Elliptic curve data - 23104.i2

Formats: - HTML - YAML - JSON - 2025-07-16T21:32:28.244349

• 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': '23104u', 'Clabel': '23104u2', 'Cnumber': 2, 'abc_quality': 1.0331037033479094, 'absD': 20652012657856, 'adelic_genus': 43, 'adelic_index': 1296, 'adelic_level': 4104, 'ainvs': [0, 1, 0, -13477, 636189], 'analytic_rank': 2, 'bad_primes': [2, 19], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 23104, 'degree': 51840, 'elladic_images': ['9.36.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3029260925204558425356020418', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 8, 'isogeny_degrees': [1, 3], 'jinv': [-89915392, 6859], 'lmfdb_iso': '23104.i', 'lmfdb_label': '23104.i2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -9, -15], 'min_quad_twist_disc': -152, 'modell_images': ['3Cs'], 'modm_images': ['3.12.0.a.1', '9.36.0.b.1', '24.24.0-3.a.1.3', '38.2.0.a.1', '72.72.0.?', '114.24.1.?', '171.108.4.?', '342.216.13.?', '456.48.1.?', '513.324.16.?', '1026.648.43.?', '1368.432.13.?', '4104.1296.43.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 2, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '1.6223036438485493416002033344', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 361], [19, 200, 64]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.51586698734273704217752773487', 'prec': 107}, 'szpiro_ratio': 4.0072331086075845, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, -3, 0, -1, 0, 1, 0, -3, 0, -4, 0, 6, 0, -3, 0, 0, 0], 'aplist': [0, -2, -3, -1, -3, -4, -3, 0, 0, 6, 4, 2, 6, 1, -3, 12, -6, 1, -4, -6, -7, -8, -12, -12, -8], 'class_deg': 9, 'class_size': 3, 'conductor': 23104, 'isogeny_matrix': [[1, 3, 9], [3, 1, 3], [9, 3, 1]], 'lmfdb_iso': '23104.i', 'trace_hash': 121321027101333090}
• 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': '0.073840184876882501809583727996', 'prec': 107}, 'conductor': 23104, 'gens': [[700, 6859, 3], [-451, 6859, 2]], 'heights': [{'__RealLiteral__': 0, 'data': '1.4309579844898994870811290667', 'prec': 100}, {'__RealLiteral__': 0, 'data': '1.4791798401027003186643668582', 'prec': 100}], 'lmfdb_label': '23104.i2', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.66950279292232845475866918686', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.3445472820986968893251551632914782830', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': [44, 68]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [2, 0], '7': [2, 0], '11': [2, 0], '13': [2, 0], '17': [2, 0], '19': 'a', '23': [4, 2, 0], '29': [2, 0], '31': [2, 0], '37': [2, 0], '41': [2, 0], '43': [2, 0], '47': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '23104.i2'}
• ec_torsion_growth •

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

  
  
  • id: 1169123
    {'degree': 2, 'field': [-114, 0, 1], 'lmfdb_label': '23104.i2', 'torsion': [3]}
  • id: 1169124
    {'degree': 2, 'field': [38, 0, 1], 'lmfdb_label': '23104.i2', 'torsion': [3]}
  • id: 1169125
    {'degree': 3, 'field': [-2, -2, 0, 1], 'lmfdb_label': '23104.i2', 'torsion': [2]}
  • id: 1169126
    {'degree': 4, 'field': [1444, 0, -38, 0, 1], 'lmfdb_label': '23104.i2', 'torsion': [3, 3]}
  • id: 1169128
    {'degree': 6, 'field': [-1026, 0, 36, 0, 12, 0, 1], 'lmfdb_label': '23104.i2', 'torsion': [6]}
  • id: 1169127
    {'degree': 6, 'field': [1, -3, 4, -3, 4, -3, 1], 'lmfdb_label': '23104.i2', 'torsion': [2, 2]}
  • id: 1169129
    {'degree': 6, 'field': [38, 0, 4, 0, -4, 0, 1], 'lmfdb_label': '23104.i2', 'torsion': [6]}
  • id: 1169130
    {'degree': 12, 'field': [-19, 0, -28, 0, -13, 0, -20, 0, -13, 0, 0, 0, 1], 'lmfdb_label': '23104.i2', 'torsion': [4]}
  • id: 1169133
    {'degree': 12, 'field': [4, 0, -8, 0, 60, 0, 92, 0, 48, 0, 10, 0, 1], 'lmfdb_label': '23104.i2', 'torsion': [2, 6]}
  • id: 1169132
    {'degree': 12, 'field': [961, 1302, 2585, 306, 2970, -1374, 1183, -522, 282, -78, 29, -6, 1], 'lmfdb_label': '23104.i2', 'torsion': [2, 6]}
  • id: 1169131
    {'degree': 12, 'field': [1444, 0, -152, 0, 168, 0, 92, 0, 12, 0, 4, 0, 1], 'lmfdb_label': '23104.i2', 'torsion': [3, 6]}
  • id: 1169134
    {'degree': 18, 'field': [-3066528825, -1009317240, 10068971796, 339891564, -4469897592, -72725160, 870331096, 6029232, -98867868, -304134, 6775476, 3648, -285023, 228, 7296, -6, -114, 0, 1], 'lmfdb_label': '23104.i2', 'torsion': [9]}
  • id: 1169135
    {'degree': 18, 'field': [4528879, -2591302, 1430603, 4021352, -839252, 14692, 753194, -146438, -15053, 72698, -13971, -1158, 3748, -620, -35, 86, -5, -2, 1], 'lmfdb_label': '23104.i2', 'torsion': [9]}
• 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: 528117
    {'conductor': 23104, 'conductor_valuation': 6, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '23104.i2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 528118
    {'conductor': 23104, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '23104.i2', 'prime': 19, '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: 1818339
    {'adelic_gens': [[1, 0, 54, 1], [4051, 54, 4050, 55], [2051, 0, 0, 4103], [3169, 3314, 3390, 3551], [43, 30, 840, 85], [892, 27, 15, 676], [43, 30, 3918, 1111], [3131, 4050, 3132, 4049], [1, 27, 27, 730], [1, 54, 0, 1], [19, 54, 792, 469], [19, 54, 792, 3547], [3077, 0, 0, 4103]], 'adelic_image': '4104.1296.43.?', 'conductor': 23104, 'lmfdb_label': '23104.i2', 'prime': 0}
  • id: 106257
    {'conductor': 23104, 'elladic_image': '9.36.0.2', 'lmfdb_label': '23104.i2', 'modell_image': '3Cs', 'prime': 3}
• ec_padic •

