Elliptic curve data - 1344.g1

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '1344a', 'Clabel': '1344a5', 'Cnumber': 5, 'abc_quality': 1.0508747826837916, 'absD': 38535168, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 336, 'ainvs': [0, -1, 0, -50177, -4309503], 'analytic_rank': 1, 'bad_primes': [2, 3, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 1344, 'degree': 2048, 'elladic_images': ['16.48.0.185'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1139261542308577348841140369', 'prec': 97}, 'faltings_index': 4, 'faltings_ratio': 8, 'intrinsic_torsion': 2, 'iso_nlabel': 6, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [53297461115137, 147], 'lmfdb_iso': '1344.g', 'lmfdb_label': '1344.g1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -784, -8515], 'min_quad_twist_disc': 8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0-8.n.1.9', '12.12.0.h.1', '16.48.0-16.e.2.8', '24.48.0-24.bl.1.7', '48.96.0-48.y.1.8', '56.48.0-56.bu.1.1', '112.96.0.?', '168.96.0.?', '336.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '7.8038422515393172345396087051', 'prec': 97}, 'semistable': False, 'serre_invariants': [[2, 2, 3], [3, 4, 448], [7, 8, 192]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.074205383390939770758265854713', 'prec': 97}, 'szpiro_ratio': 6.1198219277198405, '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, 2, 0, -1, 0, 1, 0, -4, 0, 2, 0, -2, 0, -6, 0, -4, 0], 'aplist': [0, -1, 2, -1, -4, 2, -6, -4, 0, 2, 0, -6, 2, 4, 0, -6, -12, 2, -4, 0, -6, -16, 12, -14, 18], 'class_deg': 8, 'class_size': 6, 'conductor': 1344, 'isogeny_matrix': [[1, 2, 8, 4, 4, 8], [2, 1, 4, 2, 2, 4], [8, 4, 1, 8, 2, 4], [4, 2, 8, 1, 4, 8], [4, 2, 2, 4, 1, 2], [8, 4, 4, 8, 2, 1]], 'lmfdb_iso': '1344.g', 'trace_hash': 107672636314719085}
• 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': '0.10775961620464087257951965839', 'prec': 97}, 'conductor': 1344, 'gens': [[4771, 329140, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '7.8038422515393172345396087051', 'prec': 97}], 'lmfdb_label': '1344.g1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.31898676224792113396902874741', 'prec': 97}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 97}, 'special_value': {'__RealLiteral__': 0, 'data': '2.4893223729120537406536303464304659286', 'prec': 127}, 'tamagawa_product': 4, 'torsion_generators': [[-129, 0, 1]], 'xcoord_integral_points': [-129, 4771]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [3, 0], '7': [3, 0], '11': [1, 0], '13': [1, 0], '17': [3, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [3, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '1344.g1'}
• ec_torsion_growth •

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

  
  
