Elliptic curve data - 85008.p2

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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
  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': '85008be', 'Clabel': '85008be3', 'Cnumber': 3, 'abc_quality': 1.0017367140902569, 'absD': 8349326054535915896832, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 21252, 'ainvs': [0, -1, 0, -45673768, 118905271408], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 11, 23], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 85008, 'degree': 8626176, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.1368984032879965662275782021', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 3, 'intrinsic_torsion': 1, 'iso_nlabel': 15, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [-2572552807198813678947625, 2038409681283182592], 'lmfdb_iso': '85008.p', 'lmfdb_label': '85008.p2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -2854611, -1857894866], 'min_quad_twist_disc': -4, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '12.24.0-6.a.1.9', '14.6.0.b.1', '42.24.0.b.1', '84.48.0.?', '1012.6.0.?', '3036.48.0.?', '7084.12.0.?', '21252.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 7, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.2068127066108937915650376540', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 7], [3, 4, 176], [7, 8, 12144], [11, 12, 7728], [23, 24, 3696]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.4437512227280512568103460806', 'prec': 100}, 'szpiro_ratio': 5.684866014987619, '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, 0, 0, -1, 0, 1, 0, -1, 0, -4, 0, 0, 0, -6, 0, 4, 0], 'aplist': [0, -1, 0, -1, -1, -4, -6, 4, 1, -6, -8, 2, 12, 4, 0, 6, 0, -10, -8, 0, -4, 16, 0, 0, 8], 'class_deg': 6, 'class_size': 4, 'conductor': 85008, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '85008.p', 'trace_hash': 1420710182264535143}
• 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': '0.0018850577789746319117665184393', 'prec': 110}, 'conductor': 85008, 'gens': [[3972, 11776, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.2068127066108937915650376540', 'prec': 100}], 'lmfdb_label': '85008.p2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.12984416895047828307995765274', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.7607422312504529635374413639060832578', 'prec': 130}, 'tamagawa_product': 96, 'torsion_generators': [[-7804, 0, 1]], 'xcoord_integral_points': [-7804, -3043, 3834, 3972]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [1, 1, 0], '7': [3, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [2, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '85008.p2'}
• ec_torsion_growth •

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

  
  
  • id: 3986781
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '85008.p2', 'torsion': [6]}
  • id: 3986780
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '85008.p2', 'torsion': [2, 2]}
  • id: 3986782
    {'degree': 4, 'field': [-63, 0, -1, 0, 1], 'lmfdb_label': '85008.p2', 'torsion': [4]}
  • id: 3986783
    {'degree': 4, 'field': [22, 2, -1, -2, 1], 'lmfdb_label': '85008.p2', 'torsion': [2, 6]}
  • id: 3986784
    {'degree': 6, 'field': [9801, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '85008.p2', 'torsion': [6]}
  • id: 3986785
    {'degree': 8, 'field': [792, -348, -34, 12, 21, -26, 8, -2, 1], 'lmfdb_label': '85008.p2', 'torsion': [2, 4]}
  • id: 3986787
    {'degree': 8, 'field': [3249, 0, -2238, 0, -65, 0, -14, 0, 1], 'lmfdb_label': '85008.p2', 'torsion': [12]}
  • id: 3986786
    {'degree': 8, 'field': [3749, -1426, 1320, 206, -87, -22, 12, -4, 1], 'lmfdb_label': '85008.p2', 'torsion': [2, 4]}
  • id: 3986788
    {'degree': 12, 'field': [132496, 0, 76920, 0, 14361, 0, -139, 0, -192, 0, -3, 0, 1], 'lmfdb_label': '85008.p2', 'torsion': [3, 6]}
  • id: 3986789
    {'degree': 12, 'field': [96147874, -17463006, 1440603, -3904362, 264783, 13662, 58707, 0, 39, -396, -9, 0, 1], 'lmfdb_label': '85008.p2', 'torsion': [2, 6]}
  • id: 3986791
    {'degree': 16, 'field': [393184, -32448, -177880, 172552, 37164, -129624, 92610, -31478, 10737, -3966, 1336, -774, 314, -98, 22, -4, 1], 'lmfdb_label': '85008.p2', 'torsion': [2, 12]}
  • id: 3986792
    {'degree': 16, 'field': [50020573, -2881876, 9478552, -13111684, 6551258, -552568, 1111872, -789916, 190043, 6424, -2904, 1060, -298, 28, 16, -8, 1], 'lmfdb_label': '85008.p2', 'torsion': [2, 12]}
  • id: 3986790
    {'degree': 16, 'field': [39375486950121, 0, 10075783415922, 0, -293175643943, 0, -13904867690, 0, 91153300, 0, 399182, 0, -2903, 0, -134, 0, 1], 'lmfdb_label': '85008.p2', 'torsion': [8]}
  • id: 3986793
    {'degree': 18, 'field': [-315524363959728, 0, 182841428933856, 0, -25825968652176, 0, 2124215615313, 0, -119801941974, 0, 2113414479, 0, 19055196, 0, 137439, 0, 426, 0, 1], 'lmfdb_label': '85008.p2', 'torsion': [18]}
• 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: 2073170
    {'conductor': 85008, 'conductor_valuation': 4, 'discriminant_valuation': 24, 'j_denominator_valuation': 12, 'kodaira_symbol': -20, 'lmfdb_label': '85008.p2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 2073171
    {'conductor': 85008, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '85008.p2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2073172
    {'conductor': 85008, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '85008.p2', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 2073173
    {'conductor': 85008, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '85008.p2', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2073174
    {'conductor': 85008, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '85008.p2', 'prime': 23, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
• ec_galrep •