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

  
  
  • id: 1090156
    {'lmfdb_iso': '23104.i', 'p': 5, 'prec': 20, 'unit': 8915437460271, 'val': 2}
  • id: 1090157
    {'lmfdb_iso': '23104.i', 'p': 7, 'prec': 20, 'unit': 10235164435449677, 'val': 2}
  • id: 1090155
    {'lmfdb_iso': '23104.i', 'p': 11, 'prec': 20, 'unit': 32734913747191142316, 'val': 2}
  • id: 1090162
    {'lmfdb_iso': '23104.i', 'p': 13, 'prec': 20, 'unit': 1458582659463379032829, 'val': 2}
  • id: 1090164
    {'lmfdb_iso': '23104.i', 'p': 17, 'prec': 20, 'unit': 180596351348128331753501, 'val': 2}
  • id: 1090161
    {'lmfdb_iso': '23104.i', 'p': 29, 'prec': 20, 'unit': 864057177043770876529741641, 'val': 2}
  • id: 1090158
    {'lmfdb_iso': '23104.i', 'p': 31, 'prec': 20, 'unit': 11220430066567092923290410741, 'val': 2}
  • id: 1090173
    {'lmfdb_iso': '23104.i', 'p': 37, 'prec': 20, 'unit': 398897520730538952529035785135, 'val': 2}
  • id: 1090159
    {'lmfdb_iso': '23104.i', 'p': 41, 'prec': 20, 'unit': 3542518513521369819599682878618, 'val': 2}
  • id: 1090160
    {'lmfdb_iso': '23104.i', 'p': 43, 'prec': 20, 'unit': 252217615573615750206583755310, 'val': 0}
  • id: 1090171
    {'lmfdb_iso': '23104.i', 'p': 47, 'prec': 20, 'unit': 18867829789571667491109810668734, 'val': 2}
  • id: 1090166
    {'lmfdb_iso': '23104.i', 'p': 53, 'prec': 20, 'unit': 122944877425275385028148518727100, 'val': 2}
  • id: 1090167
    {'lmfdb_iso': '23104.i', 'p': 59, 'prec': 20, 'unit': 4037362248903651003935790623093961, 'val': 2}
  • id: 1090172
    {'lmfdb_iso': '23104.i', 'p': 61, 'prec': 20, 'unit': 135218502372935850838022152834643, 'val': 0}
  • id: 1090165
    {'lmfdb_iso': '23104.i', 'p': 67, 'prec': 20, 'unit': 9164220640475170905926814641476711, 'val': 2}
  • id: 1090170
    {'lmfdb_iso': '23104.i', 'p': 71, 'prec': 20, 'unit': 116499042450235875410303902789642355, 'val': 2}
  • id: 1090168
    {'lmfdb_iso': '23104.i', 'p': 73, 'prec': 20, 'unit': 234497018977361485867693455297966138, 'val': 2}
  • id: 1090163
    {'lmfdb_iso': '23104.i', 'p': 79, 'prec': 20, 'unit': 248391465199029996372277053884500547, 'val': 2}
  • id: 1090154
    {'lmfdb_iso': '23104.i', 'p': 83, 'prec': 20, 'unit': 2202987465688223104365615152073810869, 'val': 2}
  • id: 1090169
    {'lmfdb_iso': '23104.i', 'p': 89, 'prec': 20, 'unit': 4677014282191407518155610584098659540, 'val': 2}
  • id: 1090153
    {'lmfdb_iso': '23104.i', 'p': 97, 'prec': 20, 'unit': 46497328980999231945028602313722764925, 'val': 2}