Elliptic curve data - 2574.u3

Formats: - HTML - YAML - JSON - 2024-11-01T00:04:16.468610

• 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': '2574x', 'Clabel': '2574x2', 'Cnumber': 2, 'abc_quality': 1.033360901289125, 'absD': 183931773874992, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 1716, 'ainvs': [1, -1, 1, -16205, -448315], 'analytic_rank': 1, 'bad_primes': [2, 3, 11, 13], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 2574, 'degree': 9216, 'elladic_images': ['2.3.0.1', '3.8.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4358247187422841881905294782', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 20, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [645532578015625, 252306960048], 'lmfdb_iso': '2574.u', 'lmfdb_label': '2574.u3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -1801, 16604], 'min_quad_twist_disc': -3, 'modell_images': ['2B', '3B.1.2'], 'modm_images': ['2.3.0.a.1', '3.8.0-3.a.1.1', '6.24.0-6.a.1.2', '12.48.0-12.h.1.5', '572.6.0.?', '1716.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 10, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.20568461723680442357928171822', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 9], [3, 2, 22], [11, 12, 234], [13, 14, 198]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.88651857440822934249290685974', 'prec': 103}, 'szpiro_ratio': 5.181669333312839, '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, 1, 0, 1, -4, 0, 1, 0, 0, -4, 0], 'aplist': [1, 0, 0, -4, 1, 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': 2574, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '2574.u', 'trace_hash': 1694823609741888679}
• 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': '0.056605482331420069463159107799', 'prec': 107}, 'conductor': 2574, 'gens': [[-39, 370, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.20568461723680442357928171822', 'prec': 103}], 'lmfdb_label': '2574.u3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.43749823068009232121298983373', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.3193594937222698374315044418812828502', 'prec': 130}, 'tamagawa_product': 192, 'torsion_generators': [[-117, 113, 2]], 'xcoord_integral_points': [-65, -39, 177, 351, 1365]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': 'a', '5': [1, 1, 0], '7': [1, 0], '11': [2, 0], '13': [2, 0], '17': [1, 1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '2574.u3'}
• ec_torsion_growth •

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

  
  
  • id: 133402
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '2574.u3', 'torsion': [2, 2]}
  • id: 133403
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '2574.u3', 'torsion': [6]}
  • id: 133404
    {'degree': 3, 'field': [13, -7, -1, 1], 'lmfdb_label': '2574.u3', 'torsion': [6]}
  • id: 133406
    {'degree': 4, 'field': [1, 0, -1, 0, 1], 'lmfdb_label': '2574.u3', 'torsion': [2, 6]}
  • id: 133405
    {'degree': 4, 'field': [48, 0, -7, 0, 1], 'lmfdb_label': '2574.u3', 'torsion': [4]}
  • id: 133408
    {'degree': 6, 'field': [13, -22, 37, -22, -1, 0, 1], 'lmfdb_label': '2574.u3', 'torsion': [2, 6]}
  • id: 133407
    {'degree': 6, 'field': [75, 0, -29, 0, 1, 0, 1], 'lmfdb_label': '2574.u3', 'torsion': [3, 6]}
  • id: 133409
    {'degree': 8, 'field': [-26, 124, -202, 148, -53, -28, 14, -4, 1], 'lmfdb_label': '2574.u3', 'torsion': [2, 4]}
  • id: 133410
    {'degree': 8, 'field': [1296, 0, 780, 0, 241, 0, -26, 0, 1], 'lmfdb_label': '2574.u3', 'torsion': [2, 4]}
  • id: 133411
    {'degree': 8, 'field': [2304, 0, -336, 0, 1, 0, -7, 0, 1], 'lmfdb_label': '2574.u3', 'torsion': [12]}
  • id: 133412
    {'degree': 12, 'field': [169, -286, 449, -348, 222, -38, -19, 22, 8, -20, 15, -6, 1], 'lmfdb_label': '2574.u3', 'torsion': [6, 6]}
  • id: 133413
    {'degree': 12, 'field': [518076, -650052, 456212, -205396, 65146, -15146, 2939, -324, -131, 82, -7, -4, 1], 'lmfdb_label': '2574.u3', 'torsion': [12]}
  • id: 133415
    {'degree': 16, 'field': [676, -3224, 10124, -17352, 21074, -16024, 13942, -17316, 8815, -1728, 1714, -668, 137, 0, 2, -4, 1], 'lmfdb_label': '2574.u3', 'torsion': [2, 12]}
  • id: 133416
    {'degree': 16, 'field': [107584, 145632, 291272, 74620, 173201, -31332, 128828, -36396, 20032, 3552, -1610, 812, -84, -28, 16, -4, 1], 'lmfdb_label': '2574.u3', 'torsion': [2, 12]}
  • id: 133414
    {'degree': 16, 'field': [252047376, 0, -142074324, 0, 9885735, 0, 1729881, 0, 584079, 0, 45894, 0, 3385, 0, 89, 0, 1], 'lmfdb_label': '2574.u3', 'torsion': [8]}
  • id: 133417
    {'degree': 18, 'field': [6691894416, 2456083296, 4547281248, -185327664, 1874893536, 47998008, 218395804, -57736128, 12082800, -5861380, 1215792, -458604, 30873, -4716, 3627, 38, -51, -3, 1], 'lmfdb_label': '2574.u3', '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: 44825
    {'conductor': 2574, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '2574.u3', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 44826
    {'conductor': 2574, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '2574.u3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 44827
    {'conductor': 2574, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '2574.u3', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 44828
    {'conductor': 2574, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '2574.u3', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1680776
    {'adelic_gens': [[1705, 12, 1704, 13], [1002, 1585, 1001, 1574], [937, 12, 474, 73], [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': 2574, 'lmfdb_label': '2574.u3', 'prime': 0}
  • id: 12854
    {'conductor': 2574, 'elladic_image': '2.3.0.1', 'lmfdb_label': '2574.u3', 'modell_image': '2B', 'prime': 2}
  • id: 12855
    {'conductor': 2574, 'elladic_image': '3.8.0.2', 'lmfdb_label': '2574.u3', 'modell_image': '3B.1.2', 'prime': 3}
• ec_padic •

