Elliptic curve data - 57330.ep3

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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': '57330dh', 'Clabel': '57330dh2', 'Cnumber': 2, 'abc_quality': 0.9830620236547647, 'absD': 613298792204280, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 10920, 'ainvs': [1, -1, 1, -24632, 897411], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 13], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 57330, 'degree': 331776, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5374564226044481471534344266', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 119, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [520300455507, 193072360], 'lmfdb_iso': '57330.ep', 'lmfdb_label': '57330.ep3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -4524, 71288], 'min_quad_twist_disc': 21, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '21.8.0-3.a.1.1', '42.24.0-6.a.1.3', '120.24.0.?', '156.24.0.?', '520.6.0.?', '840.48.0.?', '1092.48.0.?', '1560.48.1.?', '10920.96.1.?'], '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, 'serre_invariants': [[2, 4, 735], [3, 6, 245], [5, 6, 11466], [7, 26, 1170], [13, 14, 4410]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.28984827590976407175194674565', 'prec': 103}, 'szpiro_ratio': 3.828655713912182, '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, 6, -6, 10, -10, 6, -4, -12, 12, 12, 10, 14, 0, 16, 8, -12, -6, -8], 'class_deg': 6, 'class_size': 4, 'conductor': 57330, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '57330.ep', 'trace_hash': 961104987408274614}
• 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': '0.046193654204525199476773155324', 'prec': 107}, 'conductor': 57330, 'gens': [], 'heights': [], 'lmfdb_label': '57330.ep3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.47013662539243145885693236769', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.6416395047091775062831884123277980828', 'prec': 130}, 'tamagawa_product': 48, 'torsion_generators': [[155, -159, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [6, 0], '3': 'a', '5': [1, 0], '7': 'a', '13': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '57330.ep3'}
• ec_torsion_growth •

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

  
  
  • id: 2761681
    {'degree': 2, 'field': [-30, 0, 1], 'lmfdb_label': '57330.ep3', 'torsion': [2, 2]}
  • id: 2761682
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '57330.ep3', 'torsion': [6]}
  • id: 2761684
    {'degree': 4, 'field': [994, 56, -55, -2, 1], 'lmfdb_label': '57330.ep3', 'torsion': [2, 6]}
  • id: 2761683
    {'degree': 4, 'field': [5880, 0, -126, 0, 1], 'lmfdb_label': '57330.ep3', 'torsion': [4]}
  • id: 2761685
    {'degree': 6, 'field': [-20, -240, 75, 19, -12, -3, 1], 'lmfdb_label': '57330.ep3', 'torsion': [6]}
  • id: 2761688
    {'degree': 8, 'field': [9136, -3176, 3854, -1400, 811, -136, 50, -4, 1], 'lmfdb_label': '57330.ep3', 'torsion': [12]}
  • id: 2761686
    {'degree': 8, 'field': [160000, 0, -32000, 0, -3480, 0, -80, 0, 1], 'lmfdb_label': '57330.ep3', 'torsion': [2, 4]}
  • id: 2761687
    {'degree': 8, 'field': [697225, 0, -15350, 0, 666, 0, -38, 0, 1], 'lmfdb_label': '57330.ep3', 'torsion': [2, 4]}
  • id: 2761689
    {'degree': 12, 'field': [64, 264, 825, 1457, 1776, -1377, 347, 24, -21, 19, 0, -3, 1], 'lmfdb_label': '57330.ep3', 'torsion': [3, 6]}
  • id: 2761690
    {'degree': 12, 'field': [1600, 0, 0, 0, 0, 0, -4400, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '57330.ep3', 'torsion': [2, 6]}
  • id: 2761693
    {'degree': 16, 'field': [3811144, 13161120, -3639112, -22919608, 21806774, -14316108, 8113562, -3224784, 1279849, -352032, 107890, -22016, 5004, -644, 112, -8, 1], 'lmfdb_label': '57330.ep3', 'torsion': [2, 12]}
  • id: 2761692
    {'degree': 16, 'field': [1398100096, -378925824, 507286976, -223397056, 33944648, 78067776, -1605376, -19003248, 2409193, 1460136, -193124, -51368, 6438, 952, -116, -8, 1], 'lmfdb_label': '57330.ep3', 'torsion': [2, 12]}
  • id: 2761691
    {'degree': 16, 'field': [23621708800, -13439795200, 10176448000, -3173747200, 157893920, 388269440, -92349200, -17030000, 8839852, -91104, -433880, 16692, 11377, -52, -134, 0, 1], 'lmfdb_label': '57330.ep3', 'torsion': [8]}
  • id: 2761694
    {'degree': 18, 'field': [2235610304, -930738528, 2154245808, 580398792, 799104480, 722379888, 336351522, 129082758, 48533268, 11663155, 2554365, 417474, 38976, -1968, -1560, -192, -12, -3, 1], 'lmfdb_label': '57330.ep3', '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: 1379049
    {'conductor': 57330, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '57330.ep3', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 1379050
    {'conductor': 57330, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '57330.ep3', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1379051
    {'conductor': 57330, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '57330.ep3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1379052
    {'conductor': 57330, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '57330.ep3', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1379053
    {'conductor': 57330, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '57330.ep3', '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: 2044723
    {'adelic_gens': [[1, 6, 6, 37], [1, 12, 0, 1], [3130, 4683, 6993, 7792], [8072, 6251, 7245, 3088], [3119, 0, 0, 10919], [3130, 4683, 5901, 7792], [3186, 1897, 8645, 10466], [4201, 7812, 1806, 3193], [10909, 12, 10908, 13], [1, 0, 12, 1], [11, 2, 10870, 10911]], 'adelic_image': '10920.96.1.?', 'conductor': 57330, 'lmfdb_label': '57330.ep3', 'prime': 0}
  • id: 243373
    {'conductor': 57330, 'elladic_image': '2.3.0.1', 'lmfdb_label': '57330.ep3', 'modell_image': '2B', 'prime': 2}
  • id: 243374
    {'conductor': 57330, 'elladic_image': '3.4.0.1', 'lmfdb_label': '57330.ep3', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 57330.ep does not appear in ec_padic