Elliptic curve data - 68970.cv3

Formats: - HTML - YAML - JSON - 2024-06-08T22:48:45.326438

• 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': '68970cv', 'Clabel': '68970cv6', 'Cnumber': 6, 'abc_quality': 1.035453641620829, 'absD': 1224669221170932350185574400, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 12540, 'ainvs': [1, 0, 0, -273203785, 431436105497], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11, 19], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 68970, 'degree': 46448640, 'elladic_images': ['4.12.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.8886188516818057261164517543', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 6, 'iso_nlabel': 73, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [1272998045160051207059881, 691293848290254950400], 'lmfdb_iso': '68970.cv', 'lmfdb_label': '68970.cv3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -2257883, -324349594], 'min_quad_twist_disc': -11, 'modell_images': ['2Cs', '3B'], 'modm_images': ['2.6.0.a.1', '3.4.0.a.1', '4.12.0-2.a.1.1', '6.24.0.a.1', '12.48.0-6.a.1.1', '33.8.0-3.a.1.1', '60.96.0-60.a.1.27', '66.48.0-6.a.1.2', '132.96.0.?', '220.24.0.?', '228.96.0.?', '380.24.0.?', '660.192.1.?', '836.24.0.?', '1140.192.1.?', '2508.192.1.?', '4180.48.0.?', '12540.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '7.4452673648112963902983708635', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.6896712152826204540854799653', 'prec': 100}, 'szpiro_ratio': 6.273055438913152, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, 4, 1, 1, 1, 0, 1, -2, 4, 1, 1, -6, 1, -1, 1], 'aplist': [1, 1, 1, 4, 0, -2, -6, -1, 0, 6, -4, 2, -6, -8, 0, -6, 0, -14, -4, -12, 10, -8, 0, -6, -10], 'class_deg': 12, 'class_size': 8, 'conductor': 68970, 'isogeny_matrix': [[1, 3, 2, 4, 6, 12, 12, 4], [3, 1, 6, 12, 2, 4, 4, 12], [2, 6, 1, 2, 3, 6, 6, 2], [4, 12, 2, 1, 6, 12, 3, 4], [6, 2, 3, 6, 1, 2, 2, 6], [12, 4, 6, 12, 2, 1, 4, 3], [12, 4, 6, 3, 2, 4, 1, 12], [4, 12, 2, 4, 6, 3, 12, 1]], 'lmfdb_iso': '68970.cv', 'trace_hash': 2079427269271122997}
• 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': '0.00041916844447987317073259956766', 'prec': 113}, 'conductor': 68970, 'gens': [[-16078, 825275, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '7.4452673648112963902983708635', 'prec': 100}], 'lmfdb_label': '68970.cv3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.042336108267115254306831969381', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '15.129774971245004598413190075541416293', 'prec': 130}, 'tamagawa_product': 768, 'torsion_generators': [[1594, -797, 1], [15674, -7837, 1]], 'xcoord_integral_points': [-16078, 1594, 15674]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [5, 1], '3': [4, 0], '5': [2, 0], '7': [1, 0], '11': 'a', '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [3, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '68970.cv3'}
• ec_torsion_growth •

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

  
  
