Elliptic curve data - 1200.e2

Formats: - HTML - YAML - JSON - 2026-01-01T08:34:24.895110

• 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': '1200j', 'Clabel': '1200j5', 'Cnumber': 5, 'abc_quality': 1.038972011651739, 'absD': 10497600000000, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 240, 'ainvs': [0, -1, 0, -54008, 4846512], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 1200, 'degree': 3072, 'elladic_images': ['8.96.0.27'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4421621549741243639826313516', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [272223782641, 164025], 'lmfdb_iso': '1200.e', 'lmfdb_label': '1200.e2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -135, -660], 'min_quad_twist_disc': -20, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.24.0-4.b.1.2', '8.96.0-8.k.1.8', '20.48.0-20.c.1.4', '40.192.1-40.cc.2.8', '48.192.1-48.e.2.15', '80.384.5.?', '240.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 25], [3, 4, 400], [5, 18, 48]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.055703981802871132734980436470', 'prec': 110}, 'szpiro_ratio': 6.248773456593644, '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, 0, 0, 0, 0, 1, 0, 4, 0, 2, 0, 0, 0, -2, 0, -4, 0], 'aplist': [0, -1, 0, 0, 4, 2, -2, -4, 0, -2, 0, 10, 10, 4, 8, 10, 4, -2, 12, 8, -10, 0, 12, -6, -2], 'class_deg': 16, 'class_size': 8, 'conductor': 1200, 'isogeny_matrix': [[1, 2, 4, 16, 4, 8, 16, 8], [2, 1, 2, 8, 2, 4, 8, 4], [4, 2, 1, 16, 4, 8, 16, 8], [16, 8, 16, 1, 4, 2, 4, 8], [4, 2, 4, 4, 1, 2, 4, 2], [8, 4, 8, 2, 2, 1, 2, 4], [16, 8, 16, 4, 4, 2, 1, 8], [8, 4, 8, 8, 2, 4, 8, 1]], 'lmfdb_iso': '1200.e', 'trace_hash': 1497722826863384425}
• 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': '0.055892542815438227544168569553', 'prec': 107}, 'conductor': 1200, 'gens': [], 'heights': [], 'lmfdb_label': '1200.e2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.71386122344839743930710261581', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4277224468967948786142052316113670190', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[132, 0, 1], [137, 0, 1]], 'xcoord_integral_points': [-268, 132, 137]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '5': 'a'}, 'iwp0': 3, 'lmfdb_label': '1200.e2'}
• ec_torsion_growth •

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

  
  
  • id: 59305
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '1200.e2', 'torsion': [2, 4]}
  • id: 59306
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '1200.e2', 'torsion': [2, 4]}
  • id: 59307
    {'degree': 4, 'field': [1, 0, 3, 0, 1], 'lmfdb_label': '1200.e2', 'torsion': [4, 4]}
  • id: 59308
    {'degree': 4, 'field': [4, 0, -6, 0, 1], 'lmfdb_label': '1200.e2', 'torsion': [2, 8]}
  • id: 59312
    {'degree': 8, 'field': [-75, 0, -395, 0, 30, 0, 0, 0, 1], 'lmfdb_label': '1200.e2', 'torsion': [2, 6]}
  • id: 59310
    {'degree': 8, 'field': [1, 0, 0, 0, 7, 0, 0, 0, 1], 'lmfdb_label': '1200.e2', 'torsion': [4, 8]}
  • id: 59309
    {'degree': 8, 'field': [1, 2, 2, -10, 11, -10, 8, -4, 1], 'lmfdb_label': '1200.e2', 'torsion': [4, 8]}
  • id: 59311
    {'degree': 8, 'field': [36, 0, -56, 0, 16, 0, 4, 0, 1], 'lmfdb_label': '1200.e2', 'torsion': [4, 8]}
  • id: 59313
    {'degree': 16, 'field': [1, 0, 0, 0, -36, 0, 0, 0, 646, 0, 0, 0, -36, 0, 0, 0, 1], 'lmfdb_label': '1200.e2', 'torsion': [8, 8]}
  • id: 59316
    {'degree': 16, 'field': [9, 0, 63, 0, 175, 0, 126, 0, -105, 0, -126, 0, -42, 0, 0, 0, 1], 'lmfdb_label': '1200.e2', 'torsion': [2, 12]}
  • id: 59315
    {'degree': 16, 'field': [625, 0, -10000, 0, 39500, 0, -42000, 0, 19775, 0, -4800, 0, 620, 0, -40, 0, 1], 'lmfdb_label': '1200.e2', 'torsion': [2, 16]}
  • id: 59317
    {'degree': 16, 'field': [625, 0, 1000, 0, 400, 0, 1875, 0, 600, 0, 165, 0, 25, 0, 10, 0, 1], 'lmfdb_label': '1200.e2', 'torsion': [2, 12]}
  • id: 59314
    {'degree': 16, 'field': [10000, 0, -20000, 0, 29000, 0, -18000, 0, 8000, 0, -1800, 0, 290, 0, -20, 0, 1], 'lmfdb_label': '1200.e2', 'torsion': [2, 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: 17583
    {'conductor': 1200, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '1200.e2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 17584
    {'conductor': 1200, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '1200.e2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 17585
    {'conductor': 1200, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '1200.e2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 1672092
    {'adelic_gens': [[179, 232, 70, 43], [1, 0, 16, 1], [1, 16, 0, 1], [161, 8, 0, 1], [1, 16, 4, 65], [1, 16, 0, 181], [225, 16, 224, 17], [231, 232, 62, 25]], 'adelic_image': '240.768.13.?', 'conductor': 1200, 'lmfdb_label': '1200.e2', 'prime': 0}
  • id: 5705
    {'conductor': 1200, 'elladic_image': '8.96.0.27', 'lmfdb_label': '1200.e2', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 1200.e does not appear in ec_padic