Elliptic curve data - 4641.b1

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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': '4641b', 'Clabel': '4641b5', 'Cnumber': 5, 'abc_quality': 0.958227029320478, 'absD': 6115533215337, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 74256, 'ainvs': [1, 1, 1, -40579, -3160960], 'analytic_rank': 1, 'bad_primes': [3, 7, 13, 17], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 4641, 'degree': 12288, 'elladic_images': ['8.24.0.55'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3818866827766589016152506703', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [7389727131216686257, 6115533215337], 'lmfdb_iso': '4641.b', 'lmfdb_label': '4641.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -40579, -3160960], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '8.24.0-8.n.1.6', '34.6.0.a.1', '68.24.0-68.g.1.1', '136.48.0.?', '168.48.0.?', '208.48.0.?', '2856.96.0.?', '3536.96.0.?', '4368.96.0.?', '74256.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 8, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.52166992624576069191064023017', 'prec': 103}, 'semistable': True, 'serre_invariants': [[2, 2, 17], [3, 4, 1547], [7, 8, 663], [13, 14, 357], [17, 18, 273]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.3818866827766589016152506703', 'prec': 100}, 'szpiro_ratio': 5.1460668931234, '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, -2, 1, -1, 3, 1, 2, -4, 1, 1, 1, 2, -1, 1, -1, -4, 2], 'aplist': [-1, -1, -2, -1, -4, 1, 1, -4, 0, 6, 0, -2, 2, 12, 0, -10, 12, -10, 4, 8, 10, -8, 4, 10, 2], 'class_deg': 8, 'class_size': 6, 'conductor': 4641, 'isogeny_matrix': [[1, 2, 4, 8, 8, 4], [2, 1, 2, 4, 4, 2], [4, 2, 1, 2, 2, 4], [8, 4, 2, 1, 4, 8], [8, 4, 2, 4, 1, 8], [4, 2, 4, 8, 8, 1]], 'lmfdb_iso': '4641.b', 'trace_hash': 1735675449831001850}
• 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': '0.063053395398100009011232766691', 'prec': 107}, 'conductor': 4641, 'gens': [[-116, 12, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.52166992624576069191064023017', 'prec': 103}], 'lmfdb_label': '4641.b1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.33639206258238834716179147715', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4038849798161107521651937587035361075', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-477, 473, 2]], 'xcoord_integral_points': [-116, 261, 430, 2614]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 3], '3': [1, 0], '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [2, 0], '17': [2, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '4641.b1'}
• ec_torsion_growth •

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

  
  
