Elliptic curve data - 33135.d6

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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
  serre_invariants	integer[]
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '33135a', 'Clabel': '33135a2', 'Cnumber': 2, 'abc_quality': 0.9622954410890624, 'absD': 2425323449025, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 11280, 'ainvs': [1, 1, 1, -11091, -447912], 'analytic_rank': 0, 'bad_primes': [3, 5, 47], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 33135, 'degree': 51520, 'elladic_images': ['16.48.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1762226384922128512582627770', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 3, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [13997521, 225], 'lmfdb_iso': '33135.d', 'lmfdb_label': '33135.d6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -5, 2], 'min_quad_twist_disc': -47, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.24.0.i.1', '16.48.0.d.2', '24.48.0.bb.2', '40.48.0.bd.1', '48.96.1.n.1', '60.24.0.c.1', '80.192.5.?', '120.96.1.?', '188.24.0.?', '240.384.13.?', '376.48.0.?', '752.96.0.?', '1128.96.0.?', '1880.96.0.?', '2256.192.1.?', '2820.48.0.?', '3760.384.5.?', '5640.192.1.?', '11280.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 2209], [3, 4, 11045], [5, 6, 6627], [47, 1106, 15]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.74885116236281644215221255789', 'prec': 107}, 'szpiro_ratio': 3.800342405388077, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, 0, 3, 1, 1, 4, 1, 2, 0, 1, -1, 2, -1, -4, 1], 'aplist': [-1, -1, -1, 0, 4, 2, 2, -4, 0, 2, 0, -10, -10, -4, 0, -10, -4, -2, -12, -8, -10, 0, 12, -6, 2], 'class_deg': 16, 'class_size': 8, 'conductor': 33135, 'isogeny_matrix': [[1, 2, 4, 16, 4, 8, 16, 8], [2, 1, 2, 8, 2, 4, 8, 4], [4, 2, 1, 16, 4, 8, 16, 8], [16, 8, 16, 1, 4, 2, 4, 8], [4, 2, 4, 4, 1, 2, 4, 2], [8, 4, 8, 2, 2, 1, 2, 4], [16, 8, 16, 4, 4, 2, 1, 8], [8, 4, 8, 8, 2, 4, 8, 1]], 'lmfdb_iso': '33135.d', 'trace_hash': 246767084640461369}
• 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': '0.095136243090107621351776288601', 'prec': 107}, 'conductor': 33135, 'gens': [], 'heights': [], 'lmfdb_label': '33135.d6', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.46567171631966582947733866179', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.46567171631966582947733866179439606309', 'prec': 133}, 'tamagawa_product': 16, 'torsion_generators': [[-67, 33, 1], [121, -61, 1]], 'xcoord_integral_points': [-67, 121]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [8, 0], '3': [0, 0], '5': [0, 0], '47': 'a'}, 'iwp0': 3, 'lmfdb_label': '33135.d6'}
• ec_torsion_growth •

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

  
  
  • id: 1647090
    {'degree': 2, 'field': [12, -1, 1], 'lmfdb_label': '33135.d6', 'torsion': [2, 4]}
  • id: 1647091
    {'degree': 4, 'field': [64, 0, -31, 0, 1], 'lmfdb_label': '33135.d6', 'torsion': [2, 4]}
  • id: 1647093
    {'degree': 4, 'field': [169, 0, 21, 0, 1], 'lmfdb_label': '33135.d6', 'torsion': [2, 8]}
  • id: 1647092
    {'degree': 4, 'field': [2554, 86, -85, -2, 1], 'lmfdb_label': '33135.d6', 'torsion': [2, 4]}
  • id: 1647097
    {'degree': 8, 'field': [-57165, -3, -15043, 540, -615, -31, -3, 0, 1], 'lmfdb_label': '33135.d6', 'torsion': [2, 6]}
  • id: 1647095
    {'degree': 8, 'field': [20736, 0, 3312, 0, 385, 0, 23, 0, 1], 'lmfdb_label': '33135.d6', 'torsion': [2, 8]}
  • id: 1647096
    {'degree': 8, 'field': [36661, -2233, 8095, -658, 789, -62, 40, -2, 1], 'lmfdb_label': '33135.d6', 'torsion': [2, 16]}
  • id: 1647094
    {'degree': 8, 'field': [57664, 7920, -7214, -1382, 617, 86, -24, -4, 1], 'lmfdb_label': '33135.d6', 'torsion': [4, 4]}
  • id: 1647098
    {'degree': 16, 'field': [-41933759, 58084320, 27906462, -71794680, 20056360, 21481860, -12045978, -1611480, 2020089, -3300, -161862, 3000, 6640, -60, -132, 0, 1], 'lmfdb_label': '33135.d6', 'torsion': [2, 8]}
  • id: 1647100
    {'degree': 16, 'field': [210946576, 0, -177403492, 0, 62659769, 0, -12047688, 0, 1390904, 0, -98838, 0, 4232, 0, -100, 0, 1], 'lmfdb_label': '33135.d6', 'torsion': [4, 8]}
  • id: 1647102
    {'degree': 16, 'field': [363093025, 0, 245792032, 0, 73753000, 0, 12591369, 0, 1337232, 0, 90855, 0, 3865, 0, 94, 0, 1], 'lmfdb_label': '33135.d6', 'torsion': [2, 12]}
  • id: 1647101
    {'degree': 16, 'field': [429981696, 0, 68677632, 0, 7983360, 0, 798192, 0, 72049, 0, 5543, 0, 385, 0, 23, 0, 1], 'lmfdb_label': '33135.d6', 'torsion': [2, 16]}
  • id: 1647099
    {'degree': 16, 'field': [11500956385636, 0, -2585228671992, 0, 240988454800, 0, -12126015372, 0, 360799029, 0, -6510108, 0, 69790, 0, -408, 0, 1], 'lmfdb_label': '33135.d6', '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: 775489
    {'conductor': 33135, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '33135.d6', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 775490
    {'conductor': 33135, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '33135.d6', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 775491
    {'conductor': 33135, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '33135.d6', 'prime': 47, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 1885358
    {'adelic_gens': [[4325, 6016, 4324, 4513], [4319, 0, 0, 11279], [3855, 8648, 10528, 10529], [1, 16, 0, 1], [11265, 16, 11264, 17], [3761, 6016, 6486, 2257], [1, 16, 4, 65], [8461, 8648, 3290, 8837], [1, 0, 16, 1]], 'adelic_image': '11280.768.13.?', 'conductor': 33135, 'lmfdb_label': '33135.d6', 'prime': 0}
  • id: 147795
    {'conductor': 33135, 'elladic_image': '16.48.0.3', 'lmfdb_label': '33135.d6', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 33135.d does not appear in ec_padic