Elliptic curve data - 12100.j4

Formats: - HTML - YAML - JSON - 2025-11-04T10:09:13.471467

• 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': '12100f', 'Clabel': '12100f2', 'Cnumber': 2, 'abc_quality': 0.8396384887826309, 'absD': 177156100000000, 'adelic_genus': 9, 'adelic_index': 384, 'adelic_level': 1320, 'ainvs': [0, -1, 0, 11092, -459688], 'analytic_rank': 1, 'bad_primes': [2, 5, 11], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 12100, 'degree': 34560, 'elladic_images': ['4.6.0.5', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4202900873806881428659414358', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 9, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [21296, 25], 'lmfdb_iso': '12100.j', 'lmfdb_label': '12100.j4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, 4, 4], 'min_quad_twist_disc': -55, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.a.1', '6.12.0.a.1', '12.24.0.d.1', '20.12.0.d.1', '24.48.0.bh.1', '40.24.0.bc.1', '60.48.1.h.1', '88.12.0.?', '120.192.9.?', '132.48.0.?', '165.8.0.?', '264.96.0.?', '330.24.0.?', '440.48.0.?', '660.96.1.?', '1320.384.9.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.7643767928736767751442875269', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 3025], [5, 18, 484], [11, 62, 100]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0454746256088441894102314341', 'prec': 103}, 'szpiro_ratio': 4.210591048467186, '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, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 0, 0, -6, 0, 4, 0], 'aplist': [0, 2, 0, 2, 0, 2, -6, 4, -6, -6, -4, -2, -6, -10, 6, 6, 12, -2, -2, -12, 2, -8, 6, -6, -2], 'class_deg': 6, 'class_size': 4, 'conductor': 12100, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '12100.j', 'trace_hash': 981001627960135}
• 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': '0.058391778698910274319704038138', 'prec': 107}, 'conductor': 12100, 'gens': [[1162, 39750, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.7643767928736767751442875269', 'prec': 100}], 'lmfdb_label': '12100.j4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.30664837288243770991254933999', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.9260401107067333266216015175341014526', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [[37, 0, 1]], 'xcoord_integral_points': [37, 1162]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': 'a', '7': [1, 0], '11': 'a', '13': [1, 0], '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': '12100.j4'}
• ec_torsion_growth •

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

  
  
