Elliptic curve data - 3192.k1

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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': '3192o', 'Clabel': '3192o1', 'Cnumber': 1, 'abc_quality': 0.8570171769286747, 'absD': 1551312, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1596, 'ainvs': [0, 1, 0, -35, -66], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 19], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 3192, 'degree': 768, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.10828387020030236526525633004', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2], 'jinv': [304900096, 96957], 'lmfdb_iso': '3192.k', 'lmfdb_label': '3192.k1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -35, -66], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.c.1', '266.6.0.?', '1596.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 7, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.54019793666063846644439411192', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 133], [3, 4, 1064], [7, 8, 456], [19, 20, 168]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.33933293038695080173766703719', 'prec': 107}, 'szpiro_ratio': 2.764869772073226, '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, 0, 1, 0, -4, 0, -1, 0, 1, 0, 4, 0, 2, 0, -4, 0, -4, 0, -1, 0], 'aplist': [0, 1, -4, -1, 4, 2, -4, -1, 0, 4, -8, -2, -6, 12, -10, 0, -12, -2, -8, 6, 14, -8, 6, 2, 2], 'class_deg': 2, 'class_size': 2, 'conductor': 3192, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '3192.k', 'trace_hash': 1766410087073215378}
• 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': '1.2418072030221210889864699954', 'prec': 100}, 'conductor': 3192, 'gens': [[7, 9, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.54019793666063846644439411192', 'prec': 103}], 'lmfdb_label': '3192.k1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '2.0073309476563510138934274481', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.2530681083570146817084027425760315912', 'prec': 130}, 'tamagawa_product': 12, 'torsion_generators': [[-2, 0, 1]], 'xcoord_integral_points': [-5, -2, 7, 34]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [1, 0], '7': [1, 0], '11': [1, 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, 0]}, 'iwp0': 0, 'lmfdb_label': '3192.k1'}
• ec_torsion_growth •

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

  
  
  • id: 166709
    {'degree': 2, 'field': [-33, -1, 1], 'lmfdb_label': '3192.k1', 'torsion': [2, 2]}
  • id: 166710
    {'degree': 4, 'field': [9, 3, -5, -1, 1], 'lmfdb_label': '3192.k1', 'torsion': [4]}
  • id: 166713
    {'degree': 8, 'field': [-27, 0, 20, 0, 18, 0, 0, 0, 1], 'lmfdb_label': '3192.k1', 'torsion': [6]}
  • id: 166712
    {'degree': 8, 'field': [729, 0, -2390, 0, -1093, 0, -10, 0, 1], 'lmfdb_label': '3192.k1', 'torsion': [2, 4]}
  • id: 166711
    {'degree': 8, 'field': [729, 0, 135, 0, 52, 0, -5, 0, 1], 'lmfdb_label': '3192.k1', 'torsion': [2, 4]}
  • id: 166714
    {'degree': 16, 'field': [9891, 6930, 4374, -21492, 9501, -3240, 10332, -11106, 7822, -5186, 3136, -1514, 586, -182, 46, -8, 1], 'lmfdb_label': '3192.k1', 'torsion': [8]}
  • id: 166715
    {'degree': 16, 'field': [4782969, 0, -20907720, 0, -12633570, 0, -174960, 0, 11895, 0, -6400, 0, -474, 0, 0, 0, 1], 'lmfdb_label': '3192.k1', 'torsion': [2, 6]}
• 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: 57755
    {'conductor': 3192, 'conductor_valuation': 3, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '3192.k1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 57756
    {'conductor': 3192, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '3192.k1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 57757
    {'conductor': 3192, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '3192.k1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 57758
    {'conductor': 3192, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '3192.k1', 'prime': 19, '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: 1684745
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [533, 4, 1066, 9], [1593, 4, 1592, 5], [422, 1, 587, 0], [230, 1, 683, 0], [401, 1198, 1196, 399]], 'adelic_image': '1596.12.0.?', 'conductor': 3192, 'lmfdb_label': '3192.k1', 'prime': 0}
  • id: 16016
    {'conductor': 3192, 'elladic_image': '2.3.0.1', 'lmfdb_label': '3192.k1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 104862
    {'lmfdb_iso': '3192.k', 'p': 5, 'prec': 20, 'unit': 2247881270098, 'val': -1}
  • id: 104861
    {'lmfdb_iso': '3192.k', 'p': 11, 'prec': 20, 'unit': 42252910093417503881, 'val': 1}
  • id: 104868
    {'lmfdb_iso': '3192.k', 'p': 13, 'prec': 20, 'unit': 605110474289655212507, 'val': 1}
  • id: 104870
    {'lmfdb_iso': '3192.k', 'p': 17, 'prec': 20, 'unit': 66824068772422550023809, 'val': 1}
  • id: 104867
    {'lmfdb_iso': '3192.k', 'p': 29, 'prec': 20, 'unit': 1254297701694643471015401735, 'val': 1}
  • id: 104864
    {'lmfdb_iso': '3192.k', 'p': 31, 'prec': 20, 'unit': 6720969682827501898943842803, 'val': 1}
  • id: 104877
    {'lmfdb_iso': '3192.k', 'p': 37, 'prec': 20, 'unit': 124875832828661813997870931943, 'val': 1}
  • id: 104865
    {'lmfdb_iso': '3192.k', 'p': 41, 'prec': 20, 'unit': 227927345740929370335558031533, 'val': 1}
  • id: 104866
    {'lmfdb_iso': '3192.k', 'p': 43, 'prec': 20, 'unit': 9906409306728669446743783931988, 'val': 1}
  • id: 104875
    {'lmfdb_iso': '3192.k', 'p': 47, 'prec': 20, 'unit': 23224944950111856223360604632334, 'val': 1}
  • id: 104872
    {'lmfdb_iso': '3192.k', 'p': 59, 'prec': 20, 'unit': 1528880106777141111595026814465994, 'val': 1}
  • id: 104876
    {'lmfdb_iso': '3192.k', 'p': 61, 'prec': 20, 'unit': 3412280675454534336431980636791048, 'val': 1}
  • id: 104871
    {'lmfdb_iso': '3192.k', 'p': 67, 'prec': 20, 'unit': 13791915597817975605458253688732665, 'val': 1}
  • id: 104863
    {'lmfdb_iso': '3192.k', 'p': 71, 'prec': 20, 'unit': 25161597239834715898957669395553895, 'val': 1}
  • id: 104873
    {'lmfdb_iso': '3192.k', 'p': 73, 'prec': 20, 'unit': 183797232962639919623258013124432206, 'val': 1}
  • id: 104869
    {'lmfdb_iso': '3192.k', 'p': 79, 'prec': 20, 'unit': 178967773771572311782101829153615831, 'val': 1}
  • id: 104860
    {'lmfdb_iso': '3192.k', 'p': 83, 'prec': 20, 'unit': 1055191317512930544138188916948243007, 'val': 1}
  • id: 104874
    {'lmfdb_iso': '3192.k', 'p': 89, 'prec': 20, 'unit': 3313467751604649321364864744312648883, 'val': 1}
  • id: 104859
    {'lmfdb_iso': '3192.k', 'p': 97, 'prec': 20, 'unit': 16125408656572157550610252969163715952, 'val': 1}