Elliptic curve data - 61152.x2

Formats: - HTML - YAML - JSON - 2025-11-09T01:07:57.543837

• 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': '61152c', 'Clabel': '61152c3', 'Cnumber': 3, 'abc_quality': 1.069422794221752, 'absD': 371608262258688, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 2184, 'ainvs': [0, -1, 0, -18097, 139777], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 61152, 'degree': 294912, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4856714168770380229482593206', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 23, 'isogeny_degrees': [1, 2, 4], 'jinv': [1360251712, 771147], 'lmfdb_iso': '61152.x', 'lmfdb_label': '61152.x2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -369, 513], 'min_quad_twist_disc': 28, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '12.12.0.h.1', '28.12.0-4.c.1.1', '84.24.0.?', '104.12.0.?', '312.24.0.?', '728.24.0.?', '2184.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 147], [3, 4, 20384], [7, 26, 1248], [13, 14, 4704]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.18043083821056393902164917258', 'prec': 107}, 'szpiro_ratio': 3.7223232009982534, '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, 0, 0, 1, 0, -4, 0, -1, 0, -2, 0, 6, 0, -8, 0], 'aplist': [0, -1, 2, 0, -4, -1, 6, -8, -8, 2, 8, -10, -6, 4, 0, -14, -12, 10, 8, 0, 14, 4, 4, 10, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 61152, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '61152.x', 'trace_hash': 1387711682595005967}
• 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': '0.051234464749540709641875325304', 'prec': 107}, 'conductor': 61152, 'gens': [], 'heights': [], 'lmfdb_label': '61152.x2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.46135677767163758793793628247', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.92271355534327517587587256493015517975', 'prec': 133}, 'tamagawa_product': 8, 'torsion_generators': [[131, 0, 1]], 'xcoord_integral_points': [131]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '7': 'a', '13': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '61152.x2'}
• ec_torsion_growth •

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

  
  
  • id: 2930553
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '61152.x2', 'torsion': [4]}
  • id: 2930552
    {'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '61152.x2', 'torsion': [4]}
  • id: 2930551
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '61152.x2', 'torsion': [2, 2]}
  • id: 2930554
    {'degree': 4, 'field': [1, 0, -5, 0, 1], 'lmfdb_label': '61152.x2', 'torsion': [2, 4]}
  • id: 2930558
    {'degree': 8, 'field': [-73422, -36324, 4068, 3144, -156, -36, -2, -4, 1], 'lmfdb_label': '61152.x2', 'torsion': [6]}
  • id: 2930555
    {'degree': 8, 'field': [144, 0, 0, 0, -3, 0, 0, 0, 1], 'lmfdb_label': '61152.x2', 'torsion': [2, 4]}
  • id: 2930556
    {'degree': 8, 'field': [3403, 2576, -1934, -1228, 475, 164, -50, -4, 1], 'lmfdb_label': '61152.x2', 'torsion': [8]}
  • id: 2930557
    {'degree': 8, 'field': [3844, 0, 928, 0, 380, 0, -32, 0, 1], 'lmfdb_label': '61152.x2', 'torsion': [8]}
  • id: 2930564
    {'degree': 16, 'field': [-543206, -678996, 695632, 791784, -90836, -381096, -186134, 69480, 70687, -4140, -3494, -792, -272, -36, 4, 0, 1], 'lmfdb_label': '61152.x2', 'torsion': [12]}
  • id: 2930563
    {'degree': 16, 'field': [729, 0, -15120, 0, 23722, 0, -10080, 0, -13905, 0, 12320, 0, -414, 0, 0, 0, 1], 'lmfdb_label': '61152.x2', 'torsion': [12]}
  • id: 2930561
    {'degree': 16, 'field': [1849, 0, -852548, 0, 1849486, 0, -1180232, 0, 330559, 0, -45104, 0, 3010, 0, -92, 0, 1], 'lmfdb_label': '61152.x2', 'torsion': [2, 8]}
  • id: 2930559
    {'degree': 16, 'field': [20736, 0, 0, 0, 432, 0, 0, 0, -135, 0, 0, 0, 3, 0, 0, 0, 1], 'lmfdb_label': '61152.x2', 'torsion': [4, 4]}
  • id: 2930562
    {'degree': 16, 'field': [26457, -904200, -263144, -259744, -1799096, -657756, 65082, -362652, -283321, -20576, 26618, 6084, -918, -204, 10, -4, 1], 'lmfdb_label': '61152.x2', 'torsion': [2, 6]}
  • id: 2930560
    {'degree': 16, 'field': [1155625, 0, 681692, 0, 204350, 0, 29208, 0, 10895, 0, -1392, 0, 386, 0, -28, 0, 1], 'lmfdb_label': '61152.x2', 'torsion': [2, 8]}
• 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: 1473125
    {'conductor': 61152, 'conductor_valuation': 5, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '61152.x2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1473126
    {'conductor': 61152, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '61152.x2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1473127
    {'conductor': 61152, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '61152.x2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1473128
    {'conductor': 61152, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '61152.x2', 'prime': 13, '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: 2069336
    {'adelic_gens': [[2064, 343, 1295, 1308], [2177, 8, 2176, 9], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [827, 1134, 434, 1835], [2017, 1568, 1204, 1905], [1772, 1561, 1687, 1254], [7, 6, 2178, 2179], [935, 0, 0, 2183]], 'adelic_image': '2184.48.0.?', 'conductor': 61152, 'lmfdb_label': '61152.x2', 'prime': 0}
  • id: 257819
    {'conductor': 61152, 'elladic_image': '4.6.0.1', 'lmfdb_label': '61152.x2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 61152.x does not appear in ec_padic