Elliptic curve data - 73920.gp8

Formats: - HTML - YAML - JSON - 2025-10-21T15:30:25.530515

• 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': '73920hf', 'Clabel': '73920hf1', 'Cnumber': 1, 'abc_quality': 0.9990919448660593, 'absD': 68364470845440000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 9240, 'ainvs': [0, 1, 0, 101695, -1529025], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 73920, 'degree': 663552, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.9196890771473475739359470992', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 171, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [443688652450511, 260789760000], 'lmfdb_iso': '73920.gp', 'lmfdb_label': '73920.gp8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 1589, 3185], 'min_quad_twist_disc': -8, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '12.24.0.g.1', '24.48.0-12.g.1.27', '40.12.0-4.c.1.5', '56.12.0-4.c.1.2', '84.48.0.?', '120.96.0.?', '132.48.0.?', '168.96.0.?', '264.96.0.?', '280.24.0.?', '462.24.0.?', '840.192.1.?', '924.96.1.?', '1320.192.1.?', '1848.192.1.?', '9240.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 231], [3, 4, 3520], [5, 6, 14784], [7, 8, 10560], [11, 12, 6720]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.87996830630742960981009891701', 'prec': 103}, 'szpiro_ratio': 4.1212978608816275, '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, 1, 0, -1, 0, 1, 0, -1, 0, -2, 0, 1, 0, 6, 0, -4, 0], 'aplist': [0, 1, 1, -1, -1, -2, 6, -4, 0, -6, -8, 10, -6, 8, 0, -6, 12, -2, -4, -12, -10, 4, -12, 6, -10], 'class_deg': 12, 'class_size': 8, 'conductor': 73920, 'isogeny_matrix': [[1, 4, 2, 12, 3, 4, 6, 12], [4, 1, 2, 3, 12, 4, 6, 12], [2, 2, 1, 6, 6, 2, 3, 6], [12, 3, 6, 1, 4, 12, 2, 4], [3, 12, 6, 4, 1, 12, 2, 4], [4, 4, 2, 12, 12, 1, 6, 3], [6, 6, 3, 2, 2, 6, 1, 2], [12, 12, 6, 4, 4, 3, 2, 1]], 'lmfdb_iso': '73920.gp', 'trace_hash': 1442246196141058474}
• 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': '0.021506971205342152252679321011', 'prec': 107}, 'conductor': 73920, 'gens': [], 'heights': [], 'lmfdb_label': '73920.gp8', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.20401540897373995603353770299', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.4481849076848794724024524359320298371', 'prec': 130}, 'tamagawa_product': 48, 'torsion_generators': [[15, 0, 1]], 'xcoord_integral_points': [15]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '5': [1, 0], '7': [0, 0], '11': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '73920.gp8'}
• ec_torsion_growth •

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

  
  
