Elliptic curve data - 286650.et2

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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': '286650et', 'Clabel': '286650et7', 'Cnumber': 7, 'abc_quality': 1.1217371473231392, 'absD': 5245239267667888823777625000000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 10920, 'ainvs': [1, -1, 0, -10987057692, 429360683283216], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 13], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 286650, 'degree': 764411904, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.6649070562222621161039064367', 'prec': 100}, 'faltings_index': 7, 'faltings_ratio': 12, 'iso_nlabel': 123, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [109454124781830273937129, 3914078300576808000], 'lmfdb_iso': '286650.et', 'lmfdb_label': '286650.et2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -996559, 370812482], 'min_quad_twist_disc': 105, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.24.0-6.a.1.3', '12.96.0-12.c.3.6', '104.12.0.?', '105.8.0.?', '140.12.0.?', '210.48.0.?', '312.192.1.?', '420.192.1.?', '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, 'serre_invariants': [[2, 4, 11025], [3, 8, 1225], [5, 18, 11466], [7, 32, 5850], [13, 14, 22050]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.3379268811435004305532277799', 'prec': 100}, 'szpiro_ratio': 6.443851940334191, '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, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 1, 6, 0, 4, 0], 'aplist': [-1, 0, 0, 0, 0, 1, 6, 4, 0, -6, -8, -2, 6, -8, -12, -6, -12, -14, 4, 12, 2, 8, 0, 6, 2], 'class_deg': 12, 'class_size': 8, 'conductor': 286650, 'isogeny_matrix': [[1, 4, 12, 2, 3, 6, 12, 4], [4, 1, 3, 2, 12, 6, 12, 4], [12, 3, 1, 6, 4, 2, 4, 12], [2, 2, 6, 1, 6, 3, 6, 2], [3, 12, 4, 6, 1, 2, 4, 12], [6, 6, 2, 3, 2, 1, 2, 6], [12, 12, 4, 6, 4, 2, 1, 3], [4, 4, 12, 2, 12, 6, 3, 1]], 'lmfdb_iso': '286650.et', 'trace_hash': 2115720277899302247}
• 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': '0.000088738730988825581715744673054', 'prec': 117}, 'conductor': 286650, 'gens': [], 'heights': [], 'lmfdb_label': '286650.et2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.024018193474614950702804369765', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.1528732867815176337346097486970853387', 'prec': 130}, 'tamagawa_product': 192, 'torsion_generators': [[276291, -276291, 2]], 'xcoord_integral_points': []}
• lmfdb_label 286650.et2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 12180804
    {'degree': 2, 'field': [-35, 0, 1], 'lmfdb_label': '286650.et2', 'torsion': [4]}
  • id: 12180803
    {'degree': 2, 'field': [-26, -1, 1], 'lmfdb_label': '286650.et2', 'torsion': [2, 2]}
  • id: 12180805
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '286650.et2', 'torsion': [4]}
  • id: 12180806
    {'degree': 2, 'field': [9, -1, 1], 'lmfdb_label': '286650.et2', 'torsion': [6]}
  • id: 12180807
    {'degree': 4, 'field': [64, 0, -19, 0, 1], 'lmfdb_label': '286650.et2', 'torsion': [2, 4]}
  • id: 12180808
    {'degree': 4, 'field': [81, -9, -8, -1, 1], 'lmfdb_label': '286650.et2', 'torsion': [2, 6]}
  • id: 12180809
    {'degree': 4, 'field': [81, 0, -17, 0, 1], 'lmfdb_label': '286650.et2', 'torsion': [12]}
  • id: 12180810
    {'degree': 4, 'field': [141, -12, 13, -2, 1], 'lmfdb_label': '286650.et2', 'torsion': [12]}
  • id: 12180811
    {'degree': 6, 'field': [-2625, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '286650.et2', 'torsion': [2, 6]}
  • id: 12180813
    {'degree': 8, 'field': [1, 4, -31, 4, 76, -4, -31, -4, 1], 'lmfdb_label': '286650.et2', 'torsion': [8]}
