Elliptic curve data - 4851.t2

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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
  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': '4851l', 'Clabel': '4851l2', 'Cnumber': 2, 'abc_quality': 1.012998630378065, 'absD': 13812719553171, 'adelic_genus': 37, 'adelic_index': 1200, 'adelic_level': 11550, 'ainvs': [0, 0, 1, -4557, -214461], 'analytic_rank': 1, 'bad_primes': [3, 7, 11], 'class_deg': 25, 'class_size': 3, 'cm': 0, 'conductor': 4851, 'degree': 10800, 'elladic_images': ['5.60.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.2142513777433084335612847287', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 5, 'iso_nlabel': 19, 'isogeny_degrees': [1, 5], 'jinv': [-122023936, 161051], 'lmfdb_iso': '4851.t', 'lmfdb_label': '4851.t2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 1, -10, -20], 'min_quad_twist_disc': 21, 'modell_images': ['5Cs.4.1'], 'modm_images': ['5.60.0.a.1', '22.2.0.a.1', '105.120.0.?', '110.120.5.?', '275.300.12.?', '550.600.37.?', '2310.240.5.?', '5775.600.12.?', '11550.1200.37.?'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '13.202029789822232847435750753', 'prec': 100}, 'semistable': False, 'serre_invariants': [[3, 6, 539], [5, 2, 441], [7, 26, 99], [11, 12, 441]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.30800984111840306468901426148', 'prec': 107}, 'szpiro_ratio': 4.486294106755062, '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, 2, 0, 2, 1, 0, 0, 0, 0, 2, -1, 0, -4, 0, 0, -4, -2, 0, 0, 2], 'aplist': [2, 0, 1, 0, -1, -4, -2, 0, 1, 0, -7, 3, -8, -6, 8, 6, 5, -12, -7, 3, -4, -10, -6, 15, 7], 'class_deg': 25, 'class_size': 3, 'conductor': 4851, 'isogeny_matrix': [[1, 5, 25], [5, 1, 5], [25, 5, 1]], 'lmfdb_iso': '4851.t', 'trace_hash': 2166973665655373400}
• 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': '0.088168743974093300843238414849', 'prec': 107}, 'conductor': 4851, 'gens': [[2486169, 850802697, 170]], 'heights': [{'__RealLiteral__': 0, 'data': '13.202029789822232847435750753', 'prec': 100}], 'lmfdb_label': '4851.t2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.27696417664777584386522770385', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.3129786216350477898122960883378122230', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 5, 0], '3': 'a', '5': [5, 1], '7': 'a', '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 1, 0], '23': [1, 0], '29': [1, 1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '4851.t2'}
• ec_torsion_growth •

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

  
  
  • id: 253874
    {'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '4851.t2', 'torsion': [5]}
  • id: 253875
    {'degree': 3, 'field': [1, 1, -1, 1], 'lmfdb_label': '4851.t2', 'torsion': [2]}
  • id: 253876
    {'degree': 4, 'field': [151, -26, 26, -1, 1], 'lmfdb_label': '4851.t2', 'torsion': [5]}
  • id: 253878
    {'degree': 6, 'field': [-173, -69, 82, 7, -14, -1, 1], 'lmfdb_label': '4851.t2', 'torsion': [10]}
  • id: 253877
    {'degree': 6, 'field': [1, -1, 2, -3, 2, -1, 1], 'lmfdb_label': '4851.t2', 'torsion': [2, 2]}
  • id: 253879
    {'degree': 8, 'field': [-33, 140, -98, -3, 13, -7, 9, -1, 1], 'lmfdb_label': '4851.t2', 'torsion': [3]}
  • id: 253880
    {'degree': 8, 'field': [625, 125, 150, 55, 41, -11, 6, -1, 1], 'lmfdb_label': '4851.t2', 'torsion': [5, 5]}
  • id: 253881
    {'degree': 12, 'field': [-3987002, -487960, -240556, 263724, 65212, -20948, 708, 2892, -1030, -46, 6, -2, 1], 'lmfdb_label': '4851.t2', 'torsion': [4]}
  • id: 253883
    {'degree': 12, 'field': [15625, 3125, 10625, 4750, 1925, 705, 126, -141, 77, -38, 17, -1, 1], 'lmfdb_label': '4851.t2', 'torsion': [2, 10]}
  • id: 253882
    {'degree': 12, 'field': [2276761, 234373, 1573292, 111648, 348409, 13314, 39843, 358, 2505, -22, 80, -1, 1], 'lmfdb_label': '4851.t2', 'torsion': [10]}
  • id: 253884
    {'degree': 16, 'field': [501, -516, -1616, 835, 979, -1739, 943, 799, -487, 893, 131, 26, 134, -25, 22, -2, 1], 'lmfdb_label': '4851.t2', 'torsion': [15]}
• 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: 93706
    {'conductor': 4851, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '4851.t2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 93707
    {'conductor': 4851, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '4851.t2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 93708
    {'conductor': 4851, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '4851.t2', '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: 1695680
    {'adelic_gens': [[9451, 10500, 6804, 8527], [16, 35, 1765, 3861], [7699, 0, 0, 11549], [1649, 0, 0, 11549], [1, 50, 10, 501], [5881, 10500, 11235, 8821], [11501, 50, 11500, 51], [1, 50, 0, 1], [1, 0, 50, 1]], 'adelic_image': '11550.1200.37.?', 'conductor': 4851, 'lmfdb_label': '4851.t2', 'prime': 0}
  • id: 24144
    {'conductor': 4851, 'elladic_image': '5.60.0.1', 'lmfdb_label': '4851.t2', 'modell_image': '5Cs.4.1', 'prime': 5}
• ec_padic •

