Elliptic curve data - 136242.m3

Formats: - HTML - YAML - JSON - 2026-07-02T10:02:46.294922

• 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': '136242bk', 'Clabel': '136242bk1', 'Cnumber': 1, 'abc_quality': 1.1780968639246816, 'absD': 385445512008, 'adelic_genus': 21, 'adelic_index': 768, 'adelic_level': 14616, 'ainvs': [1, -1, 0, -3942, 100828], 'analytic_rank': 1, 'bad_primes': [2, 3, 29], 'class_deg': 21, 'class_size': 4, 'cm': 0, 'conductor': 136242, 'degree': 145152, 'elladic_images': ['8.2.0.1', '3.4.0.1', '7.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.98006091934322054286979989518', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 12, 'isogeny_degrees': [1, 3, 7, 21], 'jinv': [-140625, 8], 'lmfdb_iso': '136242.m', 'lmfdb_label': '136242.m3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -42, -100], 'min_quad_twist_disc': -87, 'modell_images': ['3B', '7B'], 'modm_images': ['3.4.0.a.1', '7.8.0.a.1', '8.2.0.a.1', '21.64.1.a.3', '24.8.0.a.1', '56.16.0.a.1', '63.192.5.e.4', '87.8.0.?', '168.128.5.?', '203.16.0.?', '504.384.21.?', '609.128.1.?', '696.16.0.?', '1624.32.0.?', '1827.384.5.?', '4872.256.5.?', '14616.768.21.?'], 'nonmax_primes': [2, 3, 7], 'nonmax_rad': 42, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.4458985506985329834830356892', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 68121], [3, 8, 841], [29, 422, 162]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0697910918727197011869178666', 'prec': 103}, 'szpiro_ratio': 3.0912926924484307, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, -1, 0, 0, 3, 0, 2, -2, 0, 1, 3, 0, 1, 0], 'aplist': [-1, 0, 0, 2, 3, 2, 3, 1, -6, 0, 4, 4, -9, 1, 6, 12, 3, -8, 5, -12, -11, 4, 12, -6, -5], 'class_deg': 21, 'class_size': 4, 'conductor': 136242, 'isogeny_matrix': [[1, 3, 21, 7], [3, 1, 7, 21], [21, 7, 1, 3], [7, 21, 3, 1]], 'lmfdb_iso': '136242.m', 'trace_hash': 758962557616299786}
• 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': '0.14084125996152142274419832970', 'prec': 103}, 'conductor': 136242, 'gens': [[-527, 10462, 3]], 'heights': [{'__RealLiteral__': 0, 'data': '3.4458985506985329834830356892', 'prec': 100}], 'lmfdb_label': '136242.m3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.93811565537569458793559458227', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.4653027544934208268236802655950698680', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [6, 0], '3': 'a', '5': [1, 1, 0], '7': [1, 0], '11': [3, 0], '13': [1, 0], '17': [3, 0], '19': [1, 0], '23': [1, 0], '29': 'a', '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '136242.m3'}
• ec_torsion_growth •

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

  
  
  • id: 6166459
    {'degree': 2, 'field': [-7, -1, 1], 'lmfdb_label': '136242.m3', 'torsion': [3]}
  • id: 6166460
    {'degree': 3, 'field': [-10, -3, 0, 1], 'lmfdb_label': '136242.m3', 'torsion': [2]}
  • id: 6166463
    {'degree': 6, 'field': [-71, -192, 129, 51, -24, -3, 1], 'lmfdb_label': '136242.m3', 'torsion': [21]}
  • id: 6166461
    {'degree': 6, 'field': [8, 0, 9, 0, -6, 0, 1], 'lmfdb_label': '136242.m3', 'torsion': [2, 2]}
  • id: 6166464
    {'degree': 6, 'field': [199, -543, 156, 33, -24, -3, 1], 'lmfdb_label': '136242.m3', 'torsion': [6]}
  • id: 6166462
    {'degree': 6, 'field': [1536, 0, 0, -63, 0, 0, 1], 'lmfdb_label': '136242.m3', 'torsion': [3]}
  • id: 6166465
    {'degree': 12, 'field': [-63697654, -98500080, -57987537, -11503766, 7747041, 1235520, -345003, -30306, 7437, 256, -75, -6, 1], 'lmfdb_label': '136242.m3', 'torsion': [4]}
  • id: 6166467
    {'degree': 12, 'field': [12689, 18438, 11541, -51530, 5730, 21198, -2487, -3606, 510, 250, -39, -6, 1], 'lmfdb_label': '136242.m3', 'torsion': [2, 6]}
  • id: 6166466
    {'degree': 12, 'field': [121168, 95784, -59112, -66490, 16845, 17664, -2653, -2526, 330, 190, -27, -6, 1], 'lmfdb_label': '136242.m3', 'torsion': [3, 3]}
  • id: 6166470
    {'degree': 18, 'field': [-15865739, -10006818, 27026619, 16583743, -18940701, -10343793, 7712167, 3381255, -1994193, -644194, 326202, 73995, -33153, -5061, 2031, 190, -69, -3, 1], 'lmfdb_label': '136242.m3', 'torsion': [42]}
  • id: 6166468
    {'degree': 18, 'field': [-801739, -3624327, -3523167, 8509974, 8231292, -9237798, -5164140, 4786830, 1364391, -1257971, -161199, 180342, 5238, -14112, 504, 564, -45, -9, 1], 'lmfdb_label': '136242.m3', 'torsion': [9]}
  • id: 6166469
    {'degree': 18, 'field': [251646084, 205060086, 46327410, -100669149, -23588010, 19732491, 24908211, 10166229, 1925505, -206178, -40041, -18045, 15390, 1809, 243, -75, -9, 0, 1], 'lmfdb_label': '136242.m3', 'torsion': [6]}
• 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: 3360752
    {'conductor': 136242, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '136242.m3', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 3360753
    {'conductor': 136242, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '136242.m3', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 3360754
    {'conductor': 136242, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '136242.m3', 'prime': 29, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
• ec_galrep •

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

  
  
  • id: 2549784
    {'adelic_gens': [[10585, 4032, 10584, 10585], [1, 0, 2436, 1], [1, 0, 4032, 1], [3046, 6873, 12789, 9745], [13399, 6090, 4263, 1219], [1, 9744, 0, 1], [1, 6264, 0, 1], [10583, 0, 0, 14615], [6729, 3538, 6496, 3945], [1, 6090, 0, 2089], [4873, 9744, 4872, 9745], [8527, 3306, 2436, 13399], [11369, 12992, 1624, 12993], [12181, 6090, 12789, 6091], [1, 0, 8526, 1], [1, 7482, 6090, 7309], [1, 0, 9744, 1]], 'adelic_image': '14616.768.21.?', 'conductor': 136242, 'lmfdb_label': '136242.m3', 'prime': 0}
  • id: 527550
    {'conductor': 136242, 'elladic_image': '8.2.0.1', 'lmfdb_label': '136242.m3', 'modell_image': '2G', 'prime': 2}
  • id: 527551
    {'conductor': 136242, 'elladic_image': '3.4.0.1', 'lmfdb_label': '136242.m3', 'modell_image': '3B', 'prime': 3}
  • id: 527552
    {'conductor': 136242, 'elladic_image': '7.8.0.1', 'lmfdb_label': '136242.m3', 'modell_image': '7B', 'prime': 7}
• lmfdb_iso 136242.m does not appear in ec_padic