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

  
  
  • id: 2224091
    {'adelic_gens': [[11, 2, 21202, 21243], [1761, 8852, 1798, 8863], [925, 12, 5550, 73], [1, 0, 12, 1], [1, 6, 6, 37], [7085, 12, 7084, 1], [21241, 12, 21240, 13], [15457, 12, 7734, 73], [1, 12, 0, 1], [12154, 3, 18189, 21244]], 'adelic_image': '21252.96.1.?', 'conductor': 85008, 'lmfdb_label': '85008.p2', 'prime': 0}
  • id: 347187
    {'conductor': 85008, 'elladic_image': '2.3.0.1', 'lmfdb_label': '85008.p2', 'modell_image': '2B', 'prime': 2}
  • id: 347188
    {'conductor': 85008, 'elladic_image': '3.4.0.1', 'lmfdb_label': '85008.p2', 'modell_image': '3B', 'prime': 3}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 4388455
    {'lmfdb_iso': '85008.p', 'p': 13, 'prec': 20, 'unit': 1282864559773744100174, 'val': 1}
  • id: 4388457
    {'lmfdb_iso': '85008.p', 'p': 17, 'prec': 20, 'unit': 194990088802679493729695, 'val': 1}
  • id: 4388458
    {'lmfdb_iso': '85008.p', 'p': 19, 'prec': 20, 'unit': 34462446524018713896305, 'val': 1}
  • id: 4388454
    {'lmfdb_iso': '85008.p', 'p': 29, 'prec': 20, 'unit': 80867005082644426800604453, 'val': 1}
  • id: 4388462
    {'lmfdb_iso': '85008.p', 'p': 31, 'prec': 20, 'unit': 1384146940508024418567503685, 'val': 1}
  • id: 4388451
    {'lmfdb_iso': '85008.p', 'p': 37, 'prec': 20, 'unit': 21046800397037812148786270063, 'val': 1}
  • id: 4388452
    {'lmfdb_iso': '85008.p', 'p': 41, 'prec': 20, 'unit': 188049836383090784616914133657, 'val': 1}
  • id: 4388453
    {'lmfdb_iso': '85008.p', 'p': 43, 'prec': 20, 'unit': 4454608731462274448025720201725, 'val': 1}
  • id: 4388459
    {'lmfdb_iso': '85008.p', 'p': 53, 'prec': 20, 'unit': 224363279889617872928764221475825, 'val': 1}
  • id: 4388461
    {'lmfdb_iso': '85008.p', 'p': 61, 'prec': 20, 'unit': 2005681619577410521679921362715653, 'val': 1}
  • id: 4388450
    {'lmfdb_iso': '85008.p', 'p': 67, 'prec': 20, 'unit': 9624995081569419411480140584468239, 'val': 1}
  • id: 4388460
    {'lmfdb_iso': '85008.p', 'p': 73, 'prec': 20, 'unit': 92139668922927130320466963274193997, 'val': 1}
  • id: 4388456
    {'lmfdb_iso': '85008.p', 'p': 79, 'prec': 20, 'unit': 1035008104902922992433164164188617493, 'val': 1}
  • id: 4388449
    {'lmfdb_iso': '85008.p', 'p': 97, 'prec': 20, 'unit': 32007504168057261407895867187787483475, 'val': 1}