Elliptic curve data - 12705.b1

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '12705b', 'Clabel': '12705b3', 'Cnumber': 3, 'abc_quality': 0.9461737456442991, 'absD': 23353408675125375, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 9240, 'ainvs': [1, 1, 1, -256946, 49482368], 'analytic_rank': 2, 'bad_primes': [3, 5, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 12705, 'degree': 138240, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.9505441948418713975514237961', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 4], 'jinv': [1058993490188089, 13182390375], 'lmfdb_iso': '12705.b', 'lmfdb_label': '12705.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -2123, -38142], 'min_quad_twist_disc': -11, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '56.12.0-4.c.1.5', '60.12.0.h.1', '132.12.0.?', '220.12.0.?', '660.24.0.?', '840.24.0.?', '1848.24.0.?', '3080.24.0.?', '9240.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 12, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '4.6628648860723494451821171135', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.75159655844268612552045200712', 'prec': 103}, 'szpiro_ratio': 5.183572296406055, '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, -1, -1, -1, 1, -1, 3, 1, 1, 0, 1, 2, 1, 1, -1, -6, -1, -4, 1], 'aplist': [-1, -1, -1, -1, 0, 2, -6, -4, -4, -10, -4, -2, -10, -12, 0, 10, -12, 2, 4, 8, 14, -4, -8, 6, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 12705, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '12705.b', 'trace_hash': 2256901621822595682}
• 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': '0.020219892343063311992969587849', 'prec': 107}, 'conductor': 12705, 'gens': [[-16, 7328, 1], [329, 668, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.3725806522960450404032244594', 'prec': 100}, {'__RealLiteral__': 0, 'data': '3.4946753717153670206361427785', 'prec': 100}], 'lmfdb_label': '12705.b1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.38112970285632894624383657755', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.5543126169759293376996954534188296069', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[1267, -1271, 2]], 'xcoord_integral_points': [-302, -16, 182, 329, 337, 3977]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 0], '3': [2, 0], '5': [2, 0], '7': [2, 0], '11': 'a', '13': [4, 0], '17': [2, 0], '19': [4, 0], '23': [2, 0], '29': [2, 0], '31': [4, 0], '37': [2, 0], '41': [2, 0], '43': [2, 0], '47': [2, 2, 0]}, 'iwp0': 0, 'lmfdb_label': '12705.b1'}
• ec_torsion_growth •

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

  
  