  • id: 624948
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '12100.j4', 'torsion': [2, 2]}
  • id: 624949
    {'degree': 2, 'field': [14, -1, 1], 'lmfdb_label': '12100.j4', 'torsion': [6]}
  • id: 624950
    {'degree': 4, 'field': [-121, 0, -11, 0, 1], 'lmfdb_label': '12100.j4', 'torsion': [4]}
  • id: 624951
    {'degree': 4, 'field': [196, 0, -27, 0, 1], 'lmfdb_label': '12100.j4', 'torsion': [2, 6]}
  • id: 624952
    {'degree': 6, 'field': [-219, -321, -110, 25, -10, -1, 1], 'lmfdb_label': '12100.j4', 'torsion': [6]}
  • id: 624955
    {'degree': 8, 'field': [81, 0, 45, 0, 2, 0, -5, 0, 1], 'lmfdb_label': '12100.j4', 'torsion': [12]}
  • id: 624954
    {'degree': 8, 'field': [361, 608, 512, -198, 63, 22, 2, -2, 1], 'lmfdb_label': '12100.j4', 'torsion': [2, 4]}
  • id: 624953
    {'degree': 8, 'field': [18056, -1712, -3336, -1104, 680, 128, -44, -4, 1], 'lmfdb_label': '12100.j4', 'torsion': [2, 4]}
  • id: 624957
    {'degree': 12, 'field': [47961, 0, 54861, 0, 32530, 0, -495, 0, -70, 0, 21, 0, 1], 'lmfdb_label': '12100.j4', 'torsion': [2, 6]}
  • id: 624956
    {'degree': 12, 'field': [47961, 70299, 78951, 46260, 17935, -8951, -1234, -791, 235, -40, 11, -1, 1], 'lmfdb_label': '12100.j4', 'torsion': [3, 6]}
  • id: 624958
    {'degree': 16, 'field': [3721, 0, 312456, 0, 474346, 0, 300716, 0, 94999, 0, 15724, 0, 1378, 0, 60, 0, 1], 'lmfdb_label': '12100.j4', 'torsion': [4, 4]}
  • id: 624961
    {'degree': 16, 'field': [6561, -4374, 1458, -6804, 6642, 54, 2016, -1806, 43, -602, 224, 2, 82, -28, 2, -2, 1], 'lmfdb_label': '12100.j4', 'torsion': [2, 12]}
  • id: 624960
    {'degree': 16, 'field': [5354596, 0, -4778248, 0, 1981692, 0, -492328, 0, 80493, 0, -9004, 0, 698, 0, -36, 0, 1], 'lmfdb_label': '12100.j4', 'torsion': [2, 12]}
  • id: 624959
    {'degree': 16, 'field': [25361296, 0, -442848, 0, -2057200, 0, 557232, 0, -34916, 0, -5352, 0, 940, 0, -52, 0, 1], 'lmfdb_label': '12100.j4', 'torsion': [8]}
  • id: 624962
    {'degree': 18, 'field': [169696664, -166918680, 143738424, -62501140, 29742120, -6344676, 2035000, 842040, -299346, 281825, -28068, 19305, 3945, 237, 630, -52, 45, -3, 1], 'lmfdb_label': '12100.j4', '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: 261169
    {'conductor': 12100, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '12100.j4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 261170
    {'conductor': 12100, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '12100.j4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 261171
    {'conductor': 12100, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '12100.j4', 'prime': 11, '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: 1744269
    {'adelic_gens': [[1297, 24, 1296, 25], [1299, 616, 286, 243], [13, 24, 612, 13], [483, 110, 1276, 1099], [661, 264, 726, 265], [1, 24, 0, 1], [111, 484, 143, 1013], [15, 16, 314, 335], [1, 0, 24, 1], [119, 0, 0, 1319]], 'adelic_image': '1320.384.9.?', 'conductor': 12100, 'lmfdb_label': '12100.j4', 'prime': 0}
  • id: 57754
    {'conductor': 12100, 'elladic_image': '4.6.0.5', 'lmfdb_label': '12100.j4', 'modell_image': '2B', 'prime': 2}
  • id: 57755
    {'conductor': 12100, 'elladic_image': '3.4.0.1', 'lmfdb_label': '12100.j4', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 528171
    {'lmfdb_iso': '12100.j', 'p': 7, 'prec': 20, 'unit': 6509561285703599, 'val': 1}
  • id: 528175
    {'lmfdb_iso': '12100.j', 'p': 13, 'prec': 20, 'unit': 508008601893145919573, 'val': 1}
  • id: 528177
    {'lmfdb_iso': '12100.j', 'p': 17, 'prec': 20, 'unit': 1036009620613195513728, 'val': 1}
  • id: 528178
    {'lmfdb_iso': '12100.j', 'p': 19, 'prec': 20, 'unit': 1026912375566212514340269, 'val': 1}
  • id: 528182
    {'lmfdb_iso': '12100.j', 'p': 23, 'prec': 20, 'unit': 27723341464723189678707559, 'val': 1}
  • id: 528174
    {'lmfdb_iso': '12100.j', 'p': 29, 'prec': 20, 'unit': 4312323153781867047552143438, 'val': 1}
  • id: 528187
    {'lmfdb_iso': '12100.j', 'p': 31, 'prec': 20, 'unit': 6412768110116125022953865831, 'val': 1}
  • id: 528170
    {'lmfdb_iso': '12100.j', 'p': 37, 'prec': 20, 'unit': 424615507057641144937708591719, 'val': 1}
  • id: 528172
    {'lmfdb_iso': '12100.j', 'p': 41, 'prec': 20, 'unit': 279858666863171707205140798132, 'val': 1}
  • id: 528173
    {'lmfdb_iso': '12100.j', 'p': 43, 'prec': 20, 'unit': 9842132699471294717274177976070, 'val': 1}
  • id: 528185
    {'lmfdb_iso': '12100.j', 'p': 47, 'prec': 20, 'unit': 55724397591194508211080143684898, 'val': 1}
  • id: 528179
    {'lmfdb_iso': '12100.j', 'p': 53, 'prec': 20, 'unit': 160035601170160249914018804261345, 'val': 1}
  • id: 528180
    {'lmfdb_iso': '12100.j', 'p': 59, 'prec': 20, 'unit': 4274117424451090126449777562358537, 'val': 1}
  • id: 528186
    {'lmfdb_iso': '12100.j', 'p': 61, 'prec': 20, 'unit': 569835836422344176269298584630080, 'val': 1}
  • id: 528169
    {'lmfdb_iso': '12100.j', 'p': 67, 'prec': 20, 'unit': 30351678507370246090736499840934820, 'val': 1}
  • id: 528184
    {'lmfdb_iso': '12100.j', 'p': 71, 'prec': 20, 'unit': 42149888000809956944799752784291075, 'val': 1}
  • id: 528181
    {'lmfdb_iso': '12100.j', 'p': 73, 'prec': 20, 'unit': 200090905991081208170564192716733523, 'val': 1}
  • id: 528176
    {'lmfdb_iso': '12100.j', 'p': 79, 'prec': 20, 'unit': 567480904587169126419894783624817184, 'val': 1}
  • id: 528168
    {'lmfdb_iso': '12100.j', 'p': 83, 'prec': 20, 'unit': 501339937985517508824975153794975361, 'val': 1}
  • id: 528183
    {'lmfdb_iso': '12100.j', 'p': 89, 'prec': 20, 'unit': 7022360583817298649056073455369113025, 'val': 1}
  • id: 528167
    {'lmfdb_iso': '12100.j', 'p': 97, 'prec': 20, 'unit': 32392182787407424677428197211421865073, 'val': 1}