Elliptic curve data - 28224.eu2

Formats: - HTML - YAML - JSON - 2025-10-29T09:53:20.468394

• 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': '28224cb', 'Clabel': '28224cb6', 'Cnumber': 6, 'abc_quality': 1.0530860389430399, 'absD': 20996892513356009177088, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 336, 'ainvs': [0, 0, 0, -25797324, -49948258192], 'analytic_rank': 1, 'bad_primes': [2, 3, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 28224, 'degree': 2359296, 'elladic_images': ['8.48.0.217'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.0976567733993226259262342876', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 124, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [84448510979617, 933897762], 'lmfdb_iso': '28224.eu', 'lmfdb_label': '28224.eu2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -914, -10915], 'min_quad_twist_disc': 168, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.48.0.p.1', '48.96.0-8.p.1.2', '84.12.0.?', '112.96.1.?', '168.96.0.?', '336.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '23.518639200274887357153984630', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 441], [3, 8, 3136], [7, 32, 576]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.53567478369769316355008711523', 'prec': 103}, 'szpiro_ratio': 6.129136275737966, '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, 2, 0, 0, 0, 0, 0, -4, 0, 6, 0, 0, 0, 2, 0, -4, 0], 'aplist': [0, 0, 2, 0, -4, 6, 2, -4, -8, -2, 0, 10, -6, 4, 0, 6, -4, 6, -4, -8, -10, 0, 4, -6, 14], 'class_deg': 8, 'class_size': 6, 'conductor': 28224, 'isogeny_matrix': [[1, 8, 4, 2, 4, 8], [8, 1, 2, 4, 8, 4], [4, 2, 1, 2, 4, 2], [2, 4, 2, 1, 2, 4], [4, 8, 4, 2, 1, 8], [8, 4, 2, 4, 8, 1]], 'lmfdb_iso': '28224.eu', 'trace_hash': 1208300251228237092}
• 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': '0.0020389637888869480583102523676', 'prec': 110}, 'conductor': 28224, 'gens': [[-135333239576, 5566361600708532, 6985]], 'heights': [{'__RealLiteral__': 0, 'data': '23.518639200274887357153984630', 'prec': 100}], 'lmfdb_label': '28224.eu2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.067034148163624286363867978577', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.3062077790321959807082328668481433230', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-3164, 0, 1]], 'xcoord_integral_points': [-3164]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': 'a', '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [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': '28224.eu2'}
• ec_torsion_growth •

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

  
  
