Elliptic curve data - 77280.v3

Formats: - HTML - YAML - JSON - 2024-05-24T23:12:53.269667

• 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': '77280f', 'Clabel': '77280f1', 'Cnumber': 1, 'abc_quality': 1.005543686661075, 'absD': 3779427605625000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 120, 'ainvs': [0, -1, 0, -3307050, -2311785000], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 23], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 77280, 'degree': 1720320, 'elladic_images': ['4.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4867787155645833854473354848', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 21, 'isogeny_degrees': [1, 2], 'jinv': [62498004782515366780864, 59053556337890625], 'lmfdb_iso': '77280.v', 'lmfdb_label': '77280.v3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -3307050, -2311785000], 'min_quad_twist_disc': 1, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0-2.a.1.1', '20.24.0-20.a.1.2', '24.24.0-24.b.1.1', '120.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 7, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.7789098893703893094790073186', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.1402051252846107307387194241', 'prec': 100}, 'szpiro_ratio': 5.033082720864209, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, 0, 0, 2, 0, -1, 0, -2, 0, 4, 0], 'aplist': [0, -1, 1, 1, 0, 2, -2, 4, -1, -2, -4, 2, -6, -12, 0, -10, -8, -10, 12, 0, 10, -4, 12, -6, 18], 'class_deg': 4, 'class_size': 4, 'conductor': 77280, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '77280.v', 'trace_hash': 1921983504282347666}
• 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': '0.0069184921456089944155822871103', 'prec': 110}, 'conductor': 77280, 'gens': [[2475, 68250, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.7789098893703893094790073186', 'prec': 100}], 'lmfdb_label': '77280.v3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.11196028356353749290163742252', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.2225507842285478192960008506801646571', 'prec': 130}, 'tamagawa_product': 320, 'torsion_generators': [[-1025, 0, 1], [2100, 0, 1]], 'xcoord_integral_points': [-1074, -1025, 2100, 2475, 28550]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [2, 0], '7': [2, 0], '11': [1, 1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '77280.v3'}
• ec_torsion_growth •

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

  
  
  • id: 3650291
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '77280.v3', 'torsion': [2, 4]}
  • id: 3650292
    {'degree': 4, 'field': [9, 0, 0, 0, 1], 'lmfdb_label': '77280.v3', 'torsion': [2, 4]}
  • id: 3650293
    {'degree': 4, 'field': [19, 14, -13, -2, 1], 'lmfdb_label': '77280.v3', 'torsion': [2, 4]}
  • id: 3650296
    {'degree': 8, 'field': [-369603, 0, 55728, 0, -2106, 0, 0, 0, 1], 'lmfdb_label': '77280.v3', 'torsion': [2, 6]}
  • id: 3650294
    {'degree': 8, 'field': [145, -140, 164, -44, 13, 8, 2, -4, 1], 'lmfdb_label': '77280.v3', 'torsion': [4, 4]}
  • id: 3650295
    {'degree': 8, 'field': [6561, 0, 2844, 0, 306, 0, 4, 0, 1], 'lmfdb_label': '77280.v3', 'torsion': [2, 8]}
  • id: 3650298
    {'degree': 16, 'field': [278963548900, 0, -431446529600, 0, 185179005760, 0, -20409495920, 0, 819228076, 0, -14787104, 0, 132976, 0, -584, 0, 1], 'lmfdb_label': '77280.v3', 'torsion': [2, 8]}
  • id: 3650299
    {'degree': 16, 'field': [490375271824, 0, -45235879808, 0, 3100659040, 0, -66625376, 0, -1714760, 0, 160576, 0, -3512, 0, 40, 0, 1], 'lmfdb_label': '77280.v3', 'torsion': [2, 12]}
  • id: 3650297
    {'degree': 16, 'field': [281680568688964, 0, -34032923592448, 0, 1845412121440, 0, -58657457104, 0, 1195469212, 0, -15845632, 0, 129760, 0, -568, 0, 1], 'lmfdb_label': '77280.v3', 'torsion': [2, 8]}
• 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: 1879520
    {'conductor': 77280, 'conductor_valuation': 5, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '77280.v3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1879521
    {'conductor': 77280, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '77280.v3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1879522
    {'conductor': 77280, 'conductor_valuation': 1, 'discriminant_valuation': 10, 'j_denominator_valuation': 10, 'kodaira_symbol': 14, 'lmfdb_label': '77280.v3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 10}
  • id: 1879523
    {'conductor': 77280, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '77280.v3', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1879524
    {'conductor': 77280, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '77280.v3', 'prime': 23, '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: 2174442
    {'adelic_gens': [[3, 2, 38, 119], [117, 4, 116, 5], [97, 2, 0, 1], [93, 2, 58, 119], [63, 2, 118, 119], [1, 4, 0, 1], [1, 0, 4, 1]], 'adelic_image': '120.48.0.?', 'conductor': 77280, 'lmfdb_label': '77280.v3', 'prime': 0}
  • id: 318935
    {'conductor': 77280, 'elladic_image': '4.12.0.1', 'lmfdb_label': '77280.v3', 'modell_image': '2Cs', 'prime': 2}
• ec_padic •