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

  
  
  • id: 177322
    {'lmfdb_iso': '4851.t', 'p': 5, 'prec': 20, 'unit': 73266002099011, 'val': 0}
  • id: 177311
    {'lmfdb_iso': '4851.t', 'p': 13, 'prec': 20, 'unit': 982421059414932393459, 'val': 1}
  • id: 177313
    {'lmfdb_iso': '4851.t', 'p': 17, 'prec': 20, 'unit': 86563346262456363453828, 'val': 1}
  • id: 177318
    {'lmfdb_iso': '4851.t', 'p': 23, 'prec': 20, 'unit': 537705442302147342000099903, 'val': -1}
  • id: 177308
    {'lmfdb_iso': '4851.t', 'p': 31, 'prec': 20, 'unit': 8668421046030435186231513992, 'val': 1}
  • id: 177306
    {'lmfdb_iso': '4851.t', 'p': 37, 'prec': 20, 'unit': 230740983228716171712093750225, 'val': 1}
  • id: 177309
    {'lmfdb_iso': '4851.t', 'p': 41, 'prec': 20, 'unit': 1713155865820510860103609453666, 'val': 1}
  • id: 177310
    {'lmfdb_iso': '4851.t', 'p': 43, 'prec': 20, 'unit': 10039518679592134176454025514181, 'val': 1}
  • id: 177320
    {'lmfdb_iso': '4851.t', 'p': 47, 'prec': 20, 'unit': 745918373484565971803521606233, 'val': 1}
  • id: 177315
    {'lmfdb_iso': '4851.t', 'p': 53, 'prec': 20, 'unit': 193031288150659789199432839022592, 'val': 1}
  • id: 177316
    {'lmfdb_iso': '4851.t', 'p': 59, 'prec': 20, 'unit': 4247650845895637167469816299706775, 'val': 1}
  • id: 177321
    {'lmfdb_iso': '4851.t', 'p': 61, 'prec': 20, 'unit': 203195891712805892471632590938408, 'val': 1}
  • id: 177305
    {'lmfdb_iso': '4851.t', 'p': 67, 'prec': 20, 'unit': 32970551150922996505192444869207671, 'val': 1}
  • id: 177307
    {'lmfdb_iso': '4851.t', 'p': 71, 'prec': 20, 'unit': 132996660610968146543449321045138821, 'val': 1}
  • id: 177317
    {'lmfdb_iso': '4851.t', 'p': 73, 'prec': 20, 'unit': 199448655981537245172733128445365430, 'val': 1}
  • id: 177312
    {'lmfdb_iso': '4851.t', 'p': 79, 'prec': 20, 'unit': 184022502994170828305515233011506679, 'val': 1}
  • id: 177314
    {'lmfdb_iso': '4851.t', 'p': 83, 'prec': 20, 'unit': 371551062405053645838031200342376730, 'val': 1}
  • id: 177319
    {'lmfdb_iso': '4851.t', 'p': 89, 'prec': 20, 'unit': 3066805136000767344549260303342912870, 'val': 1}
  • id: 177304
    {'lmfdb_iso': '4851.t', 'p': 97, 'prec': 20, 'unit': 44327866870094158035442415469430990075, 'val': 1}