Elliptic curve data - 48510.cu3

Formats: - HTML - YAML - JSON - 2024-05-23T22:05:54.420497

• 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': '48510dk', 'Clabel': '48510dk5', 'Cnumber': 5, 'abc_quality': 1.0656902431070385, 'absD': 456964740613290390191865000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 9240, 'ainvs': [1, -1, 1, -193058123, -90611800653], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 48510, 'degree': 21233664, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.8051960945725503781751706842', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 4, 'iso_nlabel': 72, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [9278380528613437145689, 5328033205714065000], 'lmfdb_iso': '48510.cu', 'lmfdb_label': '48510.cu3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -437774, -9825928], 'min_quad_twist_disc': 21, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '12.24.0.g.1', '21.8.0-3.a.1.2', '24.48.0.bu.1', '40.12.0.y.1', '42.24.0-6.a.1.4', '84.48.0.?', '120.96.1.?', '132.48.0.?', '168.96.0.?', '264.96.0.?', '616.12.0.?', '840.192.1.?', '924.96.0.?', '1320.192.1.?', '1848.192.1.?', '3080.24.0.?', '9240.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '8.1318219123718876144623243576', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.2829348757108388799248716940', 'prec': 100}, 'szpiro_ratio': 6.381106402683005, '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, 0, 1, -1, 0, 0, 1, 0, -1, 1, 0, -2, 0, 0, 1, -6, 0, 4, -1], 'aplist': [1, 0, -1, 0, 1, -2, -6, 4, 0, 6, 4, 2, -6, -4, 0, 6, 12, -14, -16, 0, -2, -4, 0, -6, 10], 'class_deg': 12, 'class_size': 8, 'conductor': 48510, 'isogeny_matrix': [[1, 2, 3, 4, 6, 12, 12, 4], [2, 1, 6, 2, 3, 6, 6, 2], [3, 6, 1, 12, 2, 4, 4, 12], [4, 2, 12, 1, 6, 3, 12, 4], [6, 3, 2, 6, 1, 2, 2, 6], [12, 6, 4, 3, 2, 1, 4, 12], [12, 6, 4, 12, 2, 4, 1, 3], [4, 2, 12, 4, 6, 12, 3, 1]], 'lmfdb_iso': '48510.cu', 'trace_hash': 416798364672314282}
• 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': '0.00049527757789267017097197392464', 'prec': 113}, 'conductor': 48510, 'gens': [[134677, 16246046, 3]], 'heights': [{'__RealLiteral__': 0, 'data': '8.1318219123718876144623243576', 'prec': 100}], 'lmfdb_label': '48510.cu3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.043995940867058230383100946638', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.5864117439558866153036848953245337018', 'prec': 130}, 'tamagawa_product': 96, 'torsion_generators': [[-54613, 54609, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 2], '3': 'a', '5': [1, 0], '7': 'a', '11': [2, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '48510.cu3'}
• ec_torsion_growth •

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

  
  
