Elliptic curve data - 76050.i2

Formats: - HTML - YAML - JSON - 2024-06-08T13:00:26.792643

• 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': '76050l', 'Clabel': '76050l2', 'Cnumber': 2, 'abc_quality': 1.0039069659549966, 'absD': 86034099480468750, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 1560, 'ainvs': [1, -1, 0, -16896567, 26737105591], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 76050, 'degree': 4644864, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.6516949830246100499278814423', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 8, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [261984288445803, 42250], 'lmfdb_iso': '76050.i', 'lmfdb_label': '76050.i2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -3999, 98343], 'min_quad_twist_disc': 65, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '24.24.0-6.a.1.9', '60.24.0-6.a.1.9', '120.48.0.?', '156.24.0.?', '195.8.0.?', '312.48.0.?', '390.24.0.?', '520.6.0.?', '780.48.0.?', '1560.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.3394653176809014218529412664', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.28984827590976407175194674567', 'prec': 103}, 'szpiro_ratio': 5.475635293417996, '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, -4, -1, 0, 0, 0, 0, 0, 4, 0, 1, -6, 0, 4, 0], 'aplist': [-1, 0, 0, -4, 0, 0, -6, 4, 6, 6, 10, -10, -6, 4, -12, 12, -12, -10, 14, 0, -16, 8, -12, 6, 8], 'class_deg': 6, 'class_size': 4, 'conductor': 76050, 'isogeny_matrix': [[1, 3, 6, 2], [3, 1, 2, 6], [6, 2, 1, 3], [2, 6, 3, 1]], 'lmfdb_iso': '76050.i', 'trace_hash': 1860108982879090259}
• 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': '0.0049747012220257907128832628811', 'prec': 110}, 'conductor': 76050, 'gens': [[2379, -727, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.3394653176809014218529412664', 'prec': 100}], 'lmfdb_label': '76050.i2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.26722498090396391093878111131', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.5695542229869146314074821463744778549', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[9491, -9491, 2]], 'xcoord_integral_points': [725, 2379]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 0], '3': 'a', '5': 'a', '7': [1, 0], '11': [1, 1, 0], '13': 'a', '17': [1, 0], '19': [1, 0], '23': [3, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '76050.i2'}
• ec_torsion_growth •

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

  
  
