Elliptic curve data - 9240.a1

Formats: - HTML - YAML - JSON - 2024-05-05T12:52:05.749609

• 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': '9240q', 'Clabel': '9240q4', 'Cnumber': 4, 'abc_quality': 0.9435840641150427, 'absD': 554400000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 616, 'ainvs': [0, -1, 0, -29776, 1987276], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 9240, 'degree': 16384, 'elladic_images': ['8.12.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.2545492364697394944121991622', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [1425631925916578, 270703125], 'lmfdb_iso': '9240.a', 'lmfdb_label': '9240.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -29776, 1987276], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.5', '28.12.0-4.c.1.1', '56.24.0-56.z.1.10', '88.24.0.?', '616.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.5528500965126917584700407915', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.61916432095645629411306971753', 'prec': 103}, 'szpiro_ratio': 4.65629469577913, '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, -1, 0, -1, 0, 1, 0, 1, 0, -2, 0, 1, 0, -2, 0, 0, 0], 'aplist': [0, -1, -1, -1, 1, -2, -2, 0, 0, -2, -4, 6, 6, 12, 4, 6, -4, -10, -4, 8, -2, 0, -16, -6, -6], 'class_deg': 4, 'class_size': 4, 'conductor': 9240, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '9240.a', 'trace_hash': 898341502511032585}
• 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': '0.081341537793077940301525019827', 'prec': 107}, 'conductor': 9240, 'gens': [[105, 86, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.5528500965126917584700407915', 'prec': 100}], 'lmfdb_label': '9240.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.89523215164798063836627476122', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.1806256363837927152930819883388815546', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[101, 0, 1]], 'xcoord_integral_points': [101, 105]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [1, 0], '7': [1, 0], '11': [2, 0], '13': [1, 0], '17': [3, 0], '19': [1, 1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '9240.a1'}
• ec_torsion_growth •

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

  
  
