Elliptic curve data - 6336.bm1

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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': '6336g', 'Clabel': '6336g4', 'Cnumber': 4, 'abc_quality': 1.0886490953708667, 'absD': 36563462560677888, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 264, 'ainvs': [0, 0, 0, -84780, 2374704], 'analytic_rank': 0, 'bad_primes': [2, 3, 11], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 6336, 'degree': 36864, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8690859510622604250600038473', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 6, 'iso_nlabel': 38, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [13060888875, 7086244], 'lmfdb_iso': '6336.bm', 'lmfdb_label': '6336.bm1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -147, -135], 'min_quad_twist_disc': -24, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '12.24.0.h.1', '24.48.0-12.h.1.1', '44.6.0.e.1', '132.48.1.?', '264.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 3], [3, 2, 64], [11, 12, 576]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.0054059637212601923877217374202', 'prec': 110}, 'szpiro_ratio': 5.215562322095204, '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, 2, 0, 0, 0, 1, 0, -2, 0, 0, 0, -6, 0, -2, 0], 'aplist': [0, 0, 0, 2, 1, -2, -6, -2, 0, 6, -4, -2, 6, 10, 12, 12, -12, 10, -8, 12, 14, 2, 12, 0, 2], 'class_deg': 6, 'class_size': 4, 'conductor': 6336, 'isogeny_matrix': [[1, 3, 2, 6], [3, 1, 6, 2], [2, 6, 1, 3], [6, 2, 3, 1]], 'lmfdb_iso': '6336.bm', 'trace_hash': 1277986255878157332}
• 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': '0.023797567673387107848496137961', 'prec': 107}, 'conductor': 6336, 'gens': [], 'heights': [], 'lmfdb_label': '6336.bm1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.31906988400254030437906346095', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.9144193040152418262743807657210806776', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [[276, 0, 1]], 'xcoord_integral_points': [276]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '11': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '6336.bm1'}
• ec_torsion_growth •

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

  
  
  • id: 329696
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '6336.bm1', 'torsion': [2, 2]}
  • id: 329697
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '6336.bm1', 'torsion': [6]}
  • id: 329699
    {'degree': 4, 'field': [1, 0, 4, 0, 1], 'lmfdb_label': '6336.bm1', 'torsion': [2, 6]}
  • id: 329698
    {'degree': 4, 'field': [48, 0, -18, 0, 1], 'lmfdb_label': '6336.bm1', 'torsion': [4]}
  • id: 329700
    {'degree': 6, 'field': [-2, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '6336.bm1', 'torsion': [6]}
  • id: 329701
    {'degree': 8, 'field': [1, 4, 14, 16, 16, -16, 14, -4, 1], 'lmfdb_label': '6336.bm1', 'torsion': [2, 4]}
  • id: 329702
    {'degree': 8, 'field': [36, 0, -252, 0, 165, 0, -24, 0, 1], 'lmfdb_label': '6336.bm1', 'torsion': [2, 4]}
  • id: 329703
    {'degree': 8, 'field': [256, 0, -32, 0, 0, 0, -2, 0, 1], 'lmfdb_label': '6336.bm1', 'torsion': [12]}
  • id: 329705
    {'degree': 12, 'field': [1, 0, -12, 0, 39, 0, -52, 0, 27, 0, 0, 0, 1], 'lmfdb_label': '6336.bm1', 'torsion': [2, 6]}
  • id: 329704
    {'degree': 12, 'field': [4, 0, 24, 0, 60, 0, 44, 0, 0, 0, -6, 0, 1], 'lmfdb_label': '6336.bm1', 'torsion': [3, 6]}
  • id: 329707
    {'degree': 16, 'field': [1, 8, 18, -32, 6, -120, 346, -524, 687, -796, 718, -492, 264, -112, 36, -8, 1], 'lmfdb_label': '6336.bm1', 'torsion': [2, 12]}
  • id: 329706
    {'degree': 16, 'field': [16, 0, -1912, 0, 3584, 0, -2542, 0, 901, 0, -236, 0, 71, 0, -14, 0, 1], 'lmfdb_label': '6336.bm1', 'torsion': [8]}
  • id: 329708
    {'degree': 16, 'field': [484, 0, -1716, 0, 949, 0, 1176, 0, 111, 0, 12, 0, 31, 0, 0, 0, 1], 'lmfdb_label': '6336.bm1', 'torsion': [2, 12]}
  • id: 329709
    {'degree': 18, 'field': [34656, 0, -31824, 0, 38376, 0, 50052, 0, 50256, 0, 33408, 0, 10386, 0, 1392, 0, 66, 0, 1], 'lmfdb_label': '6336.bm1', '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: 126705
    {'conductor': 6336, 'conductor_valuation': 6, 'discriminant_valuation': 20, 'j_denominator_valuation': 2, 'kodaira_symbol': -14, 'lmfdb_label': '6336.bm1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 126706
    {'conductor': 6336, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '6336.bm1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 126707
    {'conductor': 6336, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '6336.bm1', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
• ec_galrep •

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

  
  
  • id: 1705494
    {'adelic_gens': [[131, 0, 0, 263], [78, 1, 77, 122], [253, 12, 252, 13], [1, 0, 12, 1], [11, 2, 214, 255], [251, 252, 186, 191], [253, 262, 182, 141], [1, 6, 6, 37], [56, 11, 9, 100], [143, 252, 144, 251], [1, 12, 0, 1]], 'adelic_image': '264.96.1.?', 'conductor': 6336, 'lmfdb_label': '6336.bm1', 'prime': 0}
  • id: 31112
    {'conductor': 6336, 'elladic_image': '2.3.0.1', 'lmfdb_label': '6336.bm1', 'modell_image': '2B', 'prime': 2}
  • id: 31113
    {'conductor': 6336, 'elladic_image': '3.4.0.1', 'lmfdb_label': '6336.bm1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 6336.bm does not appear in ec_padic