Elliptic curve data - 6270.l1

Formats: - HTML - YAML - JSON - 2024-06-07T01:49:18.700104

• 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': '6270l', 'Clabel': '6270l7', 'Cnumber': 7, 'abc_quality': 1.0270374871913532, 'absD': 8484255812957933638080, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 25080, 'ainvs': [1, 0, 1, -21424283, 37908785126], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 11, 19], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 6270, 'degree': 774144, 'elladic_images': ['4.6.0.1', '3.8.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.0362448055625931087940960261', 'prec': 100}, 'faltings_index': 6, 'faltings_ratio': 12, 'iso_nlabel': 11, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [1087533321226184807035053481, 8484255812957933638080], 'lmfdb_iso': '6270.l', 'lmfdb_label': '6270.l1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -21424283, 37908785126], 'min_quad_twist_disc': 1, 'modell_images': ['2B', '3B.1.2'], 'modm_images': ['2.3.0.a.1', '3.8.0-3.a.1.1', '4.6.0.c.1', '6.24.0-6.a.1.2', '12.48.0-12.g.1.10', '20.12.0-4.c.1.2', '44.12.0-4.c.1.1', '60.96.0-60.c.1.14', '132.96.0.?', '152.12.0.?', '220.24.0.?', '456.96.0.?', '660.192.1.?', '760.24.0.?', '1672.24.0.?', '2280.192.1.?', '5016.192.1.?', '8360.48.0.?', '25080.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '3.0362448055625931087940960261', 'prec': 100}, 'szpiro_ratio': 7.11997305472487, '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, 1, 1, 1, -1, -4, -1, 1, -1, -1, 1, 2, 4, 1, 1, 6, -1, 1, 1], 'aplist': [-1, 1, 1, -4, -1, 2, 6, 1, 0, -6, -4, 2, 6, 8, 0, -6, 0, 14, -4, -12, -10, 8, 0, -6, -10], 'class_deg': 12, 'class_size': 8, 'conductor': 6270, 'isogeny_matrix': [[1, 3, 2, 4, 6, 12, 12, 4], [3, 1, 6, 12, 2, 4, 4, 12], [2, 6, 1, 2, 3, 6, 6, 2], [4, 12, 2, 1, 6, 12, 3, 4], [6, 2, 3, 6, 1, 2, 2, 6], [12, 4, 6, 12, 2, 1, 4, 3], [12, 4, 6, 3, 2, 4, 1, 12], [4, 12, 2, 4, 6, 3, 12, 1]], 'lmfdb_iso': '6270.l', 'trace_hash': 2023840264930280173}
• 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': '0.0023054264446393024390292976221', 'prec': 110}, 'conductor': 6270, 'gens': [], 'heights': [], 'lmfdb_label': '6270.l1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.13135118093757530957911842531', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.5762141712509037149494211036660088588', 'prec': 130}, 'tamagawa_product': 48, 'torsion_generators': [[11399, -11403, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': [1, 1], '5': [1, 0], '11': [0, 0], '19': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '6270.l1'}
• ec_torsion_growth •

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

  
  