  • id: 1413311
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '28224.eu2', 'torsion': [2, 2]}
  • id: 1413312
    {'degree': 2, 'field': [21, 0, 1], 'lmfdb_label': '28224.eu2', 'torsion': [4]}
  • id: 1413313
    {'degree': 2, 'field': [42, 0, 1], 'lmfdb_label': '28224.eu2', 'torsion': [8]}
  • id: 1413314
    {'degree': 4, 'field': [121, 0, 20, 0, 1], 'lmfdb_label': '28224.eu2', 'torsion': [2, 8]}
  • id: 1413318
    {'degree': 8, 'field': [-9408, 0, -840, 0, 252, 0, -14, 0, 1], 'lmfdb_label': '28224.eu2', 'torsion': [6]}
  • id: 1413317
    {'degree': 8, 'field': [186, 72, 4, -88, 18, -8, 12, -4, 1], 'lmfdb_label': '28224.eu2', 'torsion': [16]}
  • id: 1413315
    {'degree': 8, 'field': [487, 628, -482, -272, 87, 56, -14, -4, 1], 'lmfdb_label': '28224.eu2', 'torsion': [2, 4]}
  • id: 1413316
    {'degree': 8, 'field': [2601, 0, 636, 0, 148, 0, -4, 0, 1], 'lmfdb_label': '28224.eu2', 'torsion': [8]}
  • id: 1413322
    {'degree': 16, 'field': [1, 0, -16, 0, 218, 0, -576, 0, 1187, 0, -576, 0, 218, 0, -16, 0, 1], 'lmfdb_label': '28224.eu2', 'torsion': [2, 16]}
  • id: 1413320
    {'degree': 16, 'field': [4, 0, 0, 0, 0, 0, 0, 0, -1054, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '28224.eu2', 'torsion': [2, 8]}
  • id: 1413321
    {'degree': 16, 'field': [16, 0, -128, 0, 1808, 0, -1200, 0, 833, 0, -240, 0, 68, 0, -8, 0, 1], 'lmfdb_label': '28224.eu2', 'torsion': [2, 16]}
  • id: 1413323
    {'degree': 16, 'field': [1296, 0, -5040, 0, -15084, 0, -11016, 0, 4764, 0, -2148, 0, 324, 0, -26, 0, 1], 'lmfdb_label': '28224.eu2', 'torsion': [2, 6]}
  • id: 1413319
    {'degree': 16, 'field': [99817, 132392, 34384, -210616, -155584, 192056, 111480, -100912, -30367, 27640, 3228, -3944, -10, 280, -20, -8, 1], 'lmfdb_label': '28224.eu2', 'torsion': [4, 8]}
  • id: 1413324
    {'degree': 16, 'field': [343396, 0, -247060, 0, 72373, 0, 392, 0, -3353, 0, 812, 0, 7, 0, -16, 0, 1], 'lmfdb_label': '28224.eu2', 'torsion': [12]}
  • id: 1413325
    {'degree': 16, 'field': [1750329, 0, 15225084, 0, -6703200, 0, 1545264, 0, -129654, 0, 7140, 0, -252, 0, 0, 0, 1], 'lmfdb_label': '28224.eu2', 'torsion': [24]}
• 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: 653705
    {'conductor': 28224, 'conductor_valuation': 6, 'discriminant_valuation': 19, 'j_denominator_valuation': 1, 'kodaira_symbol': -13, 'lmfdb_label': '28224.eu2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 653706
    {'conductor': 28224, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '28224.eu2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 653707
    {'conductor': 28224, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '28224.eu2', 'prime': 7, 'reduction_type': 0, '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: 1852505
    {'adelic_gens': [[5, 4, 332, 333], [95, 96, 312, 95], [1, 16, 0, 1], [15, 2, 238, 323], [20, 135, 165, 278], [321, 16, 320, 17], [223, 0, 0, 335], [55, 240, 318, 217], [1, 0, 16, 1]], 'adelic_image': '336.192.1.?', 'conductor': 28224, 'lmfdb_label': '28224.eu2', 'prime': 0}
  • id: 127612
    {'conductor': 28224, 'elladic_image': '8.48.0.217', 'lmfdb_label': '28224.eu2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 1356082
    {'lmfdb_iso': '28224.eu', 'p': 5, 'prec': 20, 'unit': 3555958749583, 'val': 1}
  • id: 1356088
    {'lmfdb_iso': '28224.eu', 'p': 11, 'prec': 20, 'unit': 31891187675804944028, 'val': 1}
  • id: 1356086
    {'lmfdb_iso': '28224.eu', 'p': 13, 'prec': 20, 'unit': 114667773358295038372, 'val': 1}
  • id: 1356089
    {'lmfdb_iso': '28224.eu', 'p': 17, 'prec': 20, 'unit': 34062061826795175092179, 'val': 1}
  • id: 1356090
    {'lmfdb_iso': '28224.eu', 'p': 19, 'prec': 20, 'unit': 514291562365820666653850, 'val': 1}
  • id: 1356093
    {'lmfdb_iso': '28224.eu', 'p': 23, 'prec': 20, 'unit': 10970189071260202736181426, 'val': 1}
  • id: 1356087
    {'lmfdb_iso': '28224.eu', 'p': 29, 'prec': 20, 'unit': 4527523409542704748381063921, 'val': 1}
  • id: 1356097
    {'lmfdb_iso': '28224.eu', 'p': 37, 'prec': 20, 'unit': 373652691313286217365766465834, 'val': 1}
  • id: 1356084
    {'lmfdb_iso': '28224.eu', 'p': 41, 'prec': 20, 'unit': 1628025956161215851346377509339, 'val': 1}
  • id: 1356085
    {'lmfdb_iso': '28224.eu', 'p': 43, 'prec': 20, 'unit': 3336370655679951218971812750566, 'val': 1}
  • id: 1356091
    {'lmfdb_iso': '28224.eu', 'p': 53, 'prec': 20, 'unit': 504456698300726992266923246889238, 'val': 1}
  • id: 1356095
    {'lmfdb_iso': '28224.eu', 'p': 59, 'prec': 20, 'unit': 3842807720305305287370081480448489, 'val': 1}
  • id: 1356096
    {'lmfdb_iso': '28224.eu', 'p': 61, 'prec': 20, 'unit': 1857008668385617310077516192602815, 'val': 1}
  • id: 1356081
    {'lmfdb_iso': '28224.eu', 'p': 67, 'prec': 20, 'unit': 25437272197391476183205948033760660, 'val': 1}
  • id: 1356083
    {'lmfdb_iso': '28224.eu', 'p': 71, 'prec': 20, 'unit': 93882499675399288944557660503914904, 'val': 1}
  • id: 1356092
    {'lmfdb_iso': '28224.eu', 'p': 73, 'prec': 20, 'unit': 65052397480797627838090008720387855, 'val': 1}
  • id: 1356080
    {'lmfdb_iso': '28224.eu', 'p': 83, 'prec': 20, 'unit': 168460987737094189380642989561005612, 'val': 1}
  • id: 1356094
    {'lmfdb_iso': '28224.eu', 'p': 89, 'prec': 20, 'unit': 8958479063602852767931480554348537958, 'val': 1}
  • id: 1356079
    {'lmfdb_iso': '28224.eu', 'p': 97, 'prec': 20, 'unit': 33205805202342854642565091616719151594, 'val': 1}