Elliptic curve data - 4275.e2

Formats: - HTML - YAML - JSON - 2025-08-12T04:07:26.496376

• 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': '4275q', 'Clabel': '4275q1', 'Cnumber': 1, 'abc_quality': 1.119402634915339, 'absD': 27052734375, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 380, 'ainvs': [1, -1, 1, 70, -7928], 'analytic_rank': 0, 'bad_primes': [3, 5, 19], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 4275, 'degree': 2560, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.68079325560393891517057117487', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2], 'jinv': [27, 19], 'lmfdb_iso': '4275.e', 'lmfdb_label': '4275.e2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, 0, 2], 'min_quad_twist_disc': -15, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '20.6.0.c.1', '76.6.0.?', '190.6.0.?', '380.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 855], [3, 6, 475], [5, 14, 171], [19, 20, 225]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0755913230556912114776209435', 'prec': 103}, 'szpiro_ratio': 3.76470341564657, '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, -2, 3, 0, 0, 4, 0, 2, 2, 0, -1, 4, 0, 1, 0], 'aplist': [-1, 0, 0, -2, 4, 2, 4, 1, -6, 6, -4, 10, 10, -2, -6, 10, 0, 2, -8, -4, -4, 4, -18, 2, -6], 'class_deg': 2, 'class_size': 2, 'conductor': 4275, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '4275.e', 'trace_hash': 1660489383832746964}
• 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': '0.25625390459341827726680586347', 'prec': 103}, 'conductor': 4275, 'gens': [], 'heights': [], 'lmfdb_label': '4275.e2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.55392853652305111501793649997', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.1078570730461022300358729999417395593', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[19, -10, 1]], 'xcoord_integral_points': [19]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '3': 'a', '5': 'a', '19': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '4275.e2'}
• ec_torsion_growth •

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

  
  
  • id: 222629
    {'degree': 2, 'field': [24, -1, 1], 'lmfdb_label': '4275.e2', 'torsion': [2, 2]}
  • id: 222630
    {'degree': 4, 'field': [-59, 19, -4, -1, 1], 'lmfdb_label': '4275.e2', 'torsion': [4]}
  • id: 222633
    {'degree': 8, 'field': [1, -16, 25, -49, 64, 26, 10, -1, 1], 'lmfdb_label': '4275.e2', 'torsion': [6]}
  • id: 222632
    {'degree': 8, 'field': [220, 230, 155, -135, 101, -6, 11, -1, 1], 'lmfdb_label': '4275.e2', 'torsion': [2, 4]}
  • id: 222631
    {'degree': 8, 'field': [4096, 0, 832, 0, 384, 0, 13, 0, 1], 'lmfdb_label': '4275.e2', 'torsion': [2, 4]}
  • id: 222635
    {'degree': 16, 'field': [81, 0, 29970, 0, -29187, 0, 20115, 0, -4536, 0, 765, 0, -48, 0, 0, 0, 1], 'lmfdb_label': '4275.e2', 'torsion': [2, 6]}
  • id: 222634
    {'degree': 16, 'field': [841, 0, 4444, 0, -6010, 0, 2956, 0, -641, 0, 116, 0, -10, 0, -16, 0, 1], 'lmfdb_label': '4275.e2', 'torsion': [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: 80550
    {'conductor': 4275, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '4275.e2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 80551
    {'conductor': 4275, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '4275.e2', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 80552
    {'conductor': 4275, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '4275.e2', 'prime': 19, '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: 1691758
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [377, 4, 376, 5], [42, 1, 359, 0], [1, 4, 0, 1], [97, 286, 284, 95], [308, 1, 303, 0]], 'adelic_image': '380.12.0.?', 'conductor': 4275, 'lmfdb_label': '4275.e2', 'prime': 0}
  • id: 21203
    {'conductor': 4275, 'elladic_image': '2.3.0.1', 'lmfdb_label': '4275.e2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 4275.e does not appear in ec_padic