  • id: 480167
    {'degree': 2, 'field': [-154, 0, 1], 'lmfdb_label': '9240.a1', 'torsion': [2, 2]}
  • id: 480168
    {'degree': 2, 'field': [-22, 0, 1], 'lmfdb_label': '9240.a1', 'torsion': [4]}
  • id: 480169
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '9240.a1', 'torsion': [4]}
  • id: 480171
    {'degree': 4, 'field': [154, 0, -88, 0, 1], 'lmfdb_label': '9240.a1', 'torsion': [8]}
  • id: 480170
    {'degree': 4, 'field': [225, 0, -58, 0, 1], 'lmfdb_label': '9240.a1', 'torsion': [2, 4]}
  • id: 480175
    {'degree': 8, 'field': [-702768, 0, 36784, 0, -2904, 0, 0, 0, 1], 'lmfdb_label': '9240.a1', 'torsion': [6]}
  • id: 480174
    {'degree': 8, 'field': [1089, 0, -2420, 0, 1056, 0, -132, 0, 1], 'lmfdb_label': '9240.a1', 'torsion': [2, 8]}
  • id: 480173
    {'degree': 8, 'field': [123904, 0, -9159, 0, 887, 0, -33, 0, 1], 'lmfdb_label': '9240.a1', 'torsion': [8]}
  • id: 480172
    {'degree': 8, 'field': [30730408, -110912, 99848, 22120, -11039, -28, 14, -4, 1], 'lmfdb_label': '9240.a1', 'torsion': [2, 4]}
  • id: 480177
    {'degree': 16, 'field': [64705936, 76385824, 45087008, -7150928, -8372556, -4063424, 1432224, -919208, 480568, -59896, 8928, -5200, 1845, -76, 8, -4, 1], 'lmfdb_label': '9240.a1', 'torsion': [2, 8]}
  • id: 480180
    {'degree': 16, 'field': [54875873536, 0, -19954863104, 0, 82458112, 0, -207678592, 0, 7298720, 0, -429088, 0, 352, 0, -176, 0, 1], 'lmfdb_label': '9240.a1', 'torsion': [12]}
  • id: 480181
    {'degree': 16, 'field': [568482824484, 0, -92777356968, 0, 7248339268, 0, -439036704, 0, 13985220, 0, -632424, 0, 11712, 0, -168, 0, 1], 'lmfdb_label': '9240.a1', 'torsion': [12]}
  • id: 480176
    {'degree': 16, 'field': [3695614070404, 0, 96471287376, 0, 11775886780, 0, 116422992, 0, 11013765, 0, 16380, 0, 5614, 0, -12, 0, 1], 'lmfdb_label': '9240.a1', 'torsion': [4, 4]}
  • id: 480179
    {'degree': 16, 'field': [392153264179600, 0, -35345237740736, 0, 623638781920, 0, -23117123568, 0, 238630392, 0, -4647720, 0, 29260, 0, -308, 0, 1], 'lmfdb_label': '9240.a1', 'torsion': [2, 6]}
  • id: 480178
    {'degree': 16, 'field': [944697761796096, 0, -119961620545536, 0, 5312153290752, 0, -126877943808, 0, 2011806720, 0, -22885632, 0, 172832, 0, -704, 0, 1], 'lmfdb_label': '9240.a1', 'torsion': [16]}
• 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: 193701
    {'conductor': 9240, 'conductor_valuation': 3, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '9240.a1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 193702
    {'conductor': 9240, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '9240.a1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 193703
    {'conductor': 9240, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '9240.a1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 193704
    {'conductor': 9240, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '9240.a1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 193705
    {'conductor': 9240, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '9240.a1', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 1724951
    {'adelic_gens': [[232, 547, 81, 110], [456, 3, 285, 2], [1, 0, 8, 1], [235, 232, 562, 237], [1, 8, 0, 1], [1, 4, 4, 17], [609, 8, 608, 9], [7, 6, 610, 611], [180, 1, 111, 6]], 'adelic_image': '616.48.0.?', 'conductor': 9240, 'lmfdb_label': '9240.a1', 'prime': 0}
  • id: 44770
    {'conductor': 9240, 'elladic_image': '8.12.0.6', 'lmfdb_label': '9240.a1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 386887
    {'lmfdb_iso': '9240.a', 'p': 13, 'prec': 20, 'unit': 495804285544498468800, 'val': 1}
  • id: 386889
    {'lmfdb_iso': '9240.a', 'p': 17, 'prec': 20, 'unit': 12343900409434496117405, 'val': 2}
  • id: 386886
    {'lmfdb_iso': '9240.a', 'p': 29, 'prec': 20, 'unit': 4486916866129636031369531872, 'val': 1}
  • id: 386896
    {'lmfdb_iso': '9240.a', 'p': 31, 'prec': 20, 'unit': 12235491210805375138420576759, 'val': 1}
  • id: 386882
    {'lmfdb_iso': '9240.a', 'p': 37, 'prec': 20, 'unit': 318474754358710747659324533293, 'val': 1}
  • id: 386884
    {'lmfdb_iso': '9240.a', 'p': 41, 'prec': 20, 'unit': 4068038846725363350598172509359, 'val': 1}
  • id: 386885
    {'lmfdb_iso': '9240.a', 'p': 43, 'prec': 20, 'unit': 2420450563583478851827259527634, 'val': 1}
  • id: 386888
    {'lmfdb_iso': '9240.a', 'p': 47, 'prec': 20, 'unit': 52256864950993210806011023144286, 'val': 1}
  • id: 386891
    {'lmfdb_iso': '9240.a', 'p': 53, 'prec': 20, 'unit': 371651221483043110366700295069247, 'val': 1}
  • id: 386894
    {'lmfdb_iso': '9240.a', 'p': 59, 'prec': 20, 'unit': 3017761403988670158240532040069658, 'val': 1}
  • id: 386895
    {'lmfdb_iso': '9240.a', 'p': 61, 'prec': 20, 'unit': 1664711471960023282934510938918008, 'val': 1}
  • id: 386881
    {'lmfdb_iso': '9240.a', 'p': 67, 'prec': 20, 'unit': 20795392285792979380924042398197879, 'val': 1}
  • id: 386883
    {'lmfdb_iso': '9240.a', 'p': 71, 'prec': 20, 'unit': 84773754273250232514306197611002919, 'val': 1}
  • id: 386892
    {'lmfdb_iso': '9240.a', 'p': 73, 'prec': 20, 'unit': 205381737167798208896526994726064412, 'val': 1}
  • id: 386890
    {'lmfdb_iso': '9240.a', 'p': 83, 'prec': 20, 'unit': 1319636554002580553713521794916897195, 'val': 1}
  • id: 386893
    {'lmfdb_iso': '9240.a', 'p': 89, 'prec': 20, 'unit': 7863938376721980112163368897640437081, 'val': 1}
  • id: 386880
    {'lmfdb_iso': '9240.a', 'p': 97, 'prec': 20, 'unit': 47615908190328978403037431566873639973, 'val': 1}