Elliptic curve data - 4200.t4

Formats: - HTML - YAML - JSON - 2024-06-08T15:51:22.349493

• 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': '4200x', 'Clabel': '4200x1', 'Cnumber': 1, 'abc_quality': 1.0797970787420708, 'absD': 16206750000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 840, 'ainvs': [0, 1, 0, -183, 6138], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 4200, 'degree': 3072, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.63976074995751090509729480732', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 19, 'isogeny_degrees': [1, 2, 4], 'jinv': [-2725888, 64827], 'lmfdb_iso': '4200.t', 'lmfdb_label': '4200.t4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -7, 52], 'min_quad_twist_disc': 5, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '6.6.0.a.1', '12.12.0.g.1', '20.12.0-4.c.1.2', '56.12.0.ba.1', '60.24.0-12.g.1.2', '168.24.0.?', '280.24.0.?', '840.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 7, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.66946366791822600182013260057', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.39600726644618771867549556645', 'prec': 107}, 'szpiro_ratio': 3.7142575787828385, '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': '0.27817037316019984424500317533', 'prec': 103}, 'conductor': 4200, 'gens': [[3, 75, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.66946366791822600182013260057', 'prec': 103}], 'lmfdb_label': '4200.t4', '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': [[-22, 0, 1]], 'xcoord_integral_points': [-22, -6, 3, 27]}
• 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.t4'}
• ec_torsion_growth •

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

  
  
  • id: 219631
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '4200.t4', 'torsion': [4]}
  • id: 219630
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '4200.t4', 'torsion': [2, 2]}
  • id: 219632
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '4200.t4', 'torsion': [4]}
  • id: 219633
    {'degree': 4, 'field': [1, 1, 2, -1, 1], 'lmfdb_label': '4200.t4', 'torsion': [2, 4]}
  • id: 219635
    {'degree': 8, 'field': [-19, -14, -22, 42, 51, -14, -16, 0, 1], 'lmfdb_label': '4200.t4', 'torsion': [8]}
  • id: 219637
    {'degree': 8, 'field': [-9, 36, -102, -138, 6, -14, -6, 0, 1], 'lmfdb_label': '4200.t4', 'torsion': [6]}
  • id: 219634
    {'degree': 8, 'field': [21, 102, 138, -6, -14, 10, -6, -2, 1], 'lmfdb_label': '4200.t4', 'torsion': [2, 4]}
  • id: 219636
    {'degree': 8, 'field': [144, 0, -36, 0, 57, 0, 3, 0, 1], 'lmfdb_label': '4200.t4', 'torsion': [8]}
  • id: 219638
    {'degree': 16, 'field': [1, -2, 2, -4, -22, 2, 48, 114, 163, 114, 48, 2, -22, -4, 2, -2, 1], 'lmfdb_label': '4200.t4', 'torsion': [4, 4]}
  • id: 219640
    {'degree': 16, 'field': [81, 0, 243, 0, 837, 0, -162, 0, 378, 0, 54, 0, 93, 0, -9, 0, 1], 'lmfdb_label': '4200.t4', 'torsion': [2, 8]}
  • id: 219641
    {'degree': 16, 'field': [81, 324, 378, 6156, 15426, -13770, 20268, 3900, -2499, 1704, 28, 54, 30, -28, 6, 0, 1], 'lmfdb_label': '4200.t4', 'torsion': [2, 6]}
  • id: 219642
    {'degree': 16, 'field': [144, 0, 720, 0, 1408, 0, 720, 0, -420, 0, -360, 0, -84, 0, 0, 0, 1], 'lmfdb_label': '4200.t4', 'torsion': [12]}
  • id: 219639
    {'degree': 16, 'field': [361, -266, -222, -1904, 2041, -770, 3298, -1750, 2856, -616, 968, -266, 205, -28, 16, 0, 1], 'lmfdb_label': '4200.t4', 'torsion': [2, 8]}
  • id: 219643
    {'degree': 16, 'field': [66049, 0, -5248, 0, -13268, 0, 940, 0, 902, 0, -8, 0, -20, 0, -4, 0, 1], 'lmfdb_label': '4200.t4', 'torsion': [12]}
• 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: 79212
    {'conductor': 4200, 'conductor_valuation': 3, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '4200.t4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 79213
    {'conductor': 4200, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '4200.t4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 79214
    {'conductor': 4200, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '4200.t4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 79215
    {'conductor': 4200, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '4200.t4', 'prime': 7, '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: 1691357
    {'adelic_gens': [[571, 570, 370, 451], [361, 360, 790, 31], [1, 0, 8, 1], [833, 8, 832, 9], [1, 8, 0, 1], [503, 0, 0, 839], [1, 4, 4, 17], [241, 680, 460, 201], [116, 505, 415, 6], [7, 6, 834, 835]], 'adelic_image': '840.48.0.?', 'conductor': 4200, 'lmfdb_label': '4200.t4', 'prime': 0}
  • id: 20924
    {'conductor': 4200, 'elladic_image': '4.6.0.1', 'lmfdb_label': '4200.t4', '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}