Elliptic curve data - 12240.k1

Formats: - HTML - YAML - JSON - 2025-10-27T09:41:22.522032

• 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': '12240j', 'Clabel': '12240j2', 'Cnumber': 2, 'abc_quality': 0.908379168836826, 'absD': 3569184000000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 2040, 'ainvs': [0, 0, 0, -5403, -122902], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 12240, 'degree': 18432, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1241012448451519768860428032', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2], 'jinv': [11683450802, 2390625], 'lmfdb_iso': '12240.k', 'lmfdb_label': '12240.k1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -600, -4752], 'min_quad_twist_disc': 12, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '60.6.0.c.1', '136.6.0.?', '2040.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 153], [3, 8, 272], [5, 6, 2448], [17, 18, 720]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.060589815002186069110709259931', 'prec': 110}, 'szpiro_ratio': 3.9732135735005873, '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, -1, 0, -2, 0, 0, 0, 4, 0, 4, 0, 0, 0, -1, 0, 4, 0], 'aplist': [0, 0, -1, -2, 4, 4, -1, 4, 4, 10, 0, 2, -4, 10, 0, 2, 2, 2, -6, -6, -8, -4, 16, -14, -12], 'class_deg': 2, 'class_size': 2, 'conductor': 12240, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '12240.k', 'trace_hash': 630151967141334749}
• 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': '0.10558885113144753015250223960', 'prec': 103}, 'conductor': 12240, 'gens': [], 'heights': [], 'lmfdb_label': '12240.k1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.56485839985540582972006927161', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.2594335994216233188802770864438462205', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-26, 0, 1]], 'xcoord_integral_points': [-26]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [0, 0], '17': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '12240.k1'}
• ec_torsion_growth •

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

  
  
  • id: 631484
    {'degree': 2, 'field': [-34, 0, 1], 'lmfdb_label': '12240.k1', 'torsion': [2, 2]}
  • id: 631485
    {'degree': 4, 'field': [34, 0, -11, 0, 1], 'lmfdb_label': '12240.k1', 'torsion': [4]}
  • id: 631488
    {'degree': 8, 'field': [-675, 0, 312, 0, 90, 0, 0, 0, 1], 'lmfdb_label': '12240.k1', 'torsion': [6]}
  • id: 631487
    {'degree': 8, 'field': [9726, -4800, -203, 142, 269, 52, -1, -2, 1], 'lmfdb_label': '12240.k1', 'torsion': [2, 4]}
  • id: 631486
    {'degree': 8, 'field': [178929, 0, 125004, 0, -6890, 0, 44, 0, 1], 'lmfdb_label': '12240.k1', 'torsion': [2, 4]}
  • id: 631490
    {'degree': 16, 'field': [-8655710625, 6060919500, 835822350, -1080645660, -56996928, 131802828, -2885532, -8193480, 521992, 275348, -44258, -5264, 3266, 100, -116, -4, 1], 'lmfdb_label': '12240.k1', 'torsion': [2, 6]}
  • id: 631489
    {'degree': 16, 'field': [12315672576, 0, 422360784, 0, -52895670, 0, -5329449, 0, 274669, 0, 6596, 0, 750, 0, -61, 0, 1], 'lmfdb_label': '12240.k1', '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: 264232
    {'conductor': 12240, 'conductor_valuation': 4, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '12240.k1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 264233
    {'conductor': 12240, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '12240.k1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 264234
    {'conductor': 12240, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '12240.k1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 264235
    {'conductor': 12240, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '12240.k1', 'prime': 17, '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: 1745232
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [817, 4, 1634, 9], [2037, 4, 2036, 5], [482, 1, 1799, 0], [1361, 4, 682, 9], [257, 1786, 1784, 255], [2, 1, 1019, 0]], 'adelic_image': '2040.12.0.?', 'conductor': 12240, 'lmfdb_label': '12240.k1', 'prime': 0}
  • id: 58387
    {'conductor': 12240, 'elladic_image': '2.3.0.1', 'lmfdb_label': '12240.k1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 12240.k does not appear in ec_padic