  • id: 241287
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '4641.b1', 'torsion': [2, 2]}
  • id: 241289
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '4641.b1', 'torsion': [4]}
  • id: 241288
    {'degree': 2, 'field': [17, 0, 1], 'lmfdb_label': '4641.b1', 'torsion': [4]}
  • id: 241291
    {'degree': 4, 'field': [-7497, 0, 0, 0, 1], 'lmfdb_label': '4641.b1', 'torsion': [2, 4]}
  • id: 241290
    {'degree': 4, 'field': [16, 0, 9, 0, 1], 'lmfdb_label': '4641.b1', 'torsion': [2, 4]}
  • id: 241292
    {'degree': 4, 'field': [17, 0, 0, 0, 1], 'lmfdb_label': '4641.b1', 'torsion': [8]}
  • id: 241293
    {'degree': 4, 'field': [441, 0, 0, 0, 1], 'lmfdb_label': '4641.b1', 'torsion': [8]}
  • id: 241294
    {'degree': 4, 'field': [127449, 0, 0, 0, 1], 'lmfdb_label': '4641.b1', 'torsion': [8]}
  • id: 241298
    {'degree': 8, 'field': [-3, 0, -281, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '4641.b1', 'torsion': [6]}
  • id: 241297
    {'degree': 8, 'field': [324, 0, -200, 0, 40, 0, 4, 0, 1], 'lmfdb_label': '4641.b1', 'torsion': [2, 8]}
  • id: 241295
    {'degree': 8, 'field': [184041, 74646, 15138, 1728, -833, -184, 2, -2, 1], 'lmfdb_label': '4641.b1', 'torsion': [4, 4]}
  • id: 241296
    {'degree': 8, 'field': [216346, -32676, -19998, 672, 995, -84, 18, 0, 1], 'lmfdb_label': '4641.b1', 'torsion': [2, 8]}
  • id: 241305
    {'degree': 16, 'field': [83521, 0, 39304, 0, 4624, 0, 1370727, 0, 159528, 0, 5049, 0, 289, 0, 34, 0, 1], 'lmfdb_label': '4641.b1', 'torsion': [12]}
  • id: 241306
    {'degree': 16, 'field': [83521, 0, 167042, 0, 83521, 0, -10536, 0, -7002, 0, 642, 0, 16, 0, 8, 0, 1], 'lmfdb_label': '4641.b1', 'torsion': [12]}
  • id: 241304
    {'degree': 16, 'field': [173147, 2915146, -1990508, -1882546, 1014191, -54516, -49166, 81104, -46600, 13274, 1182, -1552, -166, 168, -4, -8, 1], 'lmfdb_label': '4641.b1', 'torsion': [2, 6]}
  • id: 241300
    {'degree': 16, 'field': [44649124, 0, 88148696, 0, 33781736, 0, 6994668, 0, 917813, 0, 73968, 0, 3518, 0, 92, 0, 1], 'lmfdb_label': '4641.b1', 'torsion': [4, 8]}
  • id: 241299
    {'degree': 16, 'field': [51955264, 0, -68361216, 0, 18842800, 0, -1068144, 0, -13260, 0, -14280, 0, -68, 0, 0, 0, 1], 'lmfdb_label': '4641.b1', 'torsion': [2, 8]}
  • id: 241301
    {'degree': 16, 'field': [56205009, 0, 0, 0, -15293880, 0, 0, 0, 1690327, 0, 0, 0, -2040, 0, 0, 0, 1], 'lmfdb_label': '4641.b1', 'torsion': [16]}
  • id: 241302
    {'degree': 16, 'field': [259891961616, 0, 0, 0, 1455977376, 0, 0, 0, 35926065, 0, 0, 0, 2856, 0, 0, 0, 1], 'lmfdb_label': '4641.b1', 'torsion': [16]}
  • id: 241303
    {'degree': 16, 'field': [21706436526129936, 0, 0, 0, -7153216848288, 0, 0, 0, 10382632785, 0, 0, 0, -48552, 0, 0, 0, 1], 'lmfdb_label': '4641.b1', '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: 88454
    {'conductor': 4641, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '4641.b1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 88455
    {'conductor': 4641, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '4641.b1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 88456
    {'conductor': 4641, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '4641.b1', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 88457
    {'conductor': 4641, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '4641.b1', '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: 1694114
    {'adelic_gens': [[1, 16, 0, 1], [5, 4, 74252, 74253], [15, 2, 74158, 74243], [46423, 16, 64718, 18249], [13, 16, 18308, 18249], [42445, 16, 20960, 73941], [8752, 5, 21795, 74242], [1, 0, 16, 1], [74241, 16, 74240, 17], [49517, 16, 24496, 73941], [45697, 16, 68552, 129]], 'adelic_image': '74256.192.1.?', 'conductor': 4641, 'lmfdb_label': '4641.b1', 'prime': 0}
  • id: 22965
    {'conductor': 4641, 'elladic_image': '8.24.0.55', 'lmfdb_label': '4641.b1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 167505
    {'lmfdb_iso': '4641.b', 'p': 5, 'prec': 20, 'unit': 5893069535568, 'val': 1}
  • id: 167498
    {'lmfdb_iso': '4641.b', 'p': 11, 'prec': 20, 'unit': 31684978466222070832, 'val': 1}
  • id: 167499
    {'lmfdb_iso': '4641.b', 'p': 19, 'prec': 20, 'unit': 1497373852278408256294486, 'val': 1}
  • id: 167496
    {'lmfdb_iso': '4641.b', 'p': 29, 'prec': 20, 'unit': 955339050584004864531485424, 'val': 1}
  • id: 167492
    {'lmfdb_iso': '4641.b', 'p': 37, 'prec': 20, 'unit': 343252502062559215438596869106, 'val': 1}
  • id: 167494
    {'lmfdb_iso': '4641.b', 'p': 41, 'prec': 20, 'unit': 1318510442316643151737191284550, 'val': 1}
  • id: 167495
    {'lmfdb_iso': '4641.b', 'p': 43, 'prec': 20, 'unit': 399302119955548343751186008388, 'val': 1}
  • id: 167500
    {'lmfdb_iso': '4641.b', 'p': 53, 'prec': 20, 'unit': 354317515748985575964494473446755, 'val': 1}
  • id: 167503
    {'lmfdb_iso': '4641.b', 'p': 59, 'prec': 20, 'unit': 1162894978874827707627153852540941, 'val': 1}
  • id: 167504
    {'lmfdb_iso': '4641.b', 'p': 61, 'prec': 20, 'unit': 3777818018616859687635280546864832, 'val': 1}
  • id: 167491
    {'lmfdb_iso': '4641.b', 'p': 67, 'prec': 20, 'unit': 6302030071922649309149682076820965, 'val': 1}
  • id: 167493
    {'lmfdb_iso': '4641.b', 'p': 71, 'prec': 20, 'unit': 68144843787237120480316132895122050, 'val': 1}
  • id: 167501
    {'lmfdb_iso': '4641.b', 'p': 73, 'prec': 20, 'unit': 51752538139684912321407906959865258, 'val': 1}
  • id: 167497
    {'lmfdb_iso': '4641.b', 'p': 79, 'prec': 20, 'unit': 240368930714320174578051852431596649, 'val': 1}
  • id: 167490
    {'lmfdb_iso': '4641.b', 'p': 83, 'prec': 20, 'unit': 2072904635064481719793635212365960218, 'val': 1}
  • id: 167502
    {'lmfdb_iso': '4641.b', 'p': 89, 'prec': 20, 'unit': 2525326607833271172619475136088146857, 'val': 1}
  • id: 167489
    {'lmfdb_iso': '4641.b', 'p': 97, 'prec': 20, 'unit': 44049906238341634423222577345964474894, 'val': 1}