prec': 103}, 'szpiro_ratio': 4.720941424566268, '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, 1, 0, 0, 0, 2, 0, 1, 0, 6, 0, -2, 0, 0, 0, 0, 0, -2, 0], 'aplist': [0, 1, 0, 2, 6, -2, 0, -2, 6, 6, -8, -2, -6, 1, 6, 6, -6, 8, -4, 0, 4, -8, 0, -6, 10], 'class_deg': 6, 'class_size': 4, 'conductor': 51600, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '51600.dq', 'trace_hash': 1518574880764143431}
• 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': '0.016761541617768040397806253357', 'prec': 107}, 'conductor': 51600, 'gens': [], 'heights': [], 'lmfdb_label': '51600.dq3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.17588536053309000850818766702', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.2212486527941602041965040085988941995', 'prec': 130}, 'tamagawa_product': 96, 'torsion_generators': [[-437, 0, 1]], 'xcoord_integral_points': [-437]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '5': 'a', '43': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '51600.dq3'}
• ec_torsion_growth •

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

  
  
  • id: 2500462
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '51600.dq3', 'torsion': [2, 2]}
  • id: 2500463
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '51600.dq3', 'torsion': [6]}
  • id: 2500465
    {'degree': 4, 'field': [9, 0, -4, 0, 1], 'lmfdb_label': '51600.dq3', 'torsion': [2, 6]}
  • id: 2500464
    {'degree': 4, 'field': [10, 0, 13, 0, 1], 'lmfdb_label': '51600.dq3', 'torsion': [4]}
  • id: 2500466
    {'degree': 6, 'field': [-699, -1290, -995, -258, -5, 0, 1], 'lmfdb_label': '51600.dq3', 'torsion': [6]}
  • id: 2500469
    {'degree': 8, 'field': [900, 0, 1200, 0, 469, 0, 46, 0, 1], 'lmfdb_label': '51600.dq3', 'torsion': [12]}
  • id: 2500467
    {'degree': 8, 'field': [4225, 0, 1900, 0, -160, 0, -20, 0, 1], 'lmfdb_label': '51600.dq3', 'torsion': [2, 4]}
  • id: 2500468
    {'degree': 8, 'field': [57600, 0, -8520, 0, 529, 0, -14, 0, 1], 'lmfdb_label': '51600.dq3', 'torsion': [2, 4]}
  • id: 2500471
    {'degree': 12, 'field': [2601, 0, -31980, 0, -12149, 0, -52, 0, 159, 0, -16, 0, 1], 'lmfdb_label': '51600.dq3', 'torsion': [2, 6]}
  • id: 2500470
    {'degree': 12, 'field': [166464, 0, 1023360, 0, -194384, 0, 416, 0, 636, 0, 32, 0, 1], 'lmfdb_label': '51600.dq3', 'torsion': [3, 6]}
  • id: 2500473
    {'degree': 16, 'field': [18225, 0, -24300, 0, 162630, 0, -186240, 0, 57271, 0, -168, 0, -206, 0, -12, 0, 1], 'lmfdb_label': '51600.dq3', 'torsion': [2, 12]}
  • id: 2500474
    {'degree': 16, 'field': [7128900, 0, -4137720, 0, 534904, 0, -64764, 0, 28509, 0, 4672, 0, 666, 0, 36, 0, 1], 'lmfdb_label': '51600.dq3', 'torsion': [2, 12]}
  • id: 2500472
    {'degree': 16, 'field': [137366596900, 0, 23705464000, 0, 2040318724, 0, 112425736, 0, 5264389, 0, 160132, 0, 4666, 0, 76, 0, 1], 'lmfdb_label': '51600.dq3', 'torsion': [8]}
  • id: 2500475
    {'degree': 18, 'field': [6721488216, 9269972424, 6742629324, 4106867856, 1800088290, 562985154, 258632731, 63657876, 39427959, 6687580, 37404, -186804, -7269, 2484, 1980, 76, -51, -6, 1], 'lmfdb_label': '51600.dq3', '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: 1235255
    {'conductor': 51600, 'conductor_valuation': 4, 'discriminant_valuation': 13, 'j_denominator_valuation': 1, 'kodaira_symbol': -9, 'lmfdb_label': '51600.dq3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1235256
    {'conductor': 51600, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '51600.dq3', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 1235257
    {'conductor': 51600, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '51600.dq3', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1235258
    {'conductor': 51600, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '51600.dq3', 'prime': 43, '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: 2007010
    {'adelic_gens': [[4561, 12, 1566, 73], [3449, 2, 864, 1], [5149, 12, 5148, 13], [11, 2, 5110, 5151], [3645, 2792, 3682, 2803], [1, 0, 12, 1], [1, 6, 6, 37], [1, 12, 0, 1], [5150, 5157, 1059, 8], [10, 3, 2553, 5152]], 'adelic_image': '5160.96.1.?', 'conductor': 51600, 'lmfdb_label': '51600.dq3', 'prime': 0}
  • id: 220950
    {'conductor': 51600, 'elladic_image': '2.3.0.1', 'lmfdb_label': '51600.dq3', 'modell_image': '2B', 'prime': 2}
  • id: 220951
    {'conductor': 51600, 'elladic_image': '3.4.0.1', 'lmfdb_label': '51600.dq3', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 51600.dq does not appear in ec_padic