  • id: 326528
    {'degree': 2, 'field': [-55, 0, 1], 'lmfdb_label': '6270.l1', 'torsion': [2, 2]}
  • id: 326529
    {'degree': 2, 'field': [-11, 0, 1], 'lmfdb_label': '6270.l1', 'torsion': [4]}
  • id: 326530
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '6270.l1', 'torsion': [4]}
  • id: 326531
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '6270.l1', 'torsion': [6]}
  • id: 326532
    {'degree': 3, 'field': [-45, 0, 0, 1], 'lmfdb_label': '6270.l1', 'torsion': [6]}
  • id: 326536
    {'degree': 4, 'field': [1, 1, 2, -1, 1], 'lmfdb_label': '6270.l1', 'torsion': [12]}
  • id: 326533
    {'degree': 4, 'field': [89, 24, -23, -2, 1], 'lmfdb_label': '6270.l1', 'torsion': [2, 4]}
  • id: 326535
    {'degree': 4, 'field': [121, 0, 11, 0, 1], 'lmfdb_label': '6270.l1', 'torsion': [12]}
  • id: 326534
    {'degree': 4, 'field': [3025, 0, 55, 0, 1], 'lmfdb_label': '6270.l1', 'torsion': [2, 6]}
  • id: 326538
    {'degree': 6, 'field': [-59895, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '6270.l1', 'torsion': [2, 6]}
  • id: 326540
    {'degree': 6, 'field': [-45, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '6270.l1', 'torsion': [12]}
  • id: 326537
    {'degree': 6, 'field': [75, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '6270.l1', 'torsion': [3, 6]}
  • id: 326539
    {'degree': 6, 'field': [694, -2970, 363, -90, -33, 0, 1], 'lmfdb_label': '6270.l1', 'torsion': [12]}
  • id: 326541
    {'degree': 8, 'field': [15381, -1746, 1512, 462, -215, -22, 12, -4, 1], 'lmfdb_label': '6270.l1', 'torsion': [2, 4]}
  • id: 326544
    {'degree': 8, 'field': [19636, 1344, -5396, -592, 653, 64, -39, -2, 1], 'lmfdb_label': '6270.l1', 'torsion': [2, 12]}
  • id: 326543
    {'degree': 8, 'field': [754231, 3684, -1808, -3728, 1805, 68, -18, -4, 1], 'lmfdb_label': '6270.l1', 'torsion': [8]}
  • id: 326542
    {'degree': 8, 'field': [33779344, 0, -3318600, 0, 62009, 0, -426, 0, 1], 'lmfdb_label': '6270.l1', 'torsion': [8]}
  • id: 326547
    {'degree': 12, 'field': [1936, 264, 696, -1850, 765, 144, 51, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '6270.l1', 'torsion': [3, 12]}
  • id: 326548
    {'degree': 12, 'field': [1653796, 0, -1129656, 0, 204765, 0, -26710, 0, 1815, 0, -66, 0, 1], 'lmfdb_label': '6270.l1', 'torsion': [2, 12]}
  • id: 326546
    {'degree': 12, 'field': [1976836, 0, -694056, 0, 244365, 0, -26470, 0, 1815, 0, -66, 0, 1], 'lmfdb_label': '6270.l1', 'torsion': [3, 12]}
  • id: 326545
    {'degree': 12, 'field': [3587291236, 359364, 898446, -2395850, 898515, 359244, -119649, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '6270.l1', 'torsion': [6, 6]}
  • id: 326552
    {'degree': 16, 'field': [40401, -41406, 3844, -48396, 40391, 1862, -184, 5282, -348, -1612, 896, -202, 51, -4, 4, -4, 1], 'lmfdb_label': '6270.l1', 'torsion': [2, 12]}
  • id: 326549
    {'degree': 16, 'field': [6765201, 0, 0, 0, 420786, 0, 0, 0, -3149, 0, 0, 0, -94, 0, 0, 0, 1], 'lmfdb_label': '6270.l1', 'torsion': [4, 4]}
  • id: 326551
    {'degree': 16, 'field': [506250000, 0, -1248750000, 0, 1254779500, 0, 16501500, 0, 2831825, 0, 78600, 0, 1190, 0, 60, 0, 1], 'lmfdb_label': '6270.l1', 'torsion': [2, 8]}
  • id: 326553
    {'degree': 16, 'field': [414962718976, 0, -57294342528, 0, 9599924336, 0, 1675148184, 0, 89894625, 0, 2431458, 0, 36527, 0, 294, 0, 1], 'lmfdb_label': '6270.l1', 'torsion': [24]}
  • id: 326554
    {'degree': 16, 'field': [616145286871, 34689582804, -40017012616, -3482738336, 3615262991, 123610092, -113945794, -10336308, 5638222, 199308, -97484, -11752, 3771, 116, -26, -4, 1], 'lmfdb_label': '6270.l1', 'torsion': [24]}
  • id: 326550
    {'degree': 16, 'field': [829557978660225, 212843661644700, -197997006714480, -29257013345940, 13544521366534, 1281925691064, -396060660360, -26425106332, 6159945935, 294165032, -55456552, -1826092, 291366, 5964, -832, -8, 1], 'lmfdb_label': '6270.l1', 'torsion': [2, 8]}
  • id: 326555
    {'degree': 18, 'field': [17429379606421875, 0, 0, -140402153778750, 0, 0, 390344727675, 0, 0, -502833720, 0, 0, 596473, 0, 0, -662, 0, 0, 1], 'lmfdb_label': '6270.l1', '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: 125350
    {'conductor': 6270, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '6270.l1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 125351
    {'conductor': 6270, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '6270.l1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 125352
    {'conductor': 6270, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '6270.l1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 125353
    {'conductor': 6270, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '6270.l1', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 125354
    {'conductor': 6270, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '6270.l1', 'prime': 19, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
• ec_galrep •

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

  
  
  • id: 1705054
    {'adelic_gens': [[5241, 1048, 11036, 7229], [1, 12, 12, 145], [22441, 24, 18492, 289], [5032, 21, 24795, 24706], [6286, 21, 5985, 24706], [20536, 3, 1821, 24994], [20901, 16724, 20, 12621], [15, 106, 23774, 15851], [25057, 24, 25056, 25], [1, 24, 0, 1], [1, 0, 24, 1]], 'adelic_image': '25080.384.5.?', 'conductor': 6270, 'lmfdb_label': '6270.l1', 'prime': 0}
  • id: 30752
    {'conductor': 6270, 'elladic_image': '4.6.0.1', 'lmfdb_label': '6270.l1', 'modell_image': '2B', 'prime': 2}
  • id: 30753
    {'conductor': 6270, 'elladic_image': '3.8.0.2', 'lmfdb_label': '6270.l1', 'modell_image': '3B.1.2', 'prime': 3}
• lmfdb_iso 6270.l does not appear in ec_padic