Elliptic curve data - 36414.j1

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• 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': '36414t', 'Clabel': '36414t6', 'Cnumber': 6, 'abc_quality': 1.0624727966937526, 'absD': 315695602490628590375454792, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 816, 'ainvs': [1, -1, 0, -35682089058, 2594328654970476], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 17], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 36414, 'degree': 70778880, 'elladic_images': ['8.48.0.217'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.5450417856851806483571970485', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 9, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [285531136548675601769470657, 17941034271597192], 'lmfdb_iso': '36414.j', 'lmfdb_label': '36414.j1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -13718604, -19563199515], 'min_quad_twist_disc': -51, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.48.0.p.1', '48.96.0-8.p.1.3', '204.12.0.?', '272.96.1.?', '408.96.0.?', '816.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 2601], [3, 8, 2023], [7, 8, 5202], [17, 162, 126]], 'sha': 9, 'sha_primes': [3], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.5791289693230177625348071211', 'prec': 100}, 'szpiro_ratio': 8.046243152055524, '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, -2, 0, -1, -1, 0, 2, 4, 0, -2, 1, 0, 1, 0, 0, 4, -2], 'aplist': [-1, 0, -2, -1, 4, -2, 0, 4, 8, 6, 0, 2, 10, -4, 0, -6, 4, -6, -12, -8, 6, 0, 12, 6, -2], 'class_deg': 8, 'class_size': 6, 'conductor': 36414, 'isogeny_matrix': [[1, 2, 4, 4, 8, 8], [2, 1, 2, 2, 4, 4], [4, 2, 1, 4, 8, 8], [4, 2, 4, 1, 2, 2], [8, 4, 8, 2, 1, 4], [8, 4, 8, 2, 4, 1]], 'lmfdb_iso': '36414.j', 'trace_hash': 182158145277614735}
• 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': '0.00011277864306343700035237328251', 'prec': 113}, 'conductor': 36414, 'gens': [], 'heights': [], 'lmfdb_label': '36414.j1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.041067651518058182304853956008', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '9.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4784354546500945629747424163023745029', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[436323, -436323, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [10, 0], '3': 'a', '7': [0, 0], '17': 'a'}, 'iwp0': 5, 'lmfdb_label': '36414.j1'}
• ec_torsion_growth •

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

  
  
  • id: 1804111
    {'degree': 2, 'field': [-102, 0, 1], 'lmfdb_label': '36414.j1', 'torsion': [4]}
  • id: 1804110
    {'degree': 2, 'field': [-51, 0, 1], 'lmfdb_label': '36414.j1', 'torsion': [8]}
  • id: 1804109
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '36414.j1', 'torsion': [2, 2]}
  • id: 1804112
    {'degree': 4, 'field': [625, 0, -52, 0, 1], 'lmfdb_label': '36414.j1', 'torsion': [2, 8]}
  • id: 1804116
    {'degree': 8, 'field': [-58904, 10388, -11210, 1643, -818, -7, 7, -4, 1], 'lmfdb_label': '36414.j1', 'torsion': [6]}
  • id: 1804115
    {'degree': 8, 'field': [324, 0, 36, 0, -14, 0, 2, 0, 1], 'lmfdb_label': '36414.j1', 'torsion': [16]}
  • id: 1804113
    {'degree': 8, 'field': [10039, -23684, 24502, -1688, 975, -160, 58, -4, 1], 'lmfdb_label': '36414.j1', 'torsion': [2, 4]}
  • id: 1804114
    {'degree': 8, 'field': [66291, 6108, -4898, -2472, 1367, -160, 58, -4, 1], 'lmfdb_label': '36414.j1', 'torsion': [8]}
  • id: 1804119
    {'degree': 16, 'field': [138384, 0, -349440, 0, 242560, 0, -21504, 0, -3480, 0, -448, 0, 96, 0, 0, 0, 1], 'lmfdb_label': '36414.j1', 'torsion': [2, 16]}
  • id: 1804123
    {'degree': 16, 'field': [23669992, 70886272, -51598320, -56990800, 68838716, -32002332, -18091799, 27501400, -10508274, 2530270, -614327, 58980, -9739, -70, 30, -8, 1], 'lmfdb_label': '36414.j1', 'torsion': [12]}
  • id: 1804120
    {'degree': 16, 'field': [92236816, 0, -527067520, 0, 438595472, 0, -133111440, 0, 17789009, 0, -1070160, 0, 26852, 0, -280, 0, 1], 'lmfdb_label': '36414.j1', 'torsion': [2, 16]}
  • id: 1804117
    {'degree': 16, 'field': [266993721, 98582184, -126363840, 49824936, -7433552, -30024456, 25933320, -15366112, 6057857, -1589848, 432572, -65464, 13398, -1176, 188, -8, 1], 'lmfdb_label': '36414.j1', 'torsion': [4, 8]}
  • id: 1804118
    {'degree': 16, 'field': [805987561, -543079144, 669517988, -273949200, 191651866, -71331512, 33682320, -9252760, 3300515, -711992, 197680, -32088, 6986, -784, 132, -8, 1], 'lmfdb_label': '36414.j1', 'torsion': [2, 8]}
  • id: 1804122
    {'degree': 16, 'field': [830477124, 0, -444046947, 0, 106219426, 0, -16698525, 0, 1741059, 0, -115241, 0, 4587, 0, -102, 0, 1], 'lmfdb_label': '36414.j1', 'torsion': [24]}
  • id: 1804121
    {'degree': 16, 'field': [6773624584, -1796382544, 1947282044, -307373520, 167745638, -17184572, 6161929, -187944, -193904, 177966, -53147, 9788, -1783, 42, 14, -8, 1], 'lmfdb_label': '36414.j1', 'torsion': [2, 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: 858233
    {'conductor': 36414, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '36414.j1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 858234
    {'conductor': 36414, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '36414.j1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 858235
    {'conductor': 36414, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '36414.j1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 858236
    {'conductor': 36414, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '36414.j1', 'prime': 17, '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: 1907512
    {'adelic_gens': [[5, 4, 812, 813], [76, 345, 411, 682], [1, 16, 0, 1], [271, 0, 0, 815], [15, 2, 718, 803], [727, 288, 798, 25], [1, 0, 16, 1], [801, 16, 800, 17], [575, 528, 792, 143]], 'adelic_image': '816.192.1.?', 'conductor': 36414, 'lmfdb_label': '36414.j1', 'prime': 0}
  • id: 161368
    {'conductor': 36414, 'elladic_image': '8.48.0.217', 'lmfdb_label': '36414.j1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 36414.j does not appear in ec_padic