  • id: 655566
    {'degree': 2, 'field': [-55, 0, 1], 'lmfdb_label': '12705.b1', 'torsion': [4]}
  • id: 655565
    {'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '12705.b1', 'torsion': [2, 2]}
  • id: 655567
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '12705.b1', 'torsion': [4]}
  • id: 655568
    {'degree': 4, 'field': [100, 0, -35, 0, 1], 'lmfdb_label': '12705.b1', 'torsion': [2, 4]}
  • id: 655572
    {'degree': 8, 'field': [59, -1208, 1262, -109, 58, -7, 7, -4, 1], 'lmfdb_label': '12705.b1', 'torsion': [6]}
  • id: 655571
    {'degree': 8, 'field': [625, 0, 175, 0, 120, 0, 7, 0, 1], 'lmfdb_label': '12705.b1', 'torsion': [8]}
  • id: 655570
    {'degree': 8, 'field': [3721, 0, -35312, 0, 3974, 0, -128, 0, 1], 'lmfdb_label': '12705.b1', 'torsion': [8]}
  • id: 655569
    {'degree': 8, 'field': [24066, 16020, 5202, 1440, 339, -60, 18, 0, 1], 'lmfdb_label': '12705.b1', 'torsion': [2, 4]}
  • id: 655575
    {'degree': 16, 'field': [360000, 0, -152520000, 0, 122672500, 0, -36217500, 0, 4998225, 0, -341200, 0, 11550, 0, -180, 0, 1], 'lmfdb_label': '12705.b1', 'torsion': [2, 8]}
  • id: 655578
    {'degree': 16, 'field': [960217, 1023163, -337972, -500475, -136834, -11482, 10255, 27933, 2065, -6474, 5509, -1391, 524, -129, 23, -4, 1], 'lmfdb_label': '12705.b1', 'torsion': [12]}
  • id: 655573
    {'degree': 16, 'field': [4307656, -10403280, 9100728, -2612640, -1021940, 1108080, 56808, -90480, 55494, 23340, 1062, 0, 115, -60, -18, 0, 1], 'lmfdb_label': '12705.b1', 'torsion': [4, 4]}
  • id: 655574
    {'degree': 16, 'field': [29872084, -30393044, 16459118, 7177494, -1333435, -610504, 1491238, -138084, -186638, 59502, 24742, -5036, -358, 324, -4, -4, 1], 'lmfdb_label': '12705.b1', 'torsion': [2, 8]}
  • id: 655577
    {'degree': 16, 'field': [375390625, 0, -2727500000, 0, 447625000, 0, -65578125, 0, 3892500, 0, -159375, 0, 4825, 0, -110, 0, 1], 'lmfdb_label': '12705.b1', 'torsion': [12]}
  • id: 655576
    {'degree': 16, 'field': [6481530661, -241438904, 323522670, -127573314, -24325668, 96463740, -17218529, -11790296, 1725720, 748320, -85083, -33120, 3791, 770, -90, -8, 1], 'lmfdb_label': '12705.b1', '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: 275459
    {'conductor': 12705, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '12705.b1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 275460
    {'conductor': 12705, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '12705.b1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 275461
    {'conductor': 12705, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '12705.b1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 275462
    {'conductor': 12705, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '12705.b1', 'prime': 11, '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: 1748322
    {'adelic_gens': [[8088, 3473, 8113, 8160], [9233, 8, 9232, 9], [1, 0, 8, 1], [1, 8, 0, 1], [3088, 3, 3085, 2], [5779, 5778, 8098, 3475], [1, 4, 4, 17], [7, 6, 9234, 9235], [5281, 8, 2644, 33], [5548, 1, 1871, 6], [6719, 9232, 8396, 9207]], 'adelic_image': '9240.48.0.?', 'conductor': 12705, 'lmfdb_label': '12705.b1', 'prime': 0}
  • id: 60416
    {'conductor': 12705, 'elladic_image': '4.6.0.1', 'lmfdb_label': '12705.b1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 557722
    {'lmfdb_iso': '12705.b', 'p': 13, 'prec': 20, 'unit': 25227811601698677919, 'val': 3}
  • id: 557724
    {'lmfdb_iso': '12705.b', 'p': 17, 'prec': 20, 'unit': 85765127789498514060757, 'val': 2}
  • id: 557714
    {'lmfdb_iso': '12705.b', 'p': 19, 'prec': 20, 'unit': 18139535975778162488272, 'val': 3}
  • id: 557728
    {'lmfdb_iso': '12705.b', 'p': 23, 'prec': 20, 'unit': 74287731825405182078741309, 'val': 2}
  • id: 557721
    {'lmfdb_iso': '12705.b', 'p': 29, 'prec': 20, 'unit': 2536696306231790768845543861, 'val': 2}
  • id: 557732
    {'lmfdb_iso': '12705.b', 'p': 31, 'prec': 20, 'unit': 345495992536263679544765990, 'val': 3}
  • id: 557717
    {'lmfdb_iso': '12705.b', 'p': 37, 'prec': 20, 'unit': 153446954966235510205893101053, 'val': 2}
  • id: 557719
    {'lmfdb_iso': '12705.b', 'p': 41, 'prec': 20, 'unit': 3770927495841592862326301945282, 'val': 2}
  • id: 557720
    {'lmfdb_iso': '12705.b', 'p': 43, 'prec': 20, 'unit': 4655472558921112534489745699772, 'val': 2}
  • id: 557726
    {'lmfdb_iso': '12705.b', 'p': 53, 'prec': 20, 'unit': 481926213514788805947245841056393, 'val': 2}
  • id: 557730
    {'lmfdb_iso': '12705.b', 'p': 59, 'prec': 20, 'unit': 3585666232156808250872725878508204, 'val': 2}
  • id: 557731
    {'lmfdb_iso': '12705.b', 'p': 61, 'prec': 20, 'unit': 4091604605372014011804115958513475, 'val': 2}
  • id: 557716
    {'lmfdb_iso': '12705.b', 'p': 67, 'prec': 20, 'unit': 9579766925861882733939748164169430, 'val': 2}
  • id: 557718
    {'lmfdb_iso': '12705.b', 'p': 71, 'prec': 20, 'unit': 35136085834537508160626724255538295, 'val': 2}
  • id: 557727
    {'lmfdb_iso': '12705.b', 'p': 73, 'prec': 20, 'unit': 37663254650950995580242192887550569, 'val': 2}
  • id: 557723
    {'lmfdb_iso': '12705.b', 'p': 79, 'prec': 20, 'unit': 875960311354037352619029182786215060, 'val': 2}
  • id: 557725
    {'lmfdb_iso': '12705.b', 'p': 83, 'prec': 20, 'unit': 1148990821226997911481047834615184993, 'val': 2}
  • id: 557729
    {'lmfdb_iso': '12705.b', 'p': 89, 'prec': 20, 'unit': 2185597927367070103715832330670673064, 'val': 2}
  • id: 557715
    {'lmfdb_iso': '12705.b', 'p': 97, 'prec': 20, 'unit': 52425044253385391189229353692112870413, 'val': 2}