Elliptic curve data - 3312.p4

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '3312b', 'Clabel': '3312b1', 'Cnumber': 1, 'abc_quality': 0.8985027081418636, 'absD': 347680512, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 552, 'ainvs': [0, 0, 0, -39, 902], 'analytic_rank': 0, 'bad_primes': [2, 3, 23], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 3312, 'degree': 1024, 'elladic_images': ['8.12.0.12'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.31881739245112845414470925830', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 15, 'isogeny_degrees': [1, 2, 4], 'jinv': [-35152, 1863], 'lmfdb_iso': '3312.p', 'lmfdb_label': '3312.p4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -4, 32], 'min_quad_twist_disc': 12, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.2', '12.12.0-4.c.1.1', '24.24.0-24.y.1.10', '46.6.0.a.1', '92.12.0.?', '184.24.0.?', '276.24.0.?', '552.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.69258687225622326449773477447', 'prec': 107}, 'szpiro_ratio': 3.3474824398494616, '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, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 4, 0], 'aplist': [0, 0, 2, 4, 0, -2, 2, 4, -1, 2, 8, 2, -10, 4, 0, -6, 12, 2, 12, -16, 10, 4, 0, -6, -14], 'class_deg': 4, 'class_size': 4, 'conductor': 3312, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '3312.p', 'trace_hash': 1661713393460512702}
• 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': '0.52854106010966121017173830871', 'prec': 103}, 'conductor': 3312, 'gens': [], 'heights': [], 'lmfdb_label': '3312.p4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.4124937887803021440702497818', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.8249875775606042881404995636456320013', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-11, 0, 1]], 'xcoord_integral_points': [-11]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '23': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '3312.p4'}
• ec_torsion_growth •

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

  
  
  • id: 172682
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '3312.p4', 'torsion': [4]}
  • id: 172681
    {'degree': 2, 'field': [6, -1, 1], 'lmfdb_label': '3312.p4', 'torsion': [2, 2]}
  • id: 172683
    {'degree': 2, 'field': [69, 0, 1], 'lmfdb_label': '3312.p4', 'torsion': [4]}
  • id: 172684
    {'degree': 4, 'field': [78, -6, 7, -2, 1], 'lmfdb_label': '3312.p4', 'torsion': [2, 4]}
  • id: 172688
    {'degree': 8, 'field': [-108, 0, -300, 0, -36, 0, 0, 0, 1], 'lmfdb_label': '3312.p4', 'torsion': [6]}
  • id: 172686
    {'degree': 8, 'field': [1, 0, -6, 0, -13, 0, -6, 0, 1], 'lmfdb_label': '3312.p4', 'torsion': [8]}
  • id: 172687
    {'degree': 8, 'field': [36, 0, 840, 0, 496, 0, -44, 0, 1], 'lmfdb_label': '3312.p4', 'torsion': [8]}
  • id: 172685
    {'degree': 8, 'field': [529, 0, 0, 0, -23, 0, 0, 0, 1], 'lmfdb_label': '3312.p4', 'torsion': [2, 4]}
  • id: 172689
    {'degree': 16, 'field': [1296, -432, 72, -1320, 328, -396, 786, -254, 233, -278, 200, -86, 27, -12, 8, -4, 1], 'lmfdb_label': '3312.p4', 'torsion': [4, 4]}
  • id: 172693
    {'degree': 16, 'field': [2916, 0, -1944, 0, 324, 0, -1404, 0, -1332, 0, 168, 0, 144, 0, -24, 0, 1], 'lmfdb_label': '3312.p4', 'torsion': [12]}
  • id: 172690
    {'degree': 16, 'field': [6084, -936, 1692, 72, -566, -2640, 2814, -316, 221, -880, 794, -340, 96, -24, 20, -8, 1], 'lmfdb_label': '3312.p4', 'torsion': [2, 8]}
  • id: 172691
    {'degree': 16, 'field': [46656, 0, 28512, 0, 79092, 0, -7404, 0, 13945, 0, 5168, 0, 738, 0, 44, 0, 1], 'lmfdb_label': '3312.p4', 'torsion': [2, 8]}
  • id: 172692
    {'degree': 16, 'field': [59049, 0, 37908, 0, 132516, 0, 8424, 0, 2430, 0, -156, 0, -108, 0, 0, 0, 1], 'lmfdb_label': '3312.p4', 'torsion': [2, 6]}
  • id: 172694
    {'degree': 16, 'field': [69205761, 0, -45127992, 0, 57715996, 0, -3761808, 0, 112998, 0, -13112, 0, 204, 0, 0, 0, 1], 'lmfdb_label': '3312.p4', 'torsion': [12]}
• 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: 60123
    {'conductor': 3312, 'conductor_valuation': 4, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '3312.p4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 60124
    {'conductor': 3312, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '3312.p4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 60125
    {'conductor': 3312, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '3312.p4', 'prime': 23, '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: 1685549
    {'adelic_gens': [[479, 480, 194, 473], [367, 544, 364, 519], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [7, 6, 546, 547], [491, 486, 74, 347], [545, 8, 544, 9], [388, 1, 23, 6]], 'adelic_image': '552.48.0.?', 'conductor': 3312, 'lmfdb_label': '3312.p4', 'prime': 0}
  • id: 16631
    {'conductor': 3312, 'elladic_image': '8.12.0.12', 'lmfdb_label': '3312.p4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 3312.p does not appear in ec_padic