Elliptic curve data - 8325.j1

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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': '8325p', 'Clabel': '8325p1', 'Cnumber': 1, 'abc_quality': 1.2558893603224681, 'absD': 19766541796875, 'adelic_genus': 0, 'adelic_index': 8, 'adelic_level': 12, 'ainvs': [0, 0, 1, 6750, 13906], 'analytic_rank': 1, 'bad_primes': [3, 5, 37], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 8325, 'degree': 15360, 'elladic_images': ['4.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.2406961004962983985838527281', 'prec': 97}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 9, 'isogeny_degrees': [1], 'jinv': [3224862720, 1874161], 'lmfdb_iso': '8325.j', 'lmfdb_label': '8325.j1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 1, 270, 111], 'min_quad_twist_disc': 5, 'modell_images': [], 'modm_images': ['4.4.0.a.1', '6.2.0.a.1', '12.8.0.c.1'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.28341294112056244811686823310', 'prec': 97}, 'semistable': False, 'serre_invariants': [[2, 2, 75], [3, 6, 925], [5, 14, 333], [37, 38, 225]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.10691557996012927399879813662', 'prec': 97}, 'szpiro_ratio': 4.2168404955719465, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, -2, 0, 0, -3, 0, 0, 0, -4, 0, 1, 0, 0, 4, 4, 0, -5, 0], 'aplist': [0, 0, 0, -3, -4, 1, 4, -5, -4, 8, 5, 1, 8, 9, -12, 0, -4, -1, 5, 4, 6, 4, 16, -16, 1], 'class_deg': 1, 'class_size': 1, 'conductor': 8325, 'isogeny_matrix': [[1]], 'lmfdb_iso': '8325.j', 'trace_hash': 772681315639180293}
• 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': '0.083626719309302523794584362536', 'prec': 97}, 'conductor': 8325, 'gens': [[250, 4162, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.28341294112056244811686823310', 'prec': 97}], 'lmfdb_label': '8325.j1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.41249176922507245085256242176', 'prec': 97}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 97}, 'special_value': {'__RealLiteral__': 0, 'data': '2.8057321320984502022408557253754324688', 'prec': 127}, 'tamagawa_product': 24, 'torsion_generators': [], 'xcoord_integral_points': [250]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 3, 0], '3': 'a', '5': 'a', '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [2, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '8325.j1'}
• ec_torsion_growth •

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

  
  
  • id: 435191
    {'degree': 3, 'field': [-3, -3, -1, 1], 'lmfdb_label': '8325.j1', 'torsion': [2]}
  • id: 435192
    {'degree': 6, 'field': [3, 3, -2, -3, 4, -3, 1], 'lmfdb_label': '8325.j1', 'torsion': [2, 2]}
  • id: 435193
    {'degree': 8, 'field': [192, -42, 237, -87, 45, -6, -19, -1, 1], 'lmfdb_label': '8325.j1', 'torsion': [3]}
  • id: 435194
    {'degree': 12, 'field': [-11, 8, 36, -38, -53, 156, -176, 108, -27, -16, 16, -6, 1], 'lmfdb_label': '8325.j1', 'torsion': [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: 173185
    {'conductor': 8325, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '8325.j1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 173186
    {'conductor': 8325, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '8325.j1', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 173187
    {'conductor': 8325, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '8325.j1', 'prime': 37, 'reduction_type': 1, '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: 1719010
    {'adelic_gens': [[9, 4, 8, 5], [4, 9, 5, 1], [2, 1, 5, 3], [8, 3, 1, 4], [1, 4, 0, 1], [1, 0, 4, 1]], 'adelic_image': '12.8.0.?', 'conductor': 8325, 'lmfdb_label': '8325.j1', 'prime': 0}
  • id: 40757
    {'conductor': 8325, 'elladic_image': '4.4.0.1', 'lmfdb_label': '8325.j1', 'modell_image': '2G', 'prime': 2}
• ec_padic •

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

  
  
  • id: 344240
    {'lmfdb_iso': '8325.j', 'p': 7, 'prec': 20, 'unit': 1625248833054967, 'val': 1}
  • id: 344239
    {'lmfdb_iso': '8325.j', 'p': 11, 'prec': 20, 'unit': 7775673006653838818, 'val': 1}
  • id: 344244
    {'lmfdb_iso': '8325.j', 'p': 13, 'prec': 20, 'unit': 5954325165785466322147, 'val': -1}
  • id: 344246
    {'lmfdb_iso': '8325.j', 'p': 17, 'prec': 20, 'unit': 77176376124562245213852, 'val': 1}
  • id: 344247
    {'lmfdb_iso': '8325.j', 'p': 19, 'prec': 20, 'unit': 1824469834657039473681062, 'val': 1}
  • id: 344250
    {'lmfdb_iso': '8325.j', 'p': 23, 'prec': 20, 'unit': 24506176072134749944393249, 'val': 1}
  • id: 344243
    {'lmfdb_iso': '8325.j', 'p': 29, 'prec': 20, 'unit': 230045355804508932473532620, 'val': 1}
  • id: 344256
    {'lmfdb_iso': '8325.j', 'p': 31, 'prec': 20, 'unit': 10936290714987654516157722476, 'val': 1}
  • id: 344241
    {'lmfdb_iso': '8325.j', 'p': 41, 'prec': 20, 'unit': 1350663480128923705755527756408, 'val': 1}
  • id: 344242
    {'lmfdb_iso': '8325.j', 'p': 43, 'prec': 20, 'unit': 2315854524607035900558329772680, 'val': 1}
  • id: 344253
    {'lmfdb_iso': '8325.j', 'p': 47, 'prec': 20, 'unit': 34703459507671372912412918556692, 'val': 1}
  • id: 344248
    {'lmfdb_iso': '8325.j', 'p': 59, 'prec': 20, 'unit': 1390808482402642872263134645219006, 'val': 1}
  • id: 344254
    {'lmfdb_iso': '8325.j', 'p': 61, 'prec': 20, 'unit': 8276925744577300263229225132488268, 'val': 1}
  • id: 344238
    {'lmfdb_iso': '8325.j', 'p': 67, 'prec': 20, 'unit': 32827630730328483942380950056121108, 'val': 1}
  • id: 344252
    {'lmfdb_iso': '8325.j', 'p': 71, 'prec': 20, 'unit': 96587581391281091773594820314068463, 'val': 1}
  • id: 344249
    {'lmfdb_iso': '8325.j', 'p': 73, 'prec': 20, 'unit': 76789285006539084475461194769391331, 'val': 1}
  • id: 344245
    {'lmfdb_iso': '8325.j', 'p': 79, 'prec': 20, 'unit': 938115804341730169562872027052721592, 'val': 1}
  • id: 344255
    {'lmfdb_iso': '8325.j', 'p': 83, 'prec': 20, 'unit': 408169485739697911747830563616820099, 'val': 1}
  • id: 344251
    {'lmfdb_iso': '8325.j', 'p': 89, 'prec': 20, 'unit': 2356947195065251141171905066066098950, 'val': 1}
  • id: 344237
    {'lmfdb_iso': '8325.j', 'p': 97, 'prec': 20, 'unit': 3017407758034161161279560437197124131330, 'val': -1}