Elliptic curve data - 12675.j3

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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': '12675e', 'Clabel': '12675e8', 'Cnumber': 8, 'abc_quality': 1.0142537292135114, 'absD': 448812367916107177734375, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 6240, 'ainvs': [1, 1, 1, -33504338, -81320581594], 'analytic_rank': 1, 'bad_primes': [3, 5, 13], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 12675, 'degree': 1548288, 'elladic_images': ['32.48.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.2766107027424524423013202609', 'prec': 100}, 'faltings_index': 7, 'faltings_ratio': 16, 'iso_nlabel': 9, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [-55150149867714721, 5950927734375], 'lmfdb_iso': '12675.j', 'lmfdb_label': '12675.j3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -7930, -296725], 'min_quad_twist_disc': 65, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '16.24.0.g.1', '24.24.0.bz.2', '32.48.0-16.g.1.7', '40.24.0-8.n.1.7', '48.48.0.bv.2', '60.12.0-4.c.1.1', '78.6.0.?', '80.48.0.?', '96.96.0.?', '104.24.0.?', '120.48.0.?', '156.12.0.?', '160.96.0.?', '208.96.2.?', '240.96.0.?', '260.12.0.?', '312.48.0.?', '416.192.2.?', '480.192.1.?', '520.48.0.?', '624.192.5.?', '780.24.0.?', '1040.192.2.?', '1248.384.5.?', '1560.96.0.?', '2080.384.5.?', '3120.384.5.?', '6240.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '33.245415966993148175863066666', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1894170677946338869741968735', 'prec': 100}, 'szpiro_ratio': 6.7496052914080105, '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, 0, 1, 0, 3, 1, 0, -4, 1, 0, 0, 0, -1, -2, -1, 4, 0], 'aplist': [-1, -1, 0, 0, -4, 0, -2, 4, -8, -2, 8, 6, 6, 4, -8, -6, 12, -2, -4, 0, -6, 16, -4, -10, 18], 'class_deg': 16, 'class_size': 8, 'conductor': 12675, 'isogeny_matrix': [[1, 2, 4, 4, 8, 16, 16, 8], [2, 1, 2, 2, 4, 8, 8, 4], [4, 2, 1, 4, 8, 16, 16, 8], [4, 2, 4, 1, 2, 4, 4, 2], [8, 4, 8, 2, 1, 2, 2, 4], [16, 8, 16, 4, 2, 1, 4, 8], [16, 8, 16, 4, 2, 4, 1, 8], [8, 4, 8, 2, 4, 8, 8, 1]], 'lmfdb_iso': '12675.j', 'trace_hash': 2007513197825622801}
• 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': '0.0014255160285926425293903158323', 'prec': 110}, 'conductor': 12675, 'gens': [[273832395417059, 4529637259164750529349, 12322]], 'heights': [{'__RealLiteral__': 0, 'data': '33.245415966993148175863066666', 'prec': 100}], 'lmfdb_label': '12675.j3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.031185809444467604292598219867', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.0735704144974180237630023840397854906', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[26995, -26999, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [5, 4], '3': [1, 0], '5': 'a', '7': [1, 3, 0], '11': [1, 0], '13': 'a', '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '12675.j3'}
• ec_torsion_growth •

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

  
  
  • id: 654114
    {'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '12675.j3', 'torsion': [4]}