  • id: 2362245
    {'degree': 2, 'field': [-154, 0, 1], 'lmfdb_label': '48510.cu3', 'torsion': [2, 2]}
  • id: 2362248
    {'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '48510.cu3', 'torsion': [6]}
  • id: 2362247
    {'degree': 2, 'field': [33, 0, 1], 'lmfdb_label': '48510.cu3', 'torsion': [4]}
  • id: 2362246
    {'degree': 2, 'field': [42, 0, 1], 'lmfdb_label': '48510.cu3', 'torsion': [4]}
  • id: 2362251
    {'degree': 4, 'field': [51, 6, -5, -2, 1], 'lmfdb_label': '48510.cu3', 'torsion': [12]}
  • id: 2362252
    {'degree': 4, 'field': [121, 0, 55, 0, 1], 'lmfdb_label': '48510.cu3', 'torsion': [12]}
  • id: 2362250
    {'degree': 4, 'field': [484, 0, -110, 0, 1], 'lmfdb_label': '48510.cu3', 'torsion': [2, 6]}
  • id: 2362249
    {'degree': 4, 'field': [2401, 0, -56, 0, 1], 'lmfdb_label': '48510.cu3', 'torsion': [2, 4]}
  • id: 2362253
    {'degree': 6, 'field': [3308, -507, -147, 97, 9, -3, 1], 'lmfdb_label': '48510.cu3', 'torsion': [6]}
  • id: 2362257
    {'degree': 8, 'field': [19881, 0, 3036, 0, 535, 0, -44, 0, 1], 'lmfdb_label': '48510.cu3', 'torsion': [2, 12]}
  • id: 2362255
    {'degree': 8, 'field': [81796, 0, -5808, 0, 1508, 0, 72, 0, 1], 'lmfdb_label': '48510.cu3', 'torsion': [8]}
  • id: 2362256
    {'degree': 8, 'field': [13124589, -1812960, 560479, -45266, 6572, 292, -1, -2, 1], 'lmfdb_label': '48510.cu3', 'torsion': [8]}
  • id: 2362254
    {'degree': 8, 'field': [29847448, 556448, -567152, 21440, -10799, 92, -26, -4, 1], 'lmfdb_label': '48510.cu3', 'torsion': [2, 4]}
  • id: 2362258
    {'degree': 12, 'field': [19600, -29400, 18200, -5250, 3075, -255, -347, 318, 18, 12, -1, -3, 1], 'lmfdb_label': '48510.cu3', 'torsion': [3, 6]}
  • id: 2362261
    {'degree': 12, 'field': [617428, 130004, -119523, -21980, 13573, -3240, 1417, -498, 393, -190, 49, -6, 1], 'lmfdb_label': '48510.cu3', 'torsion': [12]}
  • id: 2362260
    {'degree': 12, 'field': [1216048, 269328, -211540, -111624, 46266, 10512, -1907, -1422, 429, -60, 23, -6, 1], 'lmfdb_label': '48510.cu3', 'torsion': [12]}
  • id: 2362259
    {'degree': 12, 'field': [368620778, -334491756, 105168297, -18694590, 3774693, -1119960, 297757, -32178, 8643, -520, 159, -6, 1], 'lmfdb_label': '48510.cu3', 'torsion': [2, 6]}
  • id: 2362263
    {'degree': 16, 'field': [19580625, 0, 34701000, 0, 32441200, 0, -11978920, 0, 1921266, 0, 222472, 0, 8688, 0, 152, 0, 1], 'lmfdb_label': '48510.cu3', 'torsion': [2, 8]}
  • id: 2362265
    {'degree': 16, 'field': [91470096, 0, -2407343808, 0, 148303792, 0, -99298528, 0, 13076028, 0, -28784, 0, -6972, 0, -16, 0, 1], 'lmfdb_label': '48510.cu3', 'torsion': [2, 12]}
  • id: 2362266
    {'degree': 16, 'field': [303595776, 0, 128798208, 0, 151902432, 0, -1364352, 0, -134492, 0, 2064, 0, 1148, 0, -24, 0, 1], 'lmfdb_label': '48510.cu3', 'torsion': [24]}
  • id: 2362267
    {'degree': 16, 'field': [1344395556, 0, 869846040, 0, 209446461, 0, 20478990, 0, 424411, 0, 4700, 0, 5571, 0, -130, 0, 1], 'lmfdb_label': '48510.cu3', 'torsion': [24]}
  • id: 2362262
    {'degree': 16, 'field': [148819264441, 0, -28612430608, 0, 5083879136, 0, 137863320, 0, 40410902, 0, -25200, 0, 12656, 0, 8, 0, 1], 'lmfdb_label': '48510.cu3', 'torsion': [4, 4]}
  • id: 2362264
    {'degree': 16, 'field': [304222343049, -25963751880, 27035782560, -2155376664, 1110691386, -52684968, 39009124, -17691824, 3597819, 489320, -38332, -30912, 3878, 560, -60, -8, 1], 'lmfdb_label': '48510.cu3', 'torsion': [2, 8]}
  • id: 2362268
