Elliptic curve data - 57330.cg3

Formats: - HTML - YAML - JSON - 2024-04-29T00:43:47.181856

• 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': '57330ce', 'Clabel': '57330ce7', 'Cnumber': 7, 'abc_quality': 1.0262585206734374, 'absD': 7710501723471796570953108750, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 10920, 'ainvs': [1, -1, 0, -1094136444, -14556410757050], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 13], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 57330, 'degree': 42467328, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.1100429695885301936367453165', 'prec': 100}, 'faltings_index': 7, 'faltings_ratio': 12, 'iso_nlabel': 58, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [-1688971789881664420008241, 89901485966373558750], 'lmfdb_iso': '57330.cg', 'lmfdb_label': '57330.cg3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -2481035, -1572033153], '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', '12.48.0.c.4', '21.8.0-3.a.1.1', '24.96.0-12.c.4.18', '42.24.0-6.a.1.3', '56.12.0.v.1', '84.96.0.?', '168.192.1.?', '520.12.0.?', '1560.192.1.?', '3640.24.0.?', '10920.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 9, 'sha_primes': [3], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.5877817507268186953864463263', 'prec': 100}, 'szpiro_ratio': 6.76682805310838, '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, 0, 0, -1, 0, 0, 1, 6, 0, 4, 1], 'aplist': [-1, 0, 1, 0, 0, -1, 6, 4, 0, -6, 4, -10, 6, 8, 0, 6, -12, -14, -4, 0, -2, 8, -12, 6, -2], 'class_deg': 12, 'class_size': 8, 'conductor': 57330, 'isogeny_matrix': [[1, 2, 4, 3, 4, 6, 12, 12], [2, 1, 2, 6, 2, 3, 6, 6], [4, 2, 1, 12, 4, 6, 12, 3], [3, 6, 12, 1, 12, 2, 4, 4], [4, 2, 4, 12, 1, 6, 3, 12], [6, 3, 6, 2, 6, 1, 2, 2], [12, 6, 12, 4, 3, 2, 1, 4], [12, 6, 3, 4, 12, 2, 4, 1]], 'lmfdb_iso': '57330.cg', 'trace_hash': 1188780569920021672}
• 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': '0.00026919192977864887134000974460', 'prec': 113}, 'conductor': 57330, 'gens': [], 'heights': [], 'lmfdb_label': '57330.cg3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.013084561612144725618345484774', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '9.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.8841768721488404890417498075118935968', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[153539, -153539, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [6, 2], '3': 'a', '5': [1, 0], '7': 'a', '13': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '57330.cg3'}
• ec_torsion_growth •

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

  
  
