Elliptic curve data - 28314.r3

Formats: - HTML - YAML - JSON - 2025-10-04T03:28:21.454186

• 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': '28314p', 'Clabel': '28314p2', 'Cnumber': 2, 'abc_quality': 1.033360901289125, 'absD': 325846357257754702512, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 1716, 'ainvs': [1, -1, 0, -1960767, 602589213], 'analytic_rank': 1, 'bad_primes': [2, 3, 11, 13], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 28314, 'degree': 1105920, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.6347723551414694602215012671', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 17, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [645532578015625, 252306960048], 'lmfdb_iso': '28314.r', 'lmfdb_label': '28314.r3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -1801, 16604], 'min_quad_twist_disc': 33, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '12.24.0.h.1', '33.8.0-3.a.1.1', '66.24.0-6.a.1.1', '132.48.0.?', '156.48.0.?', '572.6.0.?', '1716.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 6, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.9071409704625732022342705730', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 1089], [3, 2, 242], [11, 72, 234], [13, 14, 2178]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.88651857440822934249290685966', 'prec': 103}, 'szpiro_ratio': 5.373089669188137, '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, 0, 1, 0, 0, 4, -1, 0, 0, 0, 0, -1, -4, 0, 1, 0, 0, 4, 0], 'aplist': [-1, 0, 0, 4, 0, -1, 0, 4, 0, 0, -10, 2, -6, 10, 0, -6, 0, -2, 2, -12, 10, 10, -12, -12, -10], 'class_deg': 6, 'class_size': 4, 'conductor': 28314, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '28314.r', 'trace_hash': 2129901456606389376}
• 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': '0.0051459529392200063148326461635', 'prec': 110}, 'conductor': 28314, 'gens': [[1323, 17307, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.9071409704625732022342705730', 'prec': 100}], 'lmfdb_label': '28314.r3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.15604355758594315486618175992', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.7615529895822088777105220925351397099', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[1299, -1299, 2]], 'xcoord_integral_points': [-1323, 1323, 5727]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '3': 'a', '5': [3, 3, 0], '7': [1, 0], '11': 'a', '13': [1, 0], '17': [1, 1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [3, 1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '28314.r3'}
• ec_torsion_growth •

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

  
  