  • id: 3501682
    {'degree': 2, 'field': [-14, 0, 1], 'lmfdb_label': '73920.gp8', 'torsion': [4]}
  • id: 3501684
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '73920.gp8', 'torsion': [6]}
  • id: 3501681
    {'degree': 2, 'field': [58, -1, 1], 'lmfdb_label': '73920.gp8', 'torsion': [2, 2]}
  • id: 3501683
    {'degree': 2, 'field': [66, 0, 1], 'lmfdb_label': '73920.gp8', 'torsion': [4]}
  • id: 3501687
    {'degree': 4, 'field': [2, -8, 9, -2, 1], 'lmfdb_label': '73920.gp8', 'torsion': [12]}
  • id: 3501688
    {'degree': 4, 'field': [102, 12, -11, -2, 1], 'lmfdb_label': '73920.gp8', 'torsion': [12]}
  • id: 3501685
    {'degree': 4, 'field': [400, 0, 26, 0, 1], 'lmfdb_label': '73920.gp8', 'torsion': [2, 4]}
  • id: 3501686
    {'degree': 4, 'field': [3138, -120, 121, -2, 1], 'lmfdb_label': '73920.gp8', 'torsion': [2, 6]}
  • id: 3501689
    {'degree': 6, 'field': [-864, 0, 148, 0, -2, 0, 1], 'lmfdb_label': '73920.gp8', 'torsion': [6]}
  • id: 3501691
    {'degree': 8, 'field': [4195, 9460, -9604, 280, -119, -28, 14, -4, 1], 'lmfdb_label': '73920.gp8', 'torsion': [8]}
  • id: 3501693
    {'degree': 8, 'field': [16900, 0, -4188, 0, 341, 0, -18, 0, 1], 'lmfdb_label': '73920.gp8', 'torsion': [2, 12]}
  • id: 3501692
    {'degree': 8, 'field': [108900, 0, 43560, 0, 3696, 0, 132, 0, 1], 'lmfdb_label': '73920.gp8', 'torsion': [8]}
  • id: 3501690
    {'degree': 8, 'field': [5175625, 0, -338296, 0, 5334, 0, 56, 0, 1], 'lmfdb_label': '73920.gp8', 'torsion': [2, 4]}
  • id: 3501694
    {'degree': 12, 'field': [22788, -38088, 22962, -12072, 4681, 1806, -1681, 522, -18, -6, 11, -6, 1], 'lmfdb_label': '73920.gp8', 'torsion': [3, 6]}
  • id: 3501696
    {'degree': 12, 'field': [1254400, 0, -246400, 0, -68400, 0, -4664, 0, 48, 0, -22, 0, 1], 'lmfdb_label': '73920.gp8', 'torsion': [12]}
  • id: 3501697
    {'degree': 12, 'field': [1610955, 370530, -300435, -135402, 56128, 12762, -2335, -1734, 552, -90, 29, -6, 1], 'lmfdb_label': '73920.gp8', 'torsion': [12]}
  • id: 3501695
    {'degree': 12, 'field': [233240940, -24267960, 58637520, -7091784, 3200263, -581314, 81005, -7498, 2002, -50, 41, -2, 1], 'lmfdb_label': '73920.gp8', 'torsion': [2, 6]}
  • id: 3501703
    {'degree': 16, 'field': [360000, 0, 2052000, 0, 2685300, 0, 835620, 0, -70679, 0, -7168, 0, 1074, 0, -52, 0, 1], 'lmfdb_label': '73920.gp8', 'torsion': [24]}
  • id: 3501699
    {'degree': 16, 'field': [100000000, 0, 132000000, 0, 67360000, 0, 15180000, 0, 1937700, 0, 151800, 0, 6736, 0, 132, 0, 1], 'lmfdb_label': '73920.gp8', 'torsion': [2, 8]}
  • id: 3501702
    {'degree': 16, 'field': [314672121, 0, -207267822, 0, 64222389, 0, -11526858, 0, 1273524, 0, -87878, 0, 3717, 0, -90, 0, 1], 'lmfdb_label': '73920.gp8', 'torsion': [24]}
  • id: 3501700
    {'degree': 16, 'field': [4106246400, 0, -1203802560, 0, 188128836, 0, -10450692, 0, -104531, 0, 38794, 0, -21, 0, -2, 0, 1], 'lmfdb_label': '73920.gp8', 'torsion': [2, 8]}
  • id: 3501698
    {'degree': 16, 'field': [118990502500, -30079640000, 3801920000, -2279212600, 1345970696, -182868448, 25050312, -16229028, 3284989, 371076, -30744, 12236, -2086, -28, 32, -8, 1], 'lmfdb_label': '73920.gp8', 'torsion': [4, 4]}
  • id: 3501701
    {'degree': 16, 'field': [212159729664, 0, 2300903424, 0, -250487664, 0, -29490048, 0, 1817977, 0, 392, 0, -1302, 0, 8, 0, 1], 'lmfdb_label': '73920.gp8', 'torsion': [2, 12]}
  • id: 3501704
    {'degree': 18, 'field': [64437628032, 0, 266927654016, 0, -65407608864, 0, 3709736512, 0, 134877432, 0, 2638536, 0, -143702, 0, -3612, 0, 66, 0, 1], 'lmfdb_label': '73920.gp8', '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: 1795185
    {'conductor': 73920, 'conductor_valuation': 6, 'discriminant_valuation': 30, 'j_denominator_valuation': 12, 'kodaira_symbol': -24, 'lmfdb_label': '73920.gp8', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1795186
    {'conductor': 73920, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '73920.gp8', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 1795187
    {'conductor': 73920, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '73920.gp8', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1795188
    {'conductor': 73920, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '73920.gp8', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1795189
    {'conductor': 73920, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '73920.gp8', 'prime': 11, '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: 2152548
    {'adelic_gens': [[2303, 9216, 1818, 7553], [1, 12, 12, 145], [15, 106, 7934, 11], [3697, 24, 7404, 289], [1336, 3, 6141, 9154], [3376, 21, 2235, 8866], [16, 4641, 7415, 5786], [7311, 8852, 340, 1891], [9217, 24, 9216, 25], [1, 24, 0, 1], [1, 0, 24, 1]], 'adelic_image': '9240.384.5.?', 'conductor': 73920, 'lmfdb_label': '73920.gp8', 'prime': 0}
  • id: 306185
    {'conductor': 73920, 'elladic_image': '4.6.0.1', 'lmfdb_label': '73920.gp8', 'modell_image': '2B', 'prime': 2}
  • id: 306186
    {'conductor': 73920, 'elladic_image': '3.4.0.1', 'lmfdb_label': '73920.gp8', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 73920.gp does not appear in ec_padic