Elliptic curve data - 3192.m1

Formats: - HTML - YAML - JSON - 2025-04-29T14:41:26.652100

• 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': '3192i', 'Clabel': '3192i4', 'Cnumber': 4, 'abc_quality': 0.9266087677152098, 'absD': 893555712, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1064, 'ainvs': [0, 1, 0, -2864, 58032], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 3192, 'degree': 2048, 'elladic_images': ['8.12.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.68875733956973998728733385844', 'prec': 103}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 12, 'isogeny_degrees': [1, 2, 4], 'jinv': [2538016415428, 872613], 'lmfdb_iso': '3192.m', 'lmfdb_label': '3192.m1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -2864, 58032], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.5', '28.12.0-4.c.1.1', '56.24.0-56.ba.1.10', '76.12.0.?', '152.24.0.?', '266.6.0.?', '532.24.0.?', '1064.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 7, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.59127194678712813059886523122', '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': '0.11113468910311889610630709056', 'prec': 103}, 'szpiro_ratio': 4.399120363833573, '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, 2, 0, -1, 0], 'aplist': [0, 1, -2, 1, -4, 2, 2, -1, 0, -2, -8, -2, -2, 4, 0, -2, -12, 14, 8, -12, -14, -4, -4, -18, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 3192, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '3192.m', 'trace_hash': 261951610605323863}
• 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': '0.25220458410750647440464543015', 'prec': 103}, 'conductor': 3192, 'gens': [[4, 216, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.59127194678712813059886523122', 'prec': 103}], 'lmfdb_label': '3192.m1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.5458250509773496853335522103', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.6560119491347565319134155249380905606', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[31, 0, 1]], 'xcoord_integral_points': [4, 28, 31, 67]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [4, 0], '5': [1, 0], '7': [2, 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, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '3192.m1'}
• ec_torsion_growth •

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

  
  