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

  
  
  • id: 3977652
    {'lmfdb_iso': '77280.v', 'p': 13, 'prec': 20, 'unit': 921126230360894919828, 'val': 1}
  • id: 3977654
    {'lmfdb_iso': '77280.v', 'p': 17, 'prec': 20, 'unit': 116325859929472225698432, 'val': 1}
  • id: 3977645
    {'lmfdb_iso': '77280.v', 'p': 19, 'prec': 20, 'unit': 1060060502455903310861537, 'val': 1}
  • id: 3977651
    {'lmfdb_iso': '77280.v', 'p': 29, 'prec': 20, 'unit': 5415751233525960127848523809, 'val': 1}
  • id: 3977661
    {'lmfdb_iso': '77280.v', 'p': 31, 'prec': 20, 'unit': 12802665630408566050549505981, 'val': 1}
  • id: 3977648
    {'lmfdb_iso': '77280.v', 'p': 37, 'prec': 20, 'unit': 446230108187308689720992422069, 'val': 1}
  • id: 3977649
    {'lmfdb_iso': '77280.v', 'p': 41, 'prec': 20, 'unit': 1363543017016655587005474372650, 'val': 1}
  • id: 3977650
    {'lmfdb_iso': '77280.v', 'p': 43, 'prec': 20, 'unit': 4002437656575951335692907297002, 'val': 1}
  • id: 3977656
    {'lmfdb_iso': '77280.v', 'p': 53, 'prec': 20, 'unit': 375295681356012561668400452642653, 'val': 1}
  • id: 3977659
    {'lmfdb_iso': '77280.v', 'p': 59, 'prec': 20, 'unit': 1642337945894721343984521017939877, 'val': 1}
  • id: 3977660
    {'lmfdb_iso': '77280.v', 'p': 61, 'prec': 20, 'unit': 63122822482055221669504846979637, 'val': 1}
  • id: 3977647
    {'lmfdb_iso': '77280.v', 'p': 67, 'prec': 20, 'unit': 35260630502992751124146782459045156, 'val': 1}
  • id: 3977657
    {'lmfdb_iso': '77280.v', 'p': 73, 'prec': 20, 'unit': 123563970947559800762395288898321389, 'val': 1}
  • id: 3977653
    {'lmfdb_iso': '77280.v', 'p': 79, 'prec': 20, 'unit': 164891727564249787108289177872887886, 'val': 1}
  • id: 3977655
    {'lmfdb_iso': '77280.v', 'p': 83, 'prec': 20, 'unit': 1962220437673888725373793024131911565, 'val': 1}
  • id: 3977658
    {'lmfdb_iso': '77280.v', 'p': 89, 'prec': 20, 'unit': 8528343134399582189915031998200489226, 'val': 1}
  • id: 3977646
    {'lmfdb_iso': '77280.v', 'p': 97, 'prec': 20, 'unit': 27110231861087690757132538785063258218, 'val': 1}