  • id: 654113
    {'degree': 2, 'field': [10, -1, 1], 'lmfdb_label': '12675.j3', 'torsion': [2, 2]}
  • id: 654115
    {'degree': 2, 'field': [65, 0, 1], 'lmfdb_label': '12675.j3', 'torsion': [4]}
  • id: 654118
    {'degree': 4, 'field': [81, 0, -8, 0, 1], 'lmfdb_label': '12675.j3', 'torsion': [8]}
  • id: 654116
    {'degree': 4, 'field': [400, 0, 25, 0, 1], 'lmfdb_label': '12675.j3', 'torsion': [2, 4]}
  • id: 654117
    {'degree': 4, 'field': [3481, 0, 142, 0, 1], 'lmfdb_label': '12675.j3', 'torsion': [8]}
  • id: 654124
    {'degree': 8, 'field': [65, -260, 455, -455, 260, -65, 4, -4, 1], 'lmfdb_label': '12675.j3', 'torsion': [6]}
  • id: 654121
    {'degree': 8, 'field': [1210, -3740, 4574, -1724, 1003, -172, 62, -4, 1], 'lmfdb_label': '12675.j3', 'torsion': [2, 8]}
  • id: 654119
    {'degree': 8, 'field': [2440, 1460, -1286, -364, 223, -52, 22, -4, 1], 'lmfdb_label': '12675.j3', 'torsion': [2, 4]}
  • id: 654120
    {'degree': 8, 'field': [24336, 0, 0, 0, -2847, 0, 0, 0, 1], 'lmfdb_label': '12675.j3', 'torsion': [8]}
  • id: 654122
    {'degree': 8, 'field': [268225, -252200, 94280, -17680, 2566, -520, 88, 0, 1], 'lmfdb_label': '12675.j3', 'torsion': [16]}
  • id: 654123
    {'degree': 8, 'field': [28225089, -1384344, -1625880, 54288, 37510, -312, -328, 0, 1], 'lmfdb_label': '12675.j3', 'torsion': [16]}
  • id: 654125
    {'degree': 16, 'field': [19600, 0, 225920, 0, 433276, 0, 68432, 0, 21049, 0, 3536, 0, 394, 0, 32, 0, 1], 'lmfdb_label': '12675.j3', 'torsion': [4, 4]}
  • id: 654132
    {'degree': 16, 'field': [426465, -852930, 1279395, -937170, 468585, -63180, 45094, -46118, 26691, -15458, 7141, -1164, 79, 82, 24, -8, 1], 'lmfdb_label': '12675.j3', 'torsion': [12]}
  • id: 654129
    {'degree': 16, 'field': [2313441, 0, -12338352, 0, 50144328, 0, -5370144, 0, 12594920, 0, 137696, 0, 32968, 0, 208, 0, 1], 'lmfdb_label': '12675.j3', 'torsion': [32]}
  • id: 654127
    {'degree': 16, 'field': [8503056, 0, 0, 0, 629856, 0, 0, 0, 55521, 0, 0, 0, 216, 0, 0, 0, 1], 'lmfdb_label': '12675.j3', 'torsion': [16]}
  • id: 654130
    {'degree': 16, 'field': [10400625, 0, -673125, 0, 2143600, 0, 482550, 0, 43950, 0, -1705, 0, -120, 0, 0, 0, 1], 'lmfdb_label': '12675.j3', 'torsion': [2, 6]}
  • id: 654128
    {'degree': 16, 'field': [38925121, 0, 360474640, 0, 415962636, 0, 130215760, 0, 15492966, 0, 829360, 0, 20876, 0, 240, 0, 1], 'lmfdb_label': '12675.j3', 'torsion': [2, 16]}
  • id: 654126
    {'degree': 16, 'field': [605652100, 0, -80790520, 0, 17132416, 0, -1079932, 0, 113989, 0, -1036, 0, 574, 0, 8, 0, 1], 'lmfdb_label': '12675.j3', 'torsion': [2, 8]}
  • id: 654131
    {'degree': 16, 'field': [3570899049, 0, -577254663, 0, 26928540, 0, 9552624, 0, 203610, 0, -25239, 0, -347, 0, -10, 0, 1], 'lmfdb_label': '12675.j3', 'torsion': [12]}
• 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: 274828
    {'conductor': 12675, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '12675.j3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 274829