  • id: 66878
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '1344.g1', 'torsion': [2, 2]}
  • id: 66880
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '1344.g1', 'torsion': [4]}
  • id: 66879
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '1344.g1', 'torsion': [4]}
  • id: 66881
    {'degree': 4, 'field': [1, 0, 4, 0, 1], 'lmfdb_label': '1344.g1', 'torsion': [2, 4]}
  • id: 66883
    {'degree': 4, 'field': [2, -8, 9, -2, 1], 'lmfdb_label': '1344.g1', 'torsion': [8]}
  • id: 66882
    {'degree': 4, 'field': [121, 0, -20, 0, 1], 'lmfdb_label': '1344.g1', 'torsion': [8]}
  • id: 66884
    {'degree': 8, 'field': [-1151, 1564, -316, 196, -74, -28, -4, -4, 1], 'lmfdb_label': '1344.g1', 'torsion': [2, 4]}
  • id: 66887
    {'degree': 8, 'field': [-48, 0, -8, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '1344.g1', 'torsion': [6]}
  • id: 66885
    {'degree': 8, 'field': [1, 0, 4, 0, 3, 0, -2, 0, 1], 'lmfdb_label': '1344.g1', 'torsion': [8]}
  • id: 66886
    {'degree': 8, 'field': [22, -68, 130, -140, 111, -52, 22, -4, 1], 'lmfdb_label': '1344.g1', 'torsion': [2, 8]}
  • id: 66889
    {'degree': 16, 'field': [1, -12, 68, -232, 488, -564, 194, 396, -665, 444, -62, -152, 162, -92, 34, -8, 1], 'lmfdb_label': '1344.g1', 'torsion': [2, 8]}
  • id: 66893
    {'degree': 16, 'field': [9, 0, 12, 0, 253, 0, 24, 0, -546, 0, -52, 0, -84, 0, 0, 0, 1], 'lmfdb_label': '1344.g1', 'torsion': [2, 6]}
  • id: 66890
    {'degree': 16, 'field': [31, 176, 308, 60, 56, 664, -8, -348, 763, -480, 160, -76, 92, -72, 32, -8, 1], 'lmfdb_label': '1344.g1', 'torsion': [16]}
  • id: 66895
    {'degree': 16, 'field': [169, 0, 4318, 0, 4477, 0, 4980, 0, 1914, 0, 498, 0, 100, 0, 16, 0, 1], 'lmfdb_label': '1344.g1', 'torsion': [12]}
  • id: 66894
    {'degree': 16, 'field': [681, -3066, 3679, -2096, -773, 5906, 18425, 12596, 4946, 14, 32, 22, 73, -26, -5, -2, 1], 'lmfdb_label': '1344.g1', 'torsion': [12]}
  • id: 66892
    {'degree': 16, 'field': [3111696, 0, 0, 0, -296352, 0, 0, 0, 12985, 0, 0, 0, -168, 0, 0, 0, 1], 'lmfdb_label': '1344.g1', 'torsion': [16]}
  • id: 66888
    {'degree': 16, 'field': [4879681, 0, -4108740, 0, 1599418, 0, -375720, 0, 60915, 0, -7272, 0, 634, 0, -36, 0, 1], 'lmfdb_label': '1344.g1', 'torsion': [4, 4]}
  • id: 66891
    {'degree': 16, 'field': [94128804, 0, 43563744, 0, 12113388, 0, 889056, 0, 55125, 0, 3528, 0, 504, 0, 0, 0, 1], 'lmfdb_label': '1344.g1', 'torsion': [2, 16]}
• 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: 20299
    {'conductor': 1344, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '1344.g1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 20300
    {'conductor': 1344, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '1344.g1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 20301
    {'conductor': 1344, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '1344.g1', 'prime': 7, '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: 1673009
    {'adelic_gens': [[134, 89, 213, 170], [109, 16, 128, 21], [5, 4, 332, 333], [1, 16, 0, 1], [323, 320, 172, 231], [15, 2, 238, 323], [321, 16, 320, 17], [128, 5, 291, 322], [1, 0, 16, 1]], 'adelic_image': '336.192.1.?', 'conductor': 1344, 'lmfdb_label': '1344.g1', 'prime': 0}
  • id: 6490
    {'conductor': 1344, 'elladic_image': '16.48.0.185', 'lmfdb_label': '1344.g1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 34494
    {'lmfdb_iso': '1344.g', 'p': 5, 'prec': 20, 'unit': 3352463430881, 'val': 2}
  • id: 34500
    {'lmfdb_iso': '1344.g', 'p': 11, 'prec': 20, 'unit': 25360926278664323272, 'val': 1}
  • id: 34498
    {'lmfdb_iso': '1344.g', 'p': 13, 'prec': 20, 'unit': 539699842433461821378, 'val': 1}
  • id: 34501
    {'lmfdb_iso': '1344.g', 'p': 17, 'prec': 20, 'unit': 1579211386210932945025, 'val': 2}
  • id: 34502
    {'lmfdb_iso': '1344.g', 'p': 19, 'prec': 20, 'unit': 125506217333751282265048, 'val': 1}
  • id: 34497
    {'lmfdb_iso': '1344.g', 'p': 29, 'prec': 20, 'unit': 4741197372153095737197878028, 'val': 1}
  • id: 34508
    {'lmfdb_iso': '1344.g', 'p': 37, 'prec': 20, 'unit': 507732323516291462682073535661, 'val': 1}
  • id: 34495
    {'lmfdb_iso': '1344.g', 'p': 41, 'prec': 20, 'unit': 174143200578325473894386989642, 'val': 1}
  • id: 34496
    {'lmfdb_iso': '1344.g', 'p': 43, 'prec': 20, 'unit': 10557167935240655547164606948919, 'val': 1}
  • id: 34503
    {'lmfdb_iso': '1344.g', 'p': 53, 'prec': 20, 'unit': 195604972649955561684187093586909, 'val': 1}
  • id: 34506
    {'lmfdb_iso': '1344.g', 'p': 59, 'prec': 20, 'unit': 3956658722437807730347272249564276, 'val': 1}
  • id: 34507
    {'lmfdb_iso': '1344.g', 'p': 61, 'prec': 20, 'unit': 7543428837889190999574963681951004, 'val': 1}
  • id: 34493
    {'lmfdb_iso': '1344.g', 'p': 67, 'prec': 20, 'unit': 29588370833841855297176400438120429, 'val': 1}
  • id: 34504
    {'lmfdb_iso': '1344.g', 'p': 73, 'prec': 20, 'unit': 92428216411136529046050320797866869, 'val': 1}
  • id: 34499
    {'lmfdb_iso': '1344.g', 'p': 79, 'prec': 20, 'unit': 167160512207368223188339110286636204, 'val': 1}
  • id: 34492
    {'lmfdb_iso': '1344.g', 'p': 83, 'prec': 20, 'unit': 2873973532562950163072162055776450893, 'val': 1}
  • id: 34505
    {'lmfdb_iso': '1344.g', 'p': 89, 'prec': 20, 'unit': 85937237600166541591813989268299347, 'val': 2}
  • id: 34491
    {'lmfdb_iso': '1344.g', 'p': 97, 'prec': 20, 'unit': 38595898454782697395829002295563976500, 'val': 1}