Elliptic curve data - 12480.ca8

Formats: - HTML - YAML - JSON - 2024-05-11T17:46:47.997283

• 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': '12480cj', 'Clabel': '12480cj6', 'Cnumber': 6, 'abc_quality': 1.0149811194984983, 'absD': 48113755678310400, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 6240, 'ainvs': [0, 1, 0, 38719, 10150719], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 12480, 'degree': 98304, 'elladic_images': ['8.48.0.195'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8825642483545791963914289950', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 52, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [24487529386319, 183539412225], 'lmfdb_iso': '12480.ca', 'lmfdb_label': '12480.ca8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 605, -19750], 'min_quad_twist_disc': -8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0.d.1', '8.48.0-8.q.1.5', '24.96.0-24.be.2.10', '40.96.0-40.bf.1.6', '60.24.0-4.d.1.2', '120.192.1.?', '208.96.0.?', '416.192.2.?', '624.192.1.?', '1040.192.1.?', '1248.384.5.?', '2080.384.5.?', '3120.384.5.?', '6240.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '5.2818341142992603312772372206', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.84284347751466123226558081281', 'prec': 103}, 'szpiro_ratio': 4.854461503552709, '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, 0, 0, 1, 0, 4, 0, -1, 0, -1, 0, 2, 0, -4, 0], 'aplist': [0, 1, -1, 0, 4, -1, 2, -4, -8, 2, 8, -6, -6, -4, 8, -6, -12, 2, -4, 0, -6, -16, -4, 10, 18], 'class_deg': 16, 'class_size': 8, 'conductor': 12480, 'isogeny_matrix': [[1, 2, 4, 4, 8, 16, 16, 8], [2, 1, 2, 2, 4, 8, 8, 4], [4, 2, 1, 4, 8, 16, 16, 8], [4, 2, 4, 1, 2, 4, 4, 2], [8, 4, 8, 2, 1, 2, 2, 4], [16, 8, 16, 4, 2, 1, 4, 8], [16, 8, 16, 4, 2, 4, 1, 8], [8, 4, 8, 2, 4, 8, 8, 1]], 'lmfdb_iso': '12480.ca', 'trace_hash': 1371681481631759532}
• 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': '0.023164635464630441102592632274', 'prec': 107}, 'conductor': 12480, 'gens': [[-38, 2937, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '5.2818341142992603312772372206', 'prec': 100}], 'lmfdb_label': '12480.ca8', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.26058941115196672793941201771', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.5055601665904559013280842345571203636', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-159, 0, 1]], 'xcoord_integral_points': [-159, -38]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [10, 0], '5': [1, 0], '7': [1, 1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '12480.ca8'}
• ec_torsion_growth •

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

  
  
