Elliptic curve data - 165825.k1

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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
  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': '165825h', 'Clabel': '165825h3', 'Cnumber': 3, 'abc_quality': 0.9697034959062909, 'absD': 2453890037035078125, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 8040, 'ainvs': [1, -1, 1, -1274630, 549057872], 'analytic_rank': 2, 'bad_primes': [3, 5, 11, 67], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 165825, 'degree': 2457600, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3443785904710083145318771635', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2, 4], 'jinv': [20106118884162961, 215430675405], 'lmfdb_iso': '165825.k', 'lmfdb_label': '165825.k1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -5665, -164950], 'min_quad_twist_disc': -15, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '12.12.0-4.c.1.1', '40.12.0.ba.1', '120.24.0.?', '536.12.0.?', '1340.12.0.?', '1608.24.0.?', '2010.6.0.?', '2680.24.0.?', '4020.24.0.?', '8040.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 12, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '4.1254164910438166980169941865', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 15075], [3, 8, 18425], [5, 18, 6633], [11, 12, 15075], [67, 68, 2475]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.99035348991990328153387487843', 'prec': 103}, 'szpiro_ratio': 4.475372060148166, '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, -1, 0, -1, 0, 0, 0, 3, 0, 0, 1, 0, -2, 0, 0, -1, -2, 0, 4, 0], 'aplist': [-1, 0, 0, 0, 1, -2, -2, 4, 0, -6, -4, -6, -10, -12, 0, 6, 0, -10, 1, 4, 14, -4, -12, -18, -6], 'class_deg': 4, 'class_size': 4, 'conductor': 165825, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '165825.k', 'trace_hash': 807030170673016968}
• 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': '0.0091981106426935828836346518333', 'prec': 110}, 'conductor': 165825, 'gens': [[975, 14758, 1], [84, 20995, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.0122973810264832040759121541', 'prec': 100}, {'__RealLiteral__': 0, 'data': '2.0617489979151272066961140711', 'prec': 100}], 'lmfdb_label': '165825.k1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.25877597914016715514325958300', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.5404695346468503300527619387352928876', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[2811, -2815, 2]], 'xcoord_integral_points': [-1302, -1016, 84, 370, 975, 1459]}
• lmfdb_label 165825.k1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7396629
    {'degree': 2, 'field': [-335, 0, 1], 'lmfdb_label': '165825.k1', 'torsion': [4]}
  • id: 7396628
    {'degree': 2, 'field': [-251, -1, 1], 'lmfdb_label': '165825.k1', 'torsion': [2, 2]}
  • id: 7396630
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '165825.k1', 'torsion': [4]}
  • id: 7396631
    {'degree': 4, 'field': [6889, 0, -169, 0, 1], 'lmfdb_label': '165825.k1', 'torsion': [2, 4]}
  • id: 7396635
    {'degree': 8, 'field': [-10392059, -1398286, 1137322, -623, -6385, -137, -68, -4, 1], 'lmfdb_label': '165825.k1', 'torsion': [6]}
  • id: 7396634
    {'degree': 8, 'field': [448900, 0, -60300, 0, 3505, 0, -60, 0, 1], 'lmfdb_label': '165825.k1', 'torsion': [8]}
  • id: 7396633
    {'degree': 8, 'field': [19554084, 0, -15675588, 0, 203613, 0, -804, 0, 1], 'lmfdb_label': '165825.k1', 'torsion': [8]}
  • id: 7396632
    {'degree': 8, 'field': [631265625, 0, 0, 0, 25125, 0, 0, 0, 1], 'lmfdb_label': '165825.k1', 'torsion': [2, 4]}
  • id: 7396637
    {'degree': 16, 'field': [81450625, 0, -208477500, 0, 168545125, 0, -45835500, 0, 6534000, 0, -492900, 0, 17005, 0, -180, 0, 1], 'lmfdb_label': '165825.k1', 'torsion': [2, 8]}
  • id: 7396641
    {'degree': 16, 'field': [981900646281, 0, -206312073006, 0, -8597740463, 0, -163291008, 0, 11810430, 0, 91658, 0, 7512, 0, -24, 0, 1], 'lmfdb_label': '165825.k1', 'torsion': [12]}
  • id: 7396639
    {'degree': 16, 'field': [502457738208255, -3374057843235, 2645747280054, 1459984048200, -738176920380, 9198572274, -2025705248, -895033862, 227510130, -2135950, 62078, 199074, -33088, -70, 30, -8, 1], 'lmfdb_label': '165825.k1', 'torsion': [2, 6]}
  • id: 7396636
    {'degree': 16, 'field': [1556378323823521, 495582972082, 78901922, 1982805324984, -495622347667, -710393674, 1262832754, -473612538, 118227268, 288924, -200984, 75358, -12547, -12, 8, -4, 1], 'lmfdb_label': '165825.k1', 'torsion': [4, 4]}
  • id: 7396640
    {'degree': 16, 'field': [3931022024766769, 0, -1463498542737568, 0, 29280412689640, 0, -486078387301, 0, 4622323300, 0, -36930199, 0, 178153, 0, -670, 0, 1], 'lmfdb_label': '165825.k1', 'torsion': [12]}
  • id: 7396638
    {'degree': 16, 'field': [46265826330565776, 0, -6163027874342208, 0, 271218783432456, 0, -5458732957008, 0, 56768616729, 0, -323531208, 0, 1011231, 0, -1608, 0, 1], 'lmfdb_label': '165825.k1', '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: 4105572
    {'conductor': 165825, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '165825.k1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4105573
    {'conductor': 165825, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '165825.k1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4105574
    {'conductor': 165825, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '165825.k1', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 4105575
    {'conductor': 165825, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '165825.k1', 'prime': 67, '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: 2735819
    {'adelic_gens': [[7043, 7036, 7082, 3021], [3212, 8039, 6409, 8034], [3019, 3018, 1018, 5035], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [2672, 8037, 2675, 8038], [1088, 3, 1685, 2], [8033, 8, 8032, 9], [7, 6, 8034, 8035]], 'adelic_image': '8040.48.0.?', 'conductor': 165825, 'lmfdb_label': '165825.k1', 'prime': 0}
  • id: 629015
    {'conductor': 165825, 'elladic_image': '4.6.0.1', 'lmfdb_label': '165825.k1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 165825.k does not appear in ec_padic