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

  
  
  • id: 80225
    {'lmfdb_iso': '2574.u', 'p': 7, 'prec': 20, 'unit': 8196976454462384, 'val': 1}
  • id: 80221
    {'lmfdb_iso': '2574.u', 'p': 19, 'prec': 20, 'unit': 793110008017931159353094, 'val': 1}
  • id: 80235
    {'lmfdb_iso': '2574.u', 'p': 31, 'prec': 20, 'unit': 17846644288401229908070197427, 'val': 1}
  • id: 80224
    {'lmfdb_iso': '2574.u', 'p': 37, 'prec': 20, 'unit': 335536658025362279976213152826, 'val': 1}
  • id: 80226
    {'lmfdb_iso': '2574.u', 'p': 41, 'prec': 20, 'unit': 3606456061365364562328770349071, 'val': 1}
  • id: 80227
    {'lmfdb_iso': '2574.u', 'p': 43, 'prec': 20, 'unit': 1989906058794197431447635314154, 'val': 1}
  • id: 80230
    {'lmfdb_iso': '2574.u', 'p': 53, 'prec': 20, 'unit': 471879852450391274165424297810725, 'val': 1}
  • id: 80234
    {'lmfdb_iso': '2574.u', 'p': 61, 'prec': 20, 'unit': 1454083312921592894104339985989849, 'val': 1}
  • id: 80223
    {'lmfdb_iso': '2574.u', 'p': 67, 'prec': 20, 'unit': 8633510429410716454397050648058424, 'val': 1}
  • id: 80233
    {'lmfdb_iso': '2574.u', 'p': 71, 'prec': 20, 'unit': 118633345661565683064106307776583993, 'val': 1}
  • id: 80231
    {'lmfdb_iso': '2574.u', 'p': 73, 'prec': 20, 'unit': 43865340185547778374380159247828341, 'val': 1}
  • id: 80228
    {'lmfdb_iso': '2574.u', 'p': 79, 'prec': 20, 'unit': 191844777954644096609563708468469485, 'val': 1}
  • id: 80229
    {'lmfdb_iso': '2574.u', 'p': 83, 'prec': 20, 'unit': 2326338214386458856069193473262448322, 'val': 1}
  • id: 80232
    {'lmfdb_iso': '2574.u', 'p': 89, 'prec': 20, 'unit': 3990264830380646718198301194800673808, 'val': 1}
  • id: 80222
    {'lmfdb_iso': '2574.u', 'p': 97, 'prec': 20, 'unit': 45715478517980493755483945441994627192, 'val': 1}