  • id: 1419033
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '28314.r3', 'torsion': [6]}
  • id: 1419032
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '28314.r3', 'torsion': [2, 2]}
  • id: 1419035
    {'degree': 4, 'field': [4, 0, -7, 0, 1], 'lmfdb_label': '28314.r3', 'torsion': [2, 6]}
  • id: 1419034
    {'degree': 4, 'field': [108, 0, 17, 0, 1], 'lmfdb_label': '28314.r3', 'torsion': [4]}
  • id: 1419036
    {'degree': 6, 'field': [15, -6, 23, -4, 9, -2, 1], 'lmfdb_label': '28314.r3', 'torsion': [6]}
  • id: 1419039
    {'degree': 8, 'field': [144, -312, 196, -62, 34, -5, 11, -3, 1], 'lmfdb_label': '28314.r3', 'torsion': [12]}
  • id: 1419038
    {'degree': 8, 'field': [1089, 0, -1584, 0, -21, 0, -24, 0, 1], 'lmfdb_label': '28314.r3', 'torsion': [2, 4]}
  • id: 1419037
    {'degree': 8, 'field': [10464, -2592, 2950, -730, 401, -46, 20, -4, 1], 'lmfdb_label': '28314.r3', 'torsion': [2, 4]}
  • id: 1419041
    {'degree': 12, 'field': [9, 0, 93, 0, 262, 0, -71, 0, -6, 0, 1, 0, 1], 'lmfdb_label': '28314.r3', 'torsion': [2, 6]}
  • id: 1419040
    {'degree': 12, 'field': [36, -36, -12, -12, 52, -18, 23, -39, 18, -9, 8, -3, 1], 'lmfdb_label': '28314.r3', 'torsion': [3, 6]}
  • id: 1419044
    {'degree': 16, 'field': [709, 5696, 6400, -11020, -16149, -1120, -4238, -6024, 3640, 3096, -76, -156, -157, -8, 2, 0, 1], 'lmfdb_label': '28314.r3', 'torsion': [2, 12]}
  • id: 1419043
    {'degree': 16, 'field': [20736, 0, 25488, 0, 59076, 0, 6828, 0, -1175, 0, -168, 0, 50, 0, 12, 0, 1], 'lmfdb_label': '28314.r3', 'torsion': [2, 12]}
  • id: 1419042
    {'degree': 16, 'field': [734843664, 0, -526117680, 0, 120430971, 0, -9701703, 0, 471759, 0, -25278, 0, 1477, 0, -55, 0, 1], 'lmfdb_label': '28314.r3', 'torsion': [8]}
  • id: 1419045
    {'degree': 18, 'field': [-1377778142996, -588539824380, 139495345452, 72882015594, -6655633254, -288344448, 81950529, -20555145, -28625310, -4703429, 2666043, 97686, -82428, -5796, 1890, 492, -63, -9, 1], 'lmfdb_label': '28314.r3', 'torsion': [18]}
• 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: 656303
    {'conductor': 28314, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '28314.r3', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 656304
    {'conductor': 28314, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '28314.r3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 656305
    {'conductor': 28314, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '28314.r3', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 656306
    {'conductor': 28314, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '28314.r3', 'prime': 13, '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: 1853204
    {'adelic_gens': [[1705, 12, 1704, 13], [779, 1704, 1242, 1643], [1002, 1585, 1001, 1574], [1, 0, 12, 1], [925, 12, 402, 73], [1, 6, 6, 37], [1, 12, 0, 1], [1138, 1705, 1155, 20], [11, 2, 1666, 1707]], 'adelic_image': '1716.96.1.?', 'conductor': 28314, 'lmfdb_label': '28314.r3', 'prime': 0}
  • id: 128082
    {'conductor': 28314, 'elladic_image': '2.3.0.1', 'lmfdb_label': '28314.r3', 'modell_image': '2B', 'prime': 2}
  • id: 128083
    {'conductor': 28314, 'elladic_image': '3.4.0.1', 'lmfdb_label': '28314.r3', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 1361755
    {'lmfdb_iso': '28314.r', 'p': 7, 'prec': 20, 'unit': 616337492149154, 'val': 1}
  • id: 1361751
    {'lmfdb_iso': '28314.r', 'p': 19, 'prec': 20, 'unit': 585417085043964925862070, 'val': 1}
  • id: 1361765
    {'lmfdb_iso': '28314.r', 'p': 31, 'prec': 20, 'unit': 21052584949005094926411911932, 'val': 1}
  • id: 1361754
    {'lmfdb_iso': '28314.r', 'p': 37, 'prec': 20, 'unit': 392995503777710593333535167548, 'val': 1}
  • id: 1361756
    {'lmfdb_iso': '28314.r', 'p': 41, 'prec': 20, 'unit': 4390606895916949487423861353557, 'val': 1}
  • id: 1361757
    {'lmfdb_iso': '28314.r', 'p': 43, 'prec': 20, 'unit': 483178385948520122688500145760, 'val': 1}
  • id: 1361760
    {'lmfdb_iso': '28314.r', 'p': 53, 'prec': 20, 'unit': 80453885946392658310549329243427, 'val': 1}
  • id: 1361764
    {'lmfdb_iso': '28314.r', 'p': 61, 'prec': 20, 'unit': 3817701864318841372986273813675607, 'val': 1}
  • id: 1361753
    {'lmfdb_iso': '28314.r', 'p': 67, 'prec': 20, 'unit': 23437069610943577882949832756081023, 'val': 1}
  • id: 1361763
    {'lmfdb_iso': '28314.r', 'p': 71, 'prec': 20, 'unit': 90739596582483630469886411757481423, 'val': 1}
  • id: 1361761
    {'lmfdb_iso': '28314.r', 'p': 73, 'prec': 20, 'unit': 151918449576166499218924518063102955, 'val': 1}
  • id: 1361758
    {'lmfdb_iso': '28314.r', 'p': 79, 'prec': 20, 'unit': 896921904371563833329588993467593640, 'val': 1}
  • id: 1361759
    {'lmfdb_iso': '28314.r', 'p': 83, 'prec': 20, 'unit': 2747597559331021846650596177709854407, 'val': 1}
  • id: 1361762
    {'lmfdb_iso': '28314.r', 'p': 89, 'prec': 20, 'unit': 6126812638541700839467639567795291340, 'val': 1}
  • id: 1361752
    {'lmfdb_iso': '28314.r', 'p': 97, 'prec': 20, 'unit': 35009059664915613518122007344752975741, 'val': 1}