  • id: 2760895
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '57330.cg3', 'torsion': [4]}
  • id: 2760897
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '57330.cg3', 'torsion': [6]}
  • id: 2760894
    {'degree': 2, 'field': [14, 0, 1], 'lmfdb_label': '57330.cg3', 'torsion': [2, 2]}
  • id: 2760896
    {'degree': 2, 'field': [21, 0, 1], 'lmfdb_label': '57330.cg3', 'torsion': [4]}
  • id: 2760899
    {'degree': 4, 'field': [16, 0, 6, 0, 1], 'lmfdb_label': '57330.cg3', 'torsion': [2, 6]}
  • id: 2760901
    {'degree': 4, 'field': [22, 2, -1, -2, 1], 'lmfdb_label': '57330.cg3', 'torsion': [12]}
  • id: 2760898
    {'degree': 4, 'field': [25, 0, 4, 0, 1], 'lmfdb_label': '57330.cg3', 'torsion': [2, 4]}
  • id: 2760900
    {'degree': 4, 'field': [58, 8, -7, -2, 1], 'lmfdb_label': '57330.cg3', 'torsion': [12]}
  • id: 2760902
    {'degree': 6, 'field': [-300, 0, 0, -180, 0, 0, 1], 'lmfdb_label': '57330.cg3', 'torsion': [6]}
  • id: 2760906
    {'degree': 8, 'field': [16, 0, 48, 0, 65, 0, 12, 0, 1], 'lmfdb_label': '57330.cg3', 'torsion': [2, 12]}
  • id: 2760903
    {'degree': 8, 'field': [1500, -1680, 808, -224, 136, -56, 20, 0, 1], 'lmfdb_label': '57330.cg3', 'torsion': [2, 4]}
  • id: 2760905
    {'degree': 8, 'field': [10201, 0, 1970, 0, 2178, 0, 50, 0, 1], 'lmfdb_label': '57330.cg3', 'torsion': [8]}
  • id: 2760904
    {'degree': 8, 'field': [32376100, 0, 624880, 0, 3996, 0, -248, 0, 1], 'lmfdb_label': '57330.cg3', 'torsion': [8]}
  • id: 2760910
    {'degree': 12, 'field': [90000, 0, 0, 0, 0, 0, 33000, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '57330.cg3', 'torsion': [12]}
  • id: 2760907
    {'degree': 12, 'field': [92764, -19992, 4932, 29360, -12720, -2532, 1181, -366, 195, -80, 27, -6, 1], 'lmfdb_label': '57330.cg3', 'torsion': [3, 6]}
  • id: 2760908
    {'degree': 12, 'field': [14684224, 0, -327840, 0, -44832, 0, 13240, 0, -408, 0, 30, 0, 1], 'lmfdb_label': '57330.cg3', 'torsion': [2, 6]}
  • id: 2760909
    {'degree': 12, 'field': [14684224, 0, 327840, 0, -44832, 0, -13240, 0, -408, 0, -30, 0, 1], 'lmfdb_label': '57330.cg3', 'torsion': [12]}
  • id: 2760911
    {'degree': 16, 'field': [15625, 70000, 156800, -212240, 125066, -33208, 37632, -25312, 6831, -1736, 1568, -448, 102, -56, 0, 0, 1], 'lmfdb_label': '57330.cg3', 'torsion': [4, 4]}
  • id: 2760914
    {'degree': 16, 'field': [51076, 56048, 105800, 2016, 48790, -22568, 40908, -17032, 3327, 2012, -1134, 112, 7, 0, 2, -4, 1], 'lmfdb_label': '57330.cg3', 'torsion': [2, 12]}
  • id: 2760916
    {'degree': 16, 'field': [2637376, 0, 314468, 0, 593489, 0, 78162, 0, 135359, 0, -25968, 0, 1967, 0, -70, 0, 1], 'lmfdb_label': '57330.cg3', 'torsion': [24]}
  • id: 2760912
    {'degree': 16, 'field': [182520100, 0, 116631480, 0, 32718856, 0, 5350668, 0, 738429, 0, 69024, 0, 4234, 0, 108, 0, 1], 'lmfdb_label': '57330.cg3', 'torsion': [2, 8]}
  • id: 2760915
    {'degree': 16, 'field': [913354844416, 0, 719326999552, 0, 178529699936, 0, 4624540032, 0, 149875124, 0, 1578192, 0, 25886, 0, 112, 0, 1], 'lmfdb_label': '57330.cg3', 'torsion': [24]}
  • id: 2760913
    {'degree': 16, 'field': [1250978669476, 1132486449920, 1192454326464, 291194855840, 38908264024, 18385802960, 3034803856, -169621760, 216112680, -17953040, 3439856, -150640, 34804, -1400, 184, 0, 1], 'lmfdb_label': '57330.cg3', 'torsion': [2, 8]}
  • id: 2760917
    {'degree': 18, 'field': [3890658766268, -4028398286196, 5118365899104, -861024346810, 2887861319280, -235646046258, 359798450509, 68308414545, -28171735248, -3187130100, 796828131, 65687769, -12003214, -707931, 103845, 3938, -492, -9, 1], 'lmfdb_label': '57330.cg3', '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: 1378684
    {'conductor': 57330, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '57330.cg3', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1378685
    {'conductor': 57330, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '57330.cg3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1378686
    {'conductor': 57330, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '57330.cg3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1378687
    {'conductor': 57330, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '57330.cg3', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1378688
    {'conductor': 57330, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '57330.cg3', 'prime': 13, 'reduction_type': -1, '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: 2044554
    {'adelic_gens': [[9099, 7276, 10900, 5379], [6224, 10899, 6525, 374], [1, 12, 12, 145], [4201, 24, 6732, 289], [5922, 7759, 3677, 6692], [15, 106, 9614, 1691], [8191, 24, 8190, 1], [10897, 24, 10896, 25], [1, 24, 0, 1], [1, 0, 24, 1], [8737, 24, 6564, 289]], 'adelic_image': '10920.384.5.?', 'conductor': 57330, 'lmfdb_label': '57330.cg3', 'prime': 0}
  • id: 243173
    {'conductor': 57330, 'elladic_image': '4.6.0.1', 'lmfdb_label': '57330.cg3', 'modell_image': '2B', 'prime': 2}
  • id: 243174
    {'conductor': 57330, 'elladic_image': '3.4.0.1', 'lmfdb_label': '57330.cg3', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 57330.cg does not appear in ec_padic