  • id: 12180815
    {'degree': 8, 'field': [6561, 0, 1377, 0, 208, 0, 17, 0, 1], 'lmfdb_label': '286650.et2', 'torsion': [2, 12]}
  • id: 12180814
    {'degree': 8, 'field': [176400, 0, 58800, 0, 7105, 0, 140, 0, 1], 'lmfdb_label': '286650.et2', 'torsion': [8]}
  • id: 12180812
    {'degree': 8, 'field': [14288400, 0, -793800, 0, 18480, 0, -210, 0, 1], 'lmfdb_label': '286650.et2', 'torsion': [2, 12]}
  • id: 12180817
    {'degree': 12, 'field': [28224, 0, 0, 0, 0, 0, -25179, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '286650.et2', 'torsion': [2, 12]}
  • id: 12180816
    {'degree': 12, 'field': [321489, 0, 0, 0, 0, 0, -546, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '286650.et2', 'torsion': [6, 6]}
  • id: 12180820
    {'degree': 16, 'field': [46804, 290924, 140790, -580214, -321615, 482022, 208168, -218846, -55536, 56342, 4906, -7590, 264, 434, -42, -8, 1], 'lmfdb_label': '286650.et2', 'torsion': [2, 8]}
  • id: 12180821
    {'degree': 16, 'field': [1863225, 0, 3333330, 0, 2615601, 0, 35190, 0, -14540, 0, -2642, 0, -15, 0, 10, 0, 1], 'lmfdb_label': '286650.et2', 'torsion': [24]}
  • id: 12180822
    {'degree': 16, 'field': [4270280121, -6510790584, 13469506866, -12678909516, 3322487028, 3400577376, -774284546, -293910068, 56231673, 11082896, -1806574, -218148, 31808, 2072, -276, -8, 1], 'lmfdb_label': '286650.et2', 'torsion': [24]}
  • id: 12180818
    {'degree': 16, 'field': [797493650625, 0, 0, 0, 1594049625, 0, 0, 0, 2293200, 0, 0, 0, 1785, 0, 0, 0, 1], 'lmfdb_label': '286650.et2', 'torsion': [4, 12]}
  • id: 12180819
    {'degree': 16, 'field': [5270220124416, 0, 969602537280, 0, 82473439204, 0, 4212044460, 0, 140487441, 0, 3009080, 0, 39834, 0, 300, 0, 1], 'lmfdb_label': '286650.et2', 'torsion': [2, 8]}
  • id: 12180823
    {'degree': 18, 'field': [4531905801216711, 1784626753927311, 260108553441789, 47939241589824, 27582069375810, 6819381342306, 948051584346, -58105850976, -7832156871, -636737795, 326984679, -5137776, -1190674, 11706, -6630, 1484, 39, -9, 1], 'lmfdb_label': '286650.et2', '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: 7099993
    {'conductor': 286650, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '286650.et2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 7099994
    {'conductor': 286650, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '286650.et2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 7099995
    {'conductor': 286650, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '286650.et2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 7099996
    {'conductor': 286650, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '286650.et2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 7099997
    {'conductor': 286650, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '286650.et2', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
• ec_galrep •

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

  
  
  • id: 3470813
    {'adelic_gens': [[3201, 5008, 10916, 2189], [2168, 10917, 2643, 86], [1, 12, 12, 145], [3624, 1807, 4729, 10326], [4201, 24, 6732, 289], [15, 106, 9614, 1691], [8191, 24, 8190, 1], [6224, 10917, 9819, 86], [10897, 24, 10896, 25], [1, 24, 0, 1], [1, 0, 24, 1]], 'adelic_image': '10920.384.5.?', 'conductor': 286650, 'lmfdb_label': '286650.et2', 'prime': 0}
  • id: 1016742
    {'conductor': 286650, 'elladic_image': '4.6.0.1', 'lmfdb_label': '286650.et2', 'modell_image': '2B', 'prime': 2}
  • id: 1016743
    {'conductor': 286650, 'elladic_image': '3.4.0.1', 'lmfdb_label': '286650.et2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 286650.et does not appear in ec_padic