  • id: 3280454
    {'degree': 2, 'field': [-55, 0, 1], 'lmfdb_label': '68970.cv3', 'torsion': [2, 4]}
  • id: 3280455
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '68970.cv3', 'torsion': [2, 6]}
  • id: 3280458
    {'degree': 4, 'field': [100, 0, -35, 0, 1], 'lmfdb_label': '68970.cv3', 'torsion': [2, 12]}
  • id: 3280457
    {'degree': 4, 'field': [454, -127, -7, -1, 1], 'lmfdb_label': '68970.cv3', 'torsion': [2, 4]}
  • id: 3280456
    {'degree': 4, 'field': [2704, 0, 105, 0, 1], 'lmfdb_label': '68970.cv3', 'torsion': [2, 4]}
  • id: 3280459
    {'degree': 6, 'field': [2412, -702, -99, 71, 12, -3, 1], 'lmfdb_label': '68970.cv3', 'torsion': [2, 6]}
  • id: 3280461
    {'degree': 8, 'field': [-240600, -99000, 29950, 14850, -135, -550, -60, 0, 1], 'lmfdb_label': '68970.cv3', 'torsion': [2, 8]}
  • id: 3280463
    {'degree': 8, 'field': [16, 0, 9705, 0, 1571, 0, 75, 0, 1], 'lmfdb_label': '68970.cv3', 'torsion': [2, 12]}
  • id: 3280462
    {'degree': 8, 'field': [256, 0, 240, 0, 872, 0, 15, 0, 1], 'lmfdb_label': '68970.cv3', 'torsion': [2, 12]}
  • id: 3280460
    {'degree': 8, 'field': [206116, 0, 22485, 0, 703, 0, 15, 0, 1], 'lmfdb_label': '68970.cv3', 'torsion': [4, 4]}
  • id: 3280465
    {'degree': 12, 'field': [3204, -9828, 7398, 4230, -405, -2448, 1531, -726, 330, -110, 33, -6, 1], 'lmfdb_label': '68970.cv3', 'torsion': [2, 12]}
  • id: 3280464
    {'degree': 12, 'field': [7104, -21744, 23292, -11136, 7929, -207, -1163, 546, 6, 2, -3, -3, 1], 'lmfdb_label': '68970.cv3', 'torsion': [6, 6]}
  • id: 3280469
    {'degree': 16, 'field': [-814456544, 655184992, 101489784, -324853848, 131981228, 11812192, -26199714, 7653746, 215313, -670838, 160104, -4174, -4822, 894, -54, -4, 1], 'lmfdb_label': '68970.cv3', 'torsion': [2, 24]}
  • id: 3280466
    {'degree': 16, 'field': [100000000, 0, 0, 0, 22810000, 0, 0, 0, -316200, 0, 0, 0, 2281, 0, 0, 0, 1], 'lmfdb_label': '68970.cv3', 'torsion': [2, 8]}
  • id: 3280467
    {'degree': 16, 'field': [655360000, 0, 0, 0, 83328000, 0, 0, 0, 1392400, 0, 0, 0, 120, 0, 0, 0, 1], 'lmfdb_label': '68970.cv3', 'torsion': [2, 8]}
  • id: 3280468
    {'degree': 16, 'field': [1955762176, 0, 285837824, 0, -14868592, 0, -3445464, 0, 91193, 0, 15132, 0, -418, 0, -28, 0, 1], 'lmfdb_label': '68970.cv3', 'torsion': [4, 12]}
  • id: 3280470
    {'degree': 18, 'field': [29843453911530352, 20640827922798864, -45940589013446976, 13928568198324884, 1241658210188928, -610840354900488, 11101457015372, 7971538751670, -472481168940, -51686750599, 5082960927, 364727490, -40736014, -1560084, 205464, 3824, -618, -9, 1], 'lmfdb_label': '68970.cv3', 'torsion': [2, 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: 1669802
    {'conductor': 68970, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '68970.cv3', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
  • id: 1669803
    {'conductor': 68970, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '68970.cv3', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1669804
    {'conductor': 68970, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '68970.cv3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1669805
    {'conductor': 68970, 'conductor_valuation': 2, 'discriminant_valuation': 12, 'j_denominator_valuation': 6, 'kodaira_symbol': -10, 'lmfdb_label': '68970.cv3', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1669806
    {'conductor': 68970, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '68970.cv3', 'prime': 19, 'reduction_type': -1, '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: 2120355
    {'adelic_gens': [[3419, 12534, 0, 12539], [6277, 6, 12492, 12499], [9901, 12, 9246, 73], [4181, 12, 4180, 1], [1, 0, 12, 1], [12529, 12, 12528, 13], [9, 4, 12524, 12533], [10039, 6, 7518, 12535], [1, 12, 0, 1]], 'adelic_image': '12540.384.5.?', 'conductor': 68970, 'lmfdb_label': '68970.cv3', 'prime': 0}
  • id: 287756
    {'conductor': 68970, 'elladic_image': '4.12.0.1', 'lmfdb_label': '68970.cv3', 'modell_image': '2Cs', 'prime': 2}
  • id: 287757
    {'conductor': 68970, 'elladic_image': '3.4.0.1', 'lmfdb_label': '68970.cv3', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 3530338
    {'lmfdb_iso': '68970.cv', 'p': 7, 'prec': 20, 'unit': 3932836170525373, 'val': 1}
  • id: 3530342
    {'lmfdb_iso': '68970.cv', 'p': 13, 'prec': 20, 'unit': 1364003730617970579883, 'val': 1}
  • id: 3530344
    {'lmfdb_iso': '68970.cv', 'p': 17, 'prec': 20, 'unit': 189243272368985862759296, 'val': 1}
  • id: 3530341
    {'lmfdb_iso': '68970.cv', 'p': 29, 'prec': 20, 'unit': 4927140700097079869830347890, 'val': 1}
  • id: 3530350
    {'lmfdb_iso': '68970.cv', 'p': 31, 'prec': 20, 'unit': 180681338238837273360569267, 'val': 2}
  • id: 3530337
    {'lmfdb_iso': '68970.cv', 'p': 37, 'prec': 20, 'unit': 617635264274660562425125220578, 'val': 1}
  • id: 3530339
    {'lmfdb_iso': '68970.cv', 'p': 41, 'prec': 20, 'unit': 812269283203920922147236799702, 'val': 1}
  • id: 3530340
    {'lmfdb_iso': '68970.cv', 'p': 43, 'prec': 20, 'unit': 7062415087362296219633335349627, 'val': 1}
  • id: 3530345
    {'lmfdb_iso': '68970.cv', 'p': 53, 'prec': 20, 'unit': 124486872636764745112190326567470, 'val': 1}
  • id: 3530349
    {'lmfdb_iso': '68970.cv', 'p': 61, 'prec': 20, 'unit': 170967587970074929045430168932163, 'val': 1}
  • id: 3530336
    {'lmfdb_iso': '68970.cv', 'p': 67, 'prec': 20, 'unit': 46328515592268753645279471229710036, 'val': 1}
  • id: 3530348
    {'lmfdb_iso': '68970.cv', 'p': 71, 'prec': 20, 'unit': 125428431110152344083671296498414740, 'val': 1}
  • id: 3530346
    {'lmfdb_iso': '68970.cv', 'p': 73, 'prec': 20, 'unit': 162529884673014076817043610959196170, 'val': 1}
  • id: 3530343
    {'lmfdb_iso': '68970.cv', 'p': 79, 'prec': 20, 'unit': 175398877814032348112184693534432701, 'val': 1}
  • id: 3530347
    {'lmfdb_iso': '68970.cv', 'p': 89, 'prec': 20, 'unit': 507893225673132273361996113493138390, 'val': 1}
  • id: 3530335
    {'lmfdb_iso': '68970.cv', 'p': 97, 'prec': 20, 'unit': 11441553959244265328789111393365390170, 'val': 1}