Elliptic curve data - 4200.t1

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '4200x', 'Clabel': '4200x4', 'Cnumber': 4, 'abc_quality': 1.0353416362958598, 'absD': 3024000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 840, 'ainvs': [0, 1, 0, -100808, 12285888], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 4200, 'degree': 12288, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3329079305174562145145269288', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'intrinsic_torsion': 2, 'iso_nlabel': 19, 'isogeny_degrees': [1, 2, 4], 'jinv': [7080974546692, 189], 'lmfdb_iso': '4200.t', 'lmfdb_label': '4200.t1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -4032, 99900], 'min_quad_twist_disc': 5, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0.z.1', '40.12.0-4.c.1.5', '42.6.0.a.1', '56.12.0.ba.1', '60.12.0-4.c.1.1', '84.12.0.?', '120.24.0.?', '140.12.0.?', '168.24.0.?', '280.24.0.?', '420.24.0.?', '840.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 9, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.66946366791822600182013260057', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 525], [3, 4, 1400], [5, 14, 168], [7, 8, 600]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.049433676166215063966879505695', 'prec': 110}, 'szpiro_ratio': 5.534869783615108, '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, -1, 0, 1, 0, 0, 0, -6, 0, 0, 0, 2, 0, 4, 0], 'aplist': [0, 1, 0, -1, 0, -6, 2, 4, 4, -10, -8, -6, -2, 4, -8, 10, 12, -2, -12, -12, 14, -8, -12, -2, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 4200, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '4200.t', 'trace_hash': 2005041414374307551}
• 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': '0.069542593290049961061250793833', 'prec': 107}, 'conductor': 4200, 'gens': [[184, 24, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.66946366791822600182013260057', 'prec': 103}], 'lmfdb_label': '4200.t1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.0382105228541974212355723913', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.1702653482076212564618543849546579364', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [[183, 0, 1]], 'xcoord_integral_points': [183, 184, 208, 283, 1272]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [4, 0], '5': 'a', '7': [1, 0], '11': [1, 1, 0], '13': [1, 0], '17': [1, 0], '19': [5, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '4200.t1'}
• ec_torsion_growth •

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

  
  