  • id: 644468
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '12480.ca8', 'torsion': [4]}
  • id: 644467
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '12480.ca8', 'torsion': [2, 2]}
  • id: 644469
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '12480.ca8', 'torsion': [4]}
  • id: 644470
    {'degree': 4, 'field': [1, 0, 0, 0, 1], 'lmfdb_label': '12480.ca8', 'torsion': [2, 4]}
  • id: 644474
    {'degree': 4, 'field': [1, 0, 4, 0, 1], 'lmfdb_label': '12480.ca8', 'torsion': [8]}
  • id: 644471
    {'degree': 4, 'field': [4, 0, -6, 0, 1], 'lmfdb_label': '12480.ca8', 'torsion': [8]}
  • id: 644473
    {'degree': 4, 'field': [4, 0, -2, 0, 1], 'lmfdb_label': '12480.ca8', 'torsion': [8]}
  • id: 644472
    {'degree': 4, 'field': [9, 0, 4, 0, 1], 'lmfdb_label': '12480.ca8', 'torsion': [8]}
  • id: 644478
    {'degree': 8, 'field': [-48, 0, 584, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '12480.ca8', 'torsion': [6]}
  • id: 644477
    {'degree': 8, 'field': [1, 0, 0, 0, -1, 0, 0, 0, 1], 'lmfdb_label': '12480.ca8', 'torsion': [2, 8]}
  • id: 644476
    {'degree': 8, 'field': [1, 0, 0, 0, 7, 0, 0, 0, 1], 'lmfdb_label': '12480.ca8', 'torsion': [2, 8]}
  • id: 644475
    {'degree': 8, 'field': [256, 0, 0, 0, 17, 0, 0, 0, 1], 'lmfdb_label': '12480.ca8', 'torsion': [4, 4]}
  • id: 644479
    {'degree': 16, 'field': [1, 0, 0, 0, -7, 0, 0, 0, 48, 0, 0, 0, -7, 0, 0, 0, 1], 'lmfdb_label': '12480.ca8', 'torsion': [4, 8]}
  • id: 644484
    {'degree': 16, 'field': [9, 0, 0, 0, 5293, 0, 0, 0, 30, 0, 0, 0, 12, 0, 0, 0, 1], 'lmfdb_label': '12480.ca8', 'torsion': [2, 6]}
  • id: 644482
    {'degree': 16, 'field': [144, 0, -504, 0, 168, 0, 432, 0, 217, 0, 140, 0, 51, 0, -16, 0, 1], 'lmfdb_label': '12480.ca8', 'torsion': [16]}
  • id: 644481
    {'degree': 16, 'field': [10000, 0, 0, 0, 66000, 0, 0, 0, 15500, 0, 0, 0, 660, 0, 0, 0, 1], 'lmfdb_label': '12480.ca8', 'torsion': [16]}
  • id: 644483
    {'degree': 16, 'field': [17161, 0, -4928, 0, -2708, 0, 23560, 0, 12886, 0, 880, 0, 13, 0, 16, 0, 1], 'lmfdb_label': '12480.ca8', 'torsion': [16]}
  • id: 644486
    {'degree': 16, 'field': [18225, 0, -8262, 0, -4995, 0, 14156, 0, 5762, 0, 350, 0, 100, 0, 16, 0, 1], 'lmfdb_label': '12480.ca8', 'torsion': [12]}
  • id: 644485
    {'degree': 16, 'field': [18225, 0, 8262, 0, -4995, 0, -14156, 0, 5762, 0, -350, 0, 100, 0, -16, 0, 1], 'lmfdb_label': '12480.ca8', 'torsion': [12]}
  • id: 644480
    {'degree': 16, 'field': [65610000, 0, 0, 0, -48114000, 0, 0, 0, 1255500, 0, 0, 0, -5940, 0, 0, 0, 1], 'lmfdb_label': '12480.ca8', '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: 270359
    {'conductor': 12480, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '12480.ca8', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 270360
    {'conductor': 12480, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '12480.ca8', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 270361
    {'conductor': 12480, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '12480.ca8', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 270362
    {'conductor': 12480, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '12480.ca8', '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: 1746772
    {'adelic_gens': [[1, 0, 32, 1], [6227, 6224, 4546, 4935], [1, 32, 4, 129], [5761, 24, 0, 1], [25, 16, 2358, 5353], [4189, 8, 5214, 5957], [6209, 32, 6208, 33], [3105, 6208, 983, 2175], [1, 32, 0, 1], [25, 16, 4504, 5129]], 'adelic_image': '6240.768.13.?', 'conductor': 12480, 'lmfdb_label': '12480.ca8', 'prime': 0}
  • id: 59408
    {'conductor': 12480, 'elladic_image': '8.48.0.195', 'lmfdb_label': '12480.ca8', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 546479
    {'lmfdb_iso': '12480.ca', 'p': 11, 'prec': 20, 'unit': 21322299509001511200, 'val': 1}
  • id: 546480
    {'lmfdb_iso': '12480.ca', 'p': 17, 'prec': 20, 'unit': 236378811813301169043661, 'val': 1}
  • id: 546481
    {'lmfdb_iso': '12480.ca', 'p': 19, 'prec': 20, 'unit': 1374778595623254988038764, 'val': 1}
  • id: 546485
    {'lmfdb_iso': '12480.ca', 'p': 23, 'prec': 20, 'unit': 63547120847536662963155474, 'val': 1}
  • id: 546477
    {'lmfdb_iso': '12480.ca', 'p': 29, 'prec': 20, 'unit': 849119323383113235432233928, 'val': 1}
  • id: 546489
    {'lmfdb_iso': '12480.ca', 'p': 31, 'prec': 20, 'unit': 5977960446331322874429800178, 'val': 1}
  • id: 546474
    {'lmfdb_iso': '12480.ca', 'p': 37, 'prec': 20, 'unit': 8549583266927651233866296654, 'val': 1}
  • id: 546475
    {'lmfdb_iso': '12480.ca', 'p': 41, 'prec': 20, 'unit': 903237614036852823298347213961, 'val': 1}
  • id: 546476
    {'lmfdb_iso': '12480.ca', 'p': 43, 'prec': 20, 'unit': 3603653802720470685599700320137, 'val': 1}
  • id: 546487
    {'lmfdb_iso': '12480.ca', 'p': 47, 'prec': 20, 'unit': 48799431175843306711209696056341, 'val': 1}
  • id: 546482
    {'lmfdb_iso': '12480.ca', 'p': 53, 'prec': 20, 'unit': 175295742209985303339119422995454, 'val': 1}
  • id: 546483
    {'lmfdb_iso': '12480.ca', 'p': 59, 'prec': 20, 'unit': 1661491856638902178539538206796316, 'val': 1}
  • id: 546488
    {'lmfdb_iso': '12480.ca', 'p': 61, 'prec': 20, 'unit': 1257416511678698092150196304667116, 'val': 1}
  • id: 546473
    {'lmfdb_iso': '12480.ca', 'p': 67, 'prec': 20, 'unit': 37394922914859455000698109223575453, 'val': 1}
  • id: 546484
    {'lmfdb_iso': '12480.ca', 'p': 73, 'prec': 20, 'unit': 10660210093202386294523699724596122, 'val': 1}
  • id: 546478
    {'lmfdb_iso': '12480.ca', 'p': 79, 'prec': 20, 'unit': 917909463100837053754308896423592372, 'val': 1}
  • id: 546472
    {'lmfdb_iso': '12480.ca', 'p': 83, 'prec': 20, 'unit': 1163187560715124235384783275311016162, 'val': 1}
  • id: 546486
    {'lmfdb_iso': '12480.ca', 'p': 89, 'prec': 20, 'unit': 9270346845884306712863982563179123997, 'val': 1}
  • id: 546471
    {'lmfdb_iso': '12480.ca', 'p': 97, 'prec': 20, 'unit': 19980953015744120260302864933462261880, 'val': 1}