  • id: 166558
    {'degree': 2, 'field': [-33, -1, 1], 'lmfdb_label': '3192.m1', 'torsion': [2, 2]}
  • id: 166560
    {'degree': 2, 'field': [-19, 0, 1], 'lmfdb_label': '3192.m1', 'torsion': [4]}
  • id: 166559
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '3192.m1', 'torsion': [4]}
  • id: 166561
    {'degree': 4, 'field': [9, 0, -13, 0, 1], 'lmfdb_label': '3192.m1', 'torsion': [2, 4]}
  • id: 166562
    {'degree': 4, 'field': [18, -4, -16, -2, 1], 'lmfdb_label': '3192.m1', 'torsion': [8]}
  • id: 166566
    {'degree': 8, 'field': [-7203, 0, 980, 0, -294, 0, 0, 0, 1], 'lmfdb_label': '3192.m1', 'torsion': [6]}
  • id: 166565
    {'degree': 8, 'field': [-27, 438, 58, -946, 359, 134, -40, -4, 1], 'lmfdb_label': '3192.m1', 'torsion': [2, 8]}
  • id: 166564
    {'degree': 8, 'field': [17689, 0, 0, 0, 95, 0, 0, 0, 1], 'lmfdb_label': '3192.m1', 'torsion': [8]}
  • id: 166563
    {'degree': 8, 'field': [282508, -10672, 9632, 2072, -1015, -28, 14, -4, 1], 'lmfdb_label': '3192.m1', 'torsion': [2, 4]}
  • id: 166572
    {'degree': 16, 'field': [-113176512, 1488863616, 154720192, -274897664, -88705472, 20735968, 5840032, 1964704, -591600, -198480, 38280, 4408, -1220, 196, -8, -8, 1], 'lmfdb_label': '3192.m1', 'torsion': [12]}
  • id: 166570
    {'degree': 16, 'field': [1679616, 0, -1736384256, 0, -3635996544, 0, 105777792, 0, -19344, 0, 523616, 0, 120, 0, 0, 0, 1], 'lmfdb_label': '3192.m1', 'torsion': [2, 6]}
  • id: 166571
    {'degree': 16, 'field': [5764801, 0, -6588344, 0, -336140, 0, -694232, 0, 55174, 0, -14168, 0, -140, 0, -56, 0, 1], 'lmfdb_label': '3192.m1', 'torsion': [12]}
  • id: 166568
    {'degree': 16, 'field': [314178993, 35186292, -25365186, -17979300, 4867348, 4848756, -1452402, -142420, 40301, -6724, 5186, -2428, 708, -168, 44, -8, 1], 'lmfdb_label': '3192.m1', 'torsion': [2, 8]}
  • id: 166567
    {'degree': 16, 'field': [318194244, 0, 90316872, 0, 19794712, 0, 1172052, 0, 57533, 0, 1344, 0, 602, 0, -12, 0, 1], 'lmfdb_label': '3192.m1', 'torsion': [4, 4]}
  • id: 166569
    {'degree': 16, 'field': [80102584576, 0, -14755739264, 0, -206041472, 0, 18538072, 0, 1053493, 0, 34846, 0, -728, 0, -98, 0, 1], 'lmfdb_label': '3192.m1', 'torsion': [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: 57695
    {'conductor': 3192, 'conductor_valuation': 3, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '3192.m1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 57696
    {'conductor': 3192, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '3192.m1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 57697
    {'conductor': 3192, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '3192.m1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 57698
    {'conductor': 3192, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '3192.m1', '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: 1684749
    {'adelic_gens': [[1057, 8, 1056, 9], [939, 932, 978, 405], [403, 402, 146, 675], [7, 6, 1058, 1059], [1, 0, 8, 1], [460, 1, 783, 6], [624, 3, 789, 2], [1, 8, 0, 1], [1, 4, 4, 17]], 'adelic_image': '1064.48.0.?', 'conductor': 3192, 'lmfdb_label': '3192.m1', 'prime': 0}
  • id: 16020
    {'conductor': 3192, 'elladic_image': '8.12.0.6', 'lmfdb_label': '3192.m1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 104790
    {'lmfdb_iso': '3192.m', 'p': 5, 'prec': 20, 'unit': 5889097787798, 'val': 1}
  • id: 104789
    {'lmfdb_iso': '3192.m', 'p': 11, 'prec': 20, 'unit': 34664291066373843206, 'val': 1}
  • id: 104796
    {'lmfdb_iso': '3192.m', 'p': 13, 'prec': 20, 'unit': 804152742859043314407, 'val': 1}
  • id: 104798
    {'lmfdb_iso': '3192.m', 'p': 17, 'prec': 20, 'unit': 184494953317958769334491, 'val': 1}
  • id: 104795
    {'lmfdb_iso': '3192.m', 'p': 29, 'prec': 20, 'unit': 2488615265644648100556239575, 'val': 1}
  • id: 104792
    {'lmfdb_iso': '3192.m', 'p': 31, 'prec': 20, 'unit': 16546565748939766904447816036, 'val': 1}
  • id: 104805
    {'lmfdb_iso': '3192.m', 'p': 37, 'prec': 20, 'unit': 144568882389995980401452986460, 'val': 1}
  • id: 104793
    {'lmfdb_iso': '3192.m', 'p': 41, 'prec': 20, 'unit': 1896896711244651295944943145501, 'val': 1}
  • id: 104794
    {'lmfdb_iso': '3192.m', 'p': 43, 'prec': 20, 'unit': 6738666856858105479024202441845, 'val': 1}
  • id: 104800
    {'lmfdb_iso': '3192.m', 'p': 53, 'prec': 20, 'unit': 558103444647803405127966310898860, 'val': 1}
  • id: 104803
    {'lmfdb_iso': '3192.m', 'p': 59, 'prec': 20, 'unit': 667121262626619159570993937059289, 'val': 1}
  • id: 104804
    {'lmfdb_iso': '3192.m', 'p': 61, 'prec': 20, 'unit': 8069130742893839215609109543692896, 'val': 1}
  • id: 104788
    {'lmfdb_iso': '3192.m', 'p': 67, 'prec': 20, 'unit': 43927013998297257625868063064966395, 'val': 1}
  • id: 104791
    {'lmfdb_iso': '3192.m', 'p': 71, 'prec': 20, 'unit': 87265995969767319496375453971340573, 'val': 1}
  • id: 104801
    {'lmfdb_iso': '3192.m', 'p': 73, 'prec': 20, 'unit': 208399110290736286863084701572436564, 'val': 1}
  • id: 104797
    {'lmfdb_iso': '3192.m', 'p': 79, 'prec': 20, 'unit': 103561431370220264137310606982188004, 'val': 1}
  • id: 104799
    {'lmfdb_iso': '3192.m', 'p': 83, 'prec': 20, 'unit': 1447446848631978534367432477895804014, 'val': 1}
  • id: 104802
    {'lmfdb_iso': '3192.m', 'p': 89, 'prec': 20, 'unit': 9023215431442430859789731358603758990, 'val': 1}
  • id: 104787
    {'lmfdb_iso': '3192.m', 'p': 97, 'prec': 20, 'unit': 27048107351435495676491415904035566209, 'val': 1}