  • id: 219667
    {'degree': 2, 'field': [-35, 0, 1], 'lmfdb_label': '4200.t1', 'torsion': [4]}
  • id: 219668
    {'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '4200.t1', 'torsion': [4]}
  • id: 219666
    {'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '4200.t1', 'torsion': [2, 2]}
  • id: 219669
    {'degree': 4, 'field': [25, 0, -25, 0, 1], 'lmfdb_label': '4200.t1', 'torsion': [2, 4]}
  • id: 219671
    {'degree': 8, 'field': [-139, 592, -334, -484, 163, 92, -26, -4, 1], 'lmfdb_label': '4200.t1', 'torsion': [8]}
  • id: 219673
    {'degree': 8, 'field': [-9, 36, -102, -138, 6, -14, -6, 0, 1], 'lmfdb_label': '4200.t1', 'torsion': [6]}
  • id: 219670
    {'degree': 8, 'field': [5884, -3952, 3880, 128, -23, -52, 22, -4, 1], 'lmfdb_label': '4200.t1', 'torsion': [2, 4]}
  • id: 219672
    {'degree': 8, 'field': [35721, 0, -4536, 0, 282, 0, -24, 0, 1], 'lmfdb_label': '4200.t1', 'torsion': [8]}
  • id: 219678
    {'degree': 16, 'field': [-16299, -10476, 63990, 22476, -57176, 10236, -10146, -3168, -7230, 252, -2310, -156, -144, -60, -6, 0, 1], 'lmfdb_label': '4200.t1', 'torsion': [12]}
  • id: 219677
    {'degree': 16, 'field': [-101, 28, -1254, -122, -3674, -11664, 14092, -7772, 7569, -1766, 1714, -264, 160, -56, 18, -8, 1], 'lmfdb_label': '4200.t1', 'torsion': [2, 6]}
  • id: 219675
    {'degree': 16, 'field': [324, 3456, 6120, -13560, -25682, 29892, 31128, -34910, -11239, 17626, -670, -3158, 516, 210, -46, -4, 1], 'lmfdb_label': '4200.t1', 'torsion': [2, 8]}
  • id: 219679
    {'degree': 16, 'field': [39204, -178200, 317952, -331344, 251316, -158040, 78348, -26040, 1636, 5060, -3728, 1264, -244, 4, 16, -4, 1], 'lmfdb_label': '4200.t1', 'torsion': [12]}
  • id: 219676
    {'degree': 16, 'field': [531441, 0, -236196, 0, 41553, 0, -45684, 0, 10728, 0, 1692, 0, 57, 0, 12, 0, 1], 'lmfdb_label': '4200.t1', 'torsion': [2, 8]}
  • id: 219674
    {'degree': 16, 'field': [1110916, 0, 1563464, 0, 1065208, 0, 167636, 0, -11267, 0, -2128, 0, 442, 0, -28, 0, 1], 'lmfdb_label': '4200.t1', 'torsion': [4, 4]}
• 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: 79224
    {'conductor': 4200, 'conductor_valuation': 3, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '4200.t1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 79225
    {'conductor': 4200, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '4200.t1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 79226
    {'conductor': 4200, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '4200.t1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 79227
    {'conductor': 4200, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '4200.t1', 'prime': 7, '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: 1691354
    {'adelic_gens': [[571, 570, 370, 451], [833, 8, 832, 9], [1, 0, 8, 1], [1, 8, 0, 1], [503, 0, 0, 839], [1, 4, 4, 17], [116, 505, 415, 6], [7, 6, 834, 835], [416, 675, 365, 506], [571, 400, 170, 741]], 'adelic_image': '840.48.0.?', 'conductor': 4200, 'lmfdb_label': '4200.t1', 'prime': 0}
  • id: 20921
    {'conductor': 4200, 'elladic_image': '4.6.0.1', 'lmfdb_label': '4200.t1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 148717
    {'lmfdb_iso': '4200.t', 'p': 13, 'prec': 20, 'unit': 450178610378378761274, 'val': 1}
  • id: 148719
    {'lmfdb_iso': '4200.t', 'p': 17, 'prec': 20, 'unit': 69509091304041105175340, 'val': 1}
  • id: 148720
    {'lmfdb_iso': '4200.t', 'p': 19, 'prec': 20, 'unit': 59620851717511801503202, 'val': 2}
  • id: 148724
    {'lmfdb_iso': '4200.t', 'p': 23, 'prec': 20, 'unit': 6647717463321418344059926, 'val': 1}
  • id: 148716
    {'lmfdb_iso': '4200.t', 'p': 29, 'prec': 20, 'unit': 671863893667964498477797356, 'val': 1}
  • id: 148728
    {'lmfdb_iso': '4200.t', 'p': 31, 'prec': 20, 'unit': 9508577156725047939890103619, 'val': 1}
  • id: 148712
    {'lmfdb_iso': '4200.t', 'p': 37, 'prec': 20, 'unit': 295944754497621351205263003188, 'val': 1}
  • id: 148714
    {'lmfdb_iso': '4200.t', 'p': 41, 'prec': 20, 'unit': 805842657113846992341357637397, 'val': 1}
  • id: 148715
    {'lmfdb_iso': '4200.t', 'p': 43, 'prec': 20, 'unit': 1575107106494969954226050243500, 'val': 1}
  • id: 148726
    {'lmfdb_iso': '4200.t', 'p': 47, 'prec': 20, 'unit': 23068552425067642887719423556666, 'val': 1}
  • id: 148721
    {'lmfdb_iso': '4200.t', 'p': 53, 'prec': 20, 'unit': 74038635200603675289134748000737, 'val': 1}
  • id: 148722
    {'lmfdb_iso': '4200.t', 'p': 59, 'prec': 20, 'unit': 2482300205415601866511627355323516, 'val': 1}
  • id: 148727
    {'lmfdb_iso': '4200.t', 'p': 61, 'prec': 20, 'unit': 7235975011760811978382590784809101, 'val': 1}
  • id: 148711
    {'lmfdb_iso': '4200.t', 'p': 67, 'prec': 20, 'unit': 21354762739564544123703191962100684, 'val': 1}
  • id: 148713
    {'lmfdb_iso': '4200.t', 'p': 71, 'prec': 20, 'unit': 142167290597643473720295108638428003, 'val': 1}
  • id: 148723
    {'lmfdb_iso': '4200.t', 'p': 73, 'prec': 20, 'unit': 196404932897610015779437124257618972, 'val': 1}
  • id: 148718
    {'lmfdb_iso': '4200.t', 'p': 79, 'prec': 20, 'unit': 983962429374688258765387811411788412, 'val': 1}
  • id: 148710
    {'lmfdb_iso': '4200.t', 'p': 83, 'prec': 20, 'unit': 2199260868816742548283002304460740694, 'val': 1}
  • id: 148725
    {'lmfdb_iso': '4200.t', 'p': 89, 'prec': 20, 'unit': 7907100477751664152137671541376424208, 'val': 1}
  • id: 148709
    {'lmfdb_iso': '4200.t', 'p': 97, 'prec': 20, 'unit': 25525354382548634939615908790505361453, 'val': 1}