  • id: 3594676
    {'degree': 2, 'field': [-30, 0, 1], 'lmfdb_label': '76050.i2', 'torsion': [2, 2]}
  • id: 3594677
    {'degree': 2, 'field': [-16, -1, 1], 'lmfdb_label': '76050.i2', 'torsion': [6]}
  • id: 3594679
    {'degree': 4, 'field': [144, 0, -54, 0, 1], 'lmfdb_label': '76050.i2', 'torsion': [2, 6]}
  • id: 3594678
    {'degree': 4, 'field': [270, 0, 27, 0, 1], 'lmfdb_label': '76050.i2', 'torsion': [4]}
  • id: 3594680
    {'degree': 6, 'field': [17836, 0, 0, -208, 0, 0, 1], 'lmfdb_label': '76050.i2', 'torsion': [6]}
  • id: 3594683
    {'degree': 8, 'field': [2304, 0, -972, 0, 48, 0, 9, 0, 1], 'lmfdb_label': '76050.i2', 'torsion': [12]}
  • id: 3594682
    {'degree': 8, 'field': [16900, 0, -104000, 0, 1470, 0, -80, 0, 1], 'lmfdb_label': '76050.i2', 'torsion': [2, 4]}
  • id: 3594681
    {'degree': 8, 'field': [48400, 0, 5560, 0, 249, 0, 4, 0, 1], 'lmfdb_label': '76050.i2', 'torsion': [2, 4]}
  • id: 3594684
    {'degree': 12, 'field': [164971, 101850, 34161, -292270, 198204, -66594, 29213, -6342, 2004, -290, 69, -6, 1], 'lmfdb_label': '76050.i2', 'torsion': [3, 6]}
  • id: 3594685
    {'degree': 12, 'field': [23270976, 0, -3460320, 0, -216864, 0, 28008, 0, 1224, 0, -6, 0, 1], 'lmfdb_label': '76050.i2', 'torsion': [2, 6]}
  • id: 3594687
    {'degree': 16, 'field': [8844676, 0, -4904956, 0, 1114669, 0, -122956, 0, 18931, 0, -1924, 0, 139, 0, -4, 0, 1], 'lmfdb_label': '76050.i2', 'torsion': [2, 12]}
  • id: 3594688
    {'degree': 16, 'field': [82810000, 0, -1931280000, 0, 128569000, 0, 13092000, 0, -686400, 0, -57600, 0, 4810, 0, -120, 0, 1], 'lmfdb_label': '76050.i2', 'torsion': [2, 12]}
  • id: 3594686
    {'degree': 16, 'field': [482241600, 0, -198676800, 0, -393660, 0, 4286520, 0, 386334, 0, 20916, 0, 1107, 0, 42, 0, 1], 'lmfdb_label': '76050.i2', 'torsion': [8]}
  • id: 3594689
    {'degree': 18, 'field': [25333100, 59471100, -214359600, 232660350, -75806250, -37135800, 40247295, -12696000, 184290, 1049335, -368985, 166590, -60909, 9114, -1455, 135, 30, -6, 1], 'lmfdb_label': '76050.i2', '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: 1848556
    {'conductor': 76050, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '76050.i2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1848557
    {'conductor': 76050, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '76050.i2', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1848558
    {'conductor': 76050, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '76050.i2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1848559
    {'conductor': 76050, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '76050.i2', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 2166594
    {'adelic_gens': [[10, 3, 753, 1552], [272, 11, 1005, 1528], [1, 0, 12, 1], [1, 6, 6, 37], [1550, 1557, 339, 8], [1, 12, 0, 1], [11, 2, 1510, 1551], [1549, 12, 1548, 13], [479, 1548, 1314, 1487], [66, 337, 845, 1106]], 'adelic_image': '1560.96.1.?', 'conductor': 76050, 'lmfdb_label': '76050.i2', 'prime': 0}
  • id: 314221
    {'conductor': 76050, 'elladic_image': '2.3.0.1', 'lmfdb_label': '76050.i2', 'modell_image': '2B', 'prime': 2}
  • id: 314222
    {'conductor': 76050, 'elladic_image': '3.4.0.1', 'lmfdb_label': '76050.i2', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 3914198
    {'lmfdb_iso': '76050.i', 'p': 7, 'prec': 20, 'unit': 4339955155840993, 'val': 1}
  • id: 3914203
    {'lmfdb_iso': '76050.i', 'p': 17, 'prec': 20, 'unit': 97254258735925620490590, 'val': 1}
  • id: 3914194
    {'lmfdb_iso': '76050.i', 'p': 19, 'prec': 20, 'unit': 1597133075499264378280204, 'val': 1}
  • id: 3914208
    {'lmfdb_iso': '76050.i', 'p': 23, 'prec': 20, 'unit': 1604296544248718228722374, 'val': 2}
  • id: 3914201
    {'lmfdb_iso': '76050.i', 'p': 29, 'prec': 20, 'unit': 4338651858140987212976712619, 'val': 1}
  • id: 3914212
    {'lmfdb_iso': '76050.i', 'p': 31, 'prec': 20, 'unit': 16937491566448982604887457523, 'val': 1}
  • id: 3914197
    {'lmfdb_iso': '76050.i', 'p': 37, 'prec': 20, 'unit': 244870916756918081925138865243, 'val': 1}
  • id: 3914199
    {'lmfdb_iso': '76050.i', 'p': 41, 'prec': 20, 'unit': 1575667000548305491460592871541, 'val': 1}
  • id: 3914200
    {'lmfdb_iso': '76050.i', 'p': 43, 'prec': 20, 'unit': 425677148525963028290062387748, 'val': 1}
  • id: 3914210
    {'lmfdb_iso': '76050.i', 'p': 47, 'prec': 20, 'unit': 49446700138980288731446524751337, 'val': 1}
  • id: 3914205
    {'lmfdb_iso': '76050.i', 'p': 53, 'prec': 20, 'unit': 456497867204535915498252475646609, 'val': 1}
  • id: 3914206
    {'lmfdb_iso': '76050.i', 'p': 59, 'prec': 20, 'unit': 3967921998458767671332034222517073, 'val': 1}
  • id: 3914211
    {'lmfdb_iso': '76050.i', 'p': 61, 'prec': 20, 'unit': 6233467192404763882170684951422076, 'val': 1}
  • id: 3914196
    {'lmfdb_iso': '76050.i', 'p': 67, 'prec': 20, 'unit': 27028532128298287432258278668746509, 'val': 1}
  • id: 3914207
    {'lmfdb_iso': '76050.i', 'p': 73, 'prec': 20, 'unit': 84775107048683379259218247960807915, 'val': 1}
  • id: 3914202
    {'lmfdb_iso': '76050.i', 'p': 79, 'prec': 20, 'unit': 7526987875977620808289663811873493, 'val': 1}
  • id: 3914204
    {'lmfdb_iso': '76050.i', 'p': 83, 'prec': 20, 'unit': 1157907918405141481533520837574833339, 'val': 1}
  • id: 3914209
    {'lmfdb_iso': '76050.i', 'p': 89, 'prec': 20, 'unit': 2456183949983428119338732312042679428, 'val': 1}
  • id: 3914195
    {'lmfdb_iso': '76050.i', 'p': 97, 'prec': 20, 'unit': 5985944951809966746063029317470142957, 'val': 1}