Elliptic curve data - 302016.z1

Formats: - HTML - YAML - JSON - 2026-04-16T19:25:05.768615

• 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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '302016z', 'Clabel': '302016z3', 'Cnumber': 3, 'abc_quality': 1.052193877800105, 'absD': 4527939846144, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 3432, 'ainvs': [0, -1, 0, -402849, 98549409], 'analytic_rank': 1, 'bad_primes': [2, 3, 11, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 302016, 'degree': 1474560, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7486465511818769050495851903', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'intrinsic_torsion': 2, 'iso_nlabel': 25, 'isogeny_degrees': [1, 2, 4], 'jinv': [62275269892, 39], 'lmfdb_iso': '302016.z', 'lmfdb_label': '302016.z1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -832, -9520], 'min_quad_twist_disc': -88, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0.z.1', '88.12.0.?', '104.12.0.?', '156.12.0.?', '264.24.0.?', '312.24.0.?', '1144.24.0.?', '3432.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 5, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.0263721313591056147072222924', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 4719], [3, 4, 100672], [11, 62, 2496], [13, 14, 23232]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.37449732596390211287102942729', 'prec': 107}, 'szpiro_ratio': 3.9888744868378816, '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, -1, 0, -2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, -2, 0, -4, 0], 'aplist': [0, -1, -2, 0, 0, 1, -2, -4, 0, 6, 0, 2, -6, -12, -4, -6, 8, -2, -4, -12, 14, 0, 8, -18, -6], 'class_deg': 4, 'class_size': 4, 'conductor': 302016, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '302016.z', 'trace_hash': 509136100777551536}
• 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': '0.030279235380581920924847987372', 'prec': 107}, 'conductor': 302016, 'gens': [[371, 140, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.0263721313591056147072222924', 'prec': 100}], 'lmfdb_label': '302016.z1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.63913262455283214601065764589', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.8685063263781873156541244632096034707', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[367, 0, 1]], 'xcoord_integral_points': [367, 371, 488]}
• lmfdb_label 302016.z1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 12771299
    {'degree': 2, 'field': [-286, 0, 1], 'lmfdb_label': '302016.z1', 'torsion': [4]}
  • id: 12771300
    {'degree': 2, 'field': [-66, 0, 1], 'lmfdb_label': '302016.z1', 'torsion': [4]}
  • id: 12771298
    {'degree': 2, 'field': [-39, 0, 1], 'lmfdb_label': '302016.z1', 'torsion': [2, 2]}
  • id: 12771301
    {'degree': 4, 'field': [3025, 0, -176, 0, 1], 'lmfdb_label': '302016.z1', 'torsion': [2, 4]}
  • id: 12771305
    {'degree': 8, 'field': [-702768, 0, -2129600, 0, -2904, 0, 0, 0, 1], 'lmfdb_label': '302016.z1', 'torsion': [6]}
  • id: 12771304
    {'degree': 8, 'field': [49, 0, 172, 0, 303, 0, 34, 0, 1], 'lmfdb_label': '302016.z1', 'torsion': [8]}
  • id: 12771303
    {'degree': 8, 'field': [10609, 0, -6392, 0, 1163, 0, -74, 0, 1], 'lmfdb_label': '302016.z1', 'torsion': [8]}
  • id: 12771302
    {'degree': 8, 'field': [234256, 0, 42592, 0, -1815, 0, 88, 0, 1], 'lmfdb_label': '302016.z1', 'torsion': [2, 4]}
  • id: 12771309
    {'degree': 16, 'field': [-2252266238, 169393751984, 171371799360, 43804683296, -181477929710, 42117173700, 2519988428, 737378116, -20820582, -6497240, -845470, -28776, 6736, -1444, -144, -4, 1], 'lmfdb_label': '302016.z1', 'torsion': [2, 6]}
  • id: 12771307
    {'degree': 16, 'field': [9025, 0, -816312, 0, 3898372, 0, -3573288, 0, 890502, 0, -95976, 0, 4996, 0, -120, 0, 1], 'lmfdb_label': '302016.z1', 'torsion': [2, 8]}
  • id: 12771308
    {'degree': 16, 'field': [10000, 0, -359200, 0, 12894064, 0, -298528, 0, -50516, 0, 5840, 0, 172, 0, -16, 0, 1], 'lmfdb_label': '302016.z1', 'torsion': [2, 8]}
  • id: 12771306
    {'degree': 16, 'field': [75692114884, 0, -12029592600, 0, 1712721280, 0, 85542612, 0, 13501701, 0, 286452, 0, 3262, 0, -168, 0, 1], 'lmfdb_label': '302016.z1', 'torsion': [4, 4]}
  • id: 12771311
    {'degree': 16, 'field': [277809109776, 0, -108504568128, 0, 6065824864, 0, 146878512, 0, -7379064, 0, -330088, 0, 7260, 0, -132, 0, 1], 'lmfdb_label': '302016.z1', 'torsion': [12]}
  • id: 12771310
    {'degree': 16, 'field': [1041458966978, -635305640192, 729106789320, -267188165960, 128358328994, -39916206828, 5024354104, -97010308, -4141326, -11347944, 1524594, 126372, -25770, 768, -12, -4, 1], 'lmfdb_label': '302016.z1', 'torsion': [12]}
• 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: 7478912
    {'conductor': 302016, 'conductor_valuation': 6, 'discriminant_valuation': 16, 'j_denominator_valuation': 0, 'kodaira_symbol': -10, 'lmfdb_label': '302016.z1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 7478913
    {'conductor': 302016, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '302016.z1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 7478914
    {'conductor': 302016, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '302016.z1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 7478915
    {'conductor': 302016, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '302016.z1', 'prime': 13, '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: 3563007
    {'adelic_gens': [[1517, 1518, 1430, 2837], [7, 6, 3426, 3427], [3425, 8, 3424, 9], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [892, 2497, 1463, 2190], [2608, 627, 1045, 2498], [2495, 0, 0, 3431], [1992, 1529, 1705, 3312]], 'adelic_image': '3432.48.0.?', 'conductor': 302016, 'lmfdb_label': '302016.z1', 'prime': 0}
  • id: 1064257
    {'conductor': 302016, 'elladic_image': '4.6.0.1', 'lmfdb_label': '302016.z1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 302016.z does not appear in ec_padic