    {'degree': 18, 'field': [-356319963, -6148294362, -3939719553, 3220979280, 1281511161, -873821214, 156549121, 7531776, -31458777, 5122188, 2238558, -261324, -106973, 3906, 4011, -6, -105, 0, 1], 'lmfdb_label': '48510.cu3', '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: 1159239
    {'conductor': 48510, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '48510.cu3', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 1159240
    {'conductor': 48510, 'conductor_valuation': 2, 'discriminant_valuation': 30, 'j_denominator_valuation': 24, 'kodaira_symbol': -28, 'lmfdb_label': '48510.cu3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1159241
    {'conductor': 48510, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '48510.cu3', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1159242
    {'conductor': 48510, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '48510.cu3', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1159243
    {'conductor': 48510, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '48510.cu3', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1986983
    {'adelic_gens': [[4242, 2719, 7037, 6692], [3376, 3, 7101, 9154], [2311, 24, 2310, 1], [1, 12, 12, 145], [15, 106, 7934, 11], [3697, 24, 7404, 289], [7904, 9237, 3099, 86], [4619, 9216, 6160, 7699], [9217, 24, 9216, 25], [1, 24, 0, 1], [1, 0, 24, 1]], 'adelic_image': '9240.384.5.?', 'conductor': 48510, 'lmfdb_label': '48510.cu3', 'prime': 0}
  • id: 209096
    {'conductor': 48510, 'elladic_image': '4.6.0.1', 'lmfdb_label': '48510.cu3', 'modell_image': '2B', 'prime': 2}
  • id: 209097
    {'conductor': 48510, 'elladic_image': '3.4.0.1', 'lmfdb_label': '48510.cu3', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 2435004
    {'lmfdb_iso': '48510.cu', 'p': 13, 'prec': 20, 'unit': 404748679717170664393, 'val': 1}
  • id: 2435006
    {'lmfdb_iso': '48510.cu', 'p': 17, 'prec': 20, 'unit': 59047519908733849759786, 'val': 1}
  • id: 2435007
    {'lmfdb_iso': '48510.cu', 'p': 19, 'prec': 20, 'unit': 26789549027914863229858, 'val': 1}
  • id: 2435003
    {'lmfdb_iso': '48510.cu', 'p': 29, 'prec': 20, 'unit': 1366458443716216897763475349, 'val': 1}
  • id: 2435013
    {'lmfdb_iso': '48510.cu', 'p': 31, 'prec': 20, 'unit': 16235192015916849739651050159, 'val': 1}
  • id: 2435000
    {'lmfdb_iso': '48510.cu', 'p': 37, 'prec': 20, 'unit': 453842760858795222647619080871, 'val': 1}
  • id: 2435001
    {'lmfdb_iso': '48510.cu', 'p': 41, 'prec': 20, 'unit': 13350015542087735437327838736, 'val': 1}
  • id: 2435002
    {'lmfdb_iso': '48510.cu', 'p': 43, 'prec': 20, 'unit': 5214425072831642078725574456723, 'val': 1}
  • id: 2435008
    {'lmfdb_iso': '48510.cu', 'p': 53, 'prec': 20, 'unit': 95177323059260211037536704216576, 'val': 1}
  • id: 2435011
    {'lmfdb_iso': '48510.cu', 'p': 59, 'prec': 20, 'unit': 3079080941014046919878917983210175, 'val': 1}
  • id: 2435012
    {'lmfdb_iso': '48510.cu', 'p': 61, 'prec': 20, 'unit': 6018832967011952032043792040771932, 'val': 1}
  • id: 2434999
    {'lmfdb_iso': '48510.cu', 'p': 67, 'prec': 20, 'unit': 4817333155403028370047422066266086, 'val': 1}
  • id: 2435009
    {'lmfdb_iso': '48510.cu', 'p': 73, 'prec': 20, 'unit': 224169372015734021243872510493594477, 'val': 1}
  • id: 2435005
    {'lmfdb_iso': '48510.cu', 'p': 79, 'prec': 20, 'unit': 380087041597355327665328027973673628, 'val': 1}
  • id: 2435010
    {'lmfdb_iso': '48510.cu', 'p': 89, 'prec': 20, 'unit': 6546266218807389033832110677111908186, 'val': 1}
  • id: 2434998
    {'lmfdb_iso': '48510.cu', 'p': 97, 'prec': 20, 'unit': 33769817843065143884668492105928242409, 'val': 1}