Elliptic curve data - 2304.i1

Formats: - HTML - YAML - JSON - 2024-09-12T05:33:53.932369

• 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': '2304c', 'Clabel': '2304c2', 'Cnumber': 2, 'abc_quality': 0.9029767420170889, 'absD': 23887872, 'ainvs': [0, 0, 0, -120, 448], 'analytic_rank': 0, 'bad_primes': [2, 3], 'class_deg': 2, 'class_size': 2, 'cm': -8, 'conductor': 2304, 'degree': 384, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.14533349397416072594134501285', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 8, 'isogeny_degrees': [1, 2], 'jinv': [8000, 1], 'lmfdb_iso': '2304.i', 'lmfdb_label': '2304.i1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -3, 1], 'min_quad_twist_disc': 24, 'modell_images': [], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 2, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 9], [3, 2, 256]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.2704066260598257565278177574', 'prec': 103}, 'szpiro_ratio': 3.355041263405977, '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, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 6, 0, -2, 0], 'aplist': [0, 0, 0, 0, 6, 0, 6, -2, 0, 0, 0, 0, -6, 10, 0, 0, 6, 0, 14, 0, -2, 0, 18, 18, 10], 'class_deg': 2, 'class_size': 2, 'conductor': 2304, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '2304.i', 'trace_hash': 706512102065136076}
• 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': '0.74776465120092405005512853538', 'prec': 103}, 'conductor': 2304, 'gens': [], 'heights': [], 'lmfdb_label': '2304.i1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '2.0566953213264561394655623131', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.0566953213264561394655623130780611252', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[8, 0, 1]], 'xcoord_integral_points': [8]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a'}, 'iwp0': 3, 'lmfdb_label': '2304.i1'}
• ec_torsion_growth •

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

  
  
  • id: 116622
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '2304.i1', 'torsion': [2, 2]}
  • id: 116625
    {'degree': 4, 'field': [-2, 0, 4, 0, 1], 'lmfdb_label': '2304.i1', 'torsion': [6]}
  • id: 116624
    {'degree': 4, 'field': [6, 0, -4, 0, 1], 'lmfdb_label': '2304.i1', 'torsion': [6]}
  • id: 116623
    {'degree': 4, 'field': [18, 0, -12, 0, 1], 'lmfdb_label': '2304.i1', 'torsion': [2, 4]}
  • id: 116629
    {'degree': 8, 'field': [1, 0, 0, 0, -4, 0, 0, 0, 1], 'lmfdb_label': '2304.i1', 'torsion': [2, 6]}
  • id: 116628
    {'degree': 8, 'field': [9, 0, -24, 0, 16, 0, 0, 0, 1], 'lmfdb_label': '2304.i1', 'torsion': [2, 6]}
  • id: 116627
    {'degree': 8, 'field': [36, 0, 24, 0, 10, 0, 4, 0, 1], 'lmfdb_label': '2304.i1', 'torsion': [3, 6]}
  • id: 116626
    {'degree': 8, 'field': [79, 80, 88, 24, 10, -8, 0, 0, 1], 'lmfdb_label': '2304.i1', 'torsion': [2, 4]}
  • id: 116630
    {'degree': 12, 'field': [216, 0, 576, 0, 600, 0, 296, 0, 78, 0, 12, 0, 1], 'lmfdb_label': '2304.i1', 'torsion': [18]}
  • id: 116633
    {'degree': 16, 'field': [1, 0, 0, 0, -4, 0, 0, 0, 15, 0, 0, 0, -4, 0, 0, 0, 1], 'lmfdb_label': '2304.i1', 'torsion': [6, 6]}
  • id: 116632
    {'degree': 16, 'field': [4, 0, -368, 0, 1032, 0, -1120, 0, 608, 0, -184, 0, 36, 0, -8, 0, 1], 'lmfdb_label': '2304.i1', 'torsion': [2, 8]}
  • id: 116635
    {'degree': 16, 'field': [4, 0, -48, 0, 152, 0, -224, 0, 192, 0, -104, 0, 36, 0, -8, 0, 1], 'lmfdb_label': '2304.i1', 'torsion': [2, 12]}
  • id: 116634
    {'degree': 16, 'field': [18, 0, -120, 144, 232, -680, 512, 40, -126, -224, 316, -104, -12, -8, 20, -8, 1], 'lmfdb_label': '2304.i1', 'torsion': [2, 12]}
  • id: 116631
    {'degree': 16, 'field': [196, -1344, 4608, -8416, 10144, -9568, 7808, -5392, 3044, -1696, 1024, -496, 192, -80, 32, -8, 1], 'lmfdb_label': '2304.i1', 'torsion': [4, 4]}
  • id: 116636
    {'degree': 20, 'field': [20785248, 0, -13856832, 0, 3464208, 0, -769824, 0, 256608, 0, -38880, 0, 7452, 0, -1080, 0, 162, 0, -12, 0, 1], 'lmfdb_label': '2304.i1', 'torsion': [22]}
• 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: 38619
    {'conductor': 2304, 'conductor_valuation': 8, 'discriminant_valuation': 15, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '2304.i1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 38620
    {'conductor': 2304, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '2304.i1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
• lmfdb_label 2304.i1 does not appear in ec_galrep
• lmfdb_iso 2304.i does not appear in ec_padic