    {'conductor': 12675, 'conductor_valuation': 2, 'discriminant_valuation': 22, 'j_denominator_valuation': 16, 'kodaira_symbol': -20, 'lmfdb_label': '12675.j3', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 274830
    {'conductor': 12675, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '12675.j3', 'prime': 13, '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: 1748143
    {'adelic_gens': [[1, 0, 32, 1], [1951, 32, 406, 513], [23, 18, 3678, 4235], [6209, 32, 6208, 33], [3743, 6208, 3728, 5727], [2341, 32, 2356, 513], [5, 28, 68, 381], [30, 31, 4009, 6084], [1, 32, 0, 1], [4298, 6237, 3955, 212]], 'adelic_image': '6240.768.13.?', 'conductor': 12675, 'lmfdb_label': '12675.j3', 'prime': 0}
  • id: 60308
    {'conductor': 12675, 'elladic_image': '32.48.0.2', 'lmfdb_label': '12675.j3', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 556175
    {'lmfdb_iso': '12675.j', 'p': 11, 'prec': 20, 'unit': 59427118890945873367, 'val': 1}
  • id: 556176
    {'lmfdb_iso': '12675.j', 'p': 17, 'prec': 20, 'unit': 29249578018077619547753, 'val': 1}
  • id: 556177
    {'lmfdb_iso': '12675.j', 'p': 19, 'prec': 20, 'unit': 772015395892097243678892, 'val': 1}
  • id: 556181
    {'lmfdb_iso': '12675.j', 'p': 23, 'prec': 20, 'unit': 65897955600040455224182248, 'val': 1}
  • id: 556173
    {'lmfdb_iso': '12675.j', 'p': 29, 'prec': 20, 'unit': 4770098159034499786384957552, 'val': 1}
  • id: 556185
    {'lmfdb_iso': '12675.j', 'p': 31, 'prec': 20, 'unit': 14094662954229321190294735006, 'val': 1}
  • id: 556170
    {'lmfdb_iso': '12675.j', 'p': 37, 'prec': 20, 'unit': 597365273669659837077710060096, 'val': 1}
  • id: 556171
    {'lmfdb_iso': '12675.j', 'p': 41, 'prec': 20, 'unit': 1136487823517859203163672809573, 'val': 1}
  • id: 556172
    {'lmfdb_iso': '12675.j', 'p': 43, 'prec': 20, 'unit': 2293443503151790363279013001089, 'val': 1}
  • id: 556183
    {'lmfdb_iso': '12675.j', 'p': 47, 'prec': 20, 'unit': 12991561621934599735530569604833, 'val': 1}
  • id: 556178
    {'lmfdb_iso': '12675.j', 'p': 53, 'prec': 20, 'unit': 114150450538607281226726781915339, 'val': 1}
  • id: 556179
    {'lmfdb_iso': '12675.j', 'p': 59, 'prec': 20, 'unit': 1185148064239820664251195191273558, 'val': 1}
  • id: 556184
    {'lmfdb_iso': '12675.j', 'p': 61, 'prec': 20, 'unit': 1950100747133961295055528891850708, 'val': 1}
  • id: 556169
    {'lmfdb_iso': '12675.j', 'p': 67, 'prec': 20, 'unit': 31795053712633722318144533978875326, 'val': 1}
  • id: 556180
    {'lmfdb_iso': '12675.j', 'p': 73, 'prec': 20, 'unit': 183447446280270990982640512018051667, 'val': 1}
  • id: 556174
    {'lmfdb_iso': '12675.j', 'p': 79, 'prec': 20, 'unit': 36487327002148738784582574285789889, 'val': 1}
  • id: 556168
    {'lmfdb_iso': '12675.j', 'p': 83, 'prec': 20, 'unit': 1345465494531770062491818017532184949, 'val': 1}
  • id: 556182
    {'lmfdb_iso': '12675.j', 'p': 89, 'prec': 20, 'unit': 3410244028704477168094906206670718375, 'val': 1}
  • id: 556167
    {'lmfdb_iso': '12675.j', 'p': 97, 'prec': 20, 'unit': 50520773560934964009053351829047724468, 'val': 1}