Elliptic curve data - 6150.a3

Formats: - HTML - YAML - JSON - 2025-09-30T16:35:04.420627

• 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': '6150i', 'Clabel': '6150i1', 'Cnumber': 1, 'abc_quality': 0.9582556017330255, 'absD': 92250000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1640, 'ainvs': [1, 1, 0, -225, 1125], 'analytic_rank': 2, 'bad_primes': [2, 3, 5, 41], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 6150, 'degree': 3072, 'elladic_images': ['8.12.0.11'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.27471392682994633381858962367', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [81182737, 5904], 'lmfdb_iso': '6150.a', 'lmfdb_label': '6150.a3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -9, 9], 'min_quad_twist_disc': 5, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.m.1', '20.12.0-4.c.1.2', '40.24.0-8.m.1.1', '82.6.0.?', '164.12.0.?', '328.24.0.?', '820.24.0.?', '1640.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 27, 'optimality': 1, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '0.42773393426775411835117938665', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 1025], [3, 4, 2050], [5, 14, 246], [41, 42, 150]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.53000502938710385348179004294', 'prec': 107}, 'szpiro_ratio': 3.194426668929466, '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, 0, 1, -4, -1, 1, 0, -4, -1, -2, 4, 0, 1, -2, -1, -4, 0], 'aplist': [-1, -1, 0, -4, -4, -2, -2, -4, 0, -6, -8, 2, 1, -4, -12, 6, -4, -10, -12, -12, 6, 12, -12, 2, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 6150, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '6150.a', 'trace_hash': 1056049157538162965}
• 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': '0.57728000455360788690051853443', 'prec': 103}, 'conductor': 6150, 'gens': [[15, 30, 1], [5, 10, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.60491997242264912083903665272', 'prec': 103}, {'__RealLiteral__': 0, 'data': '0.75156031540478483499815794565', 'prec': 103}], 'lmfdb_label': '6150.a3', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '1.8657556246255502337404519500', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.1921879748131105228911649860054017015', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[10, -5, 1]], 'xcoord_integral_points': [-15, -10, -6, 5, 6, 10, 11, 15, 19, 30, 59, 110, 330, 615]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '3': [2, 0], '5': 'a', '7': [2, 0], '11': [2, 0], '13': [4, 0], '17': [2, 0], '19': [2, 0], '23': [2, 2, 0], '29': [2, 0], '31': [2, 0], '37': [2, 0], '41': [3, 0], '43': [2, 0], '47': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '6150.a3'}
• ec_torsion_growth •

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

  
  
  • id: 320660
    {'degree': 2, 'field': [-51, -1, 1], 'lmfdb_label': '6150.a3', 'torsion': [4]}
  • id: 320658
    {'degree': 2, 'field': [-10, -1, 1], 'lmfdb_label': '6150.a3', 'torsion': [2, 2]}
  • id: 320659
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '6150.a3', 'torsion': [4]}
  • id: 320661
    {'degree': 4, 'field': [81, 0, -23, 0, 1], 'lmfdb_label': '6150.a3', 'torsion': [2, 4]}
  • id: 320665
    {'degree': 8, 'field': [-30000, 0, -12500, 0, -600, 0, 0, 0, 1], 'lmfdb_label': '6150.a3', 'torsion': [6]}
  • id: 320663
    {'degree': 8, 'field': [361, 0, 94, 0, 87, 0, -14, 0, 1], 'lmfdb_label': '6150.a3', 'torsion': [8]}
  • id: 320664
    {'degree': 8, 'field': [5184, 5760, -4344, -2752, 1177, 236, -74, -4, 1], 'lmfdb_label': '6150.a3', 'torsion': [8]}
  • id: 320662
    {'degree': 8, 'field': [66574, -58358, 20273, -4110, 1118, -54, 44, -2, 1], 'lmfdb_label': '6150.a3', 'torsion': [2, 4]}
  • id: 320668
    {'degree': 16, 'field': [-216900, 277200, 914870, -1045680, -1055149, 1291520, 334038, -593828, 4103, 118032, -15038, -10152, 1897, 352, -78, -4, 1], 'lmfdb_label': '6150.a3', 'torsion': [2, 8]}
  • id: 320670
    {'degree': 16, 'field': [38321, 17728, -9416, -15168, 2074, 12296, -14936, 12088, -6705, 2800, -1000, 344, -118, 0, 20, -8, 1], 'lmfdb_label': '6150.a3', 'torsion': [12]}
  • id: 320667
    {'degree': 16, 'field': [1882476, -5257440, 7703442, -6681456, 3415663, -866328, -75186, 141628, -40993, -2960, 4958, -968, -123, 72, 2, -4, 1], 'lmfdb_label': '6150.a3', 'torsion': [2, 8]}
  • id: 320666
    {'degree': 16, 'field': [71723961, 0, 19926324, 0, 5869458, 0, 370836, 0, 30643, 0, 652, 0, 402, 0, -8, 0, 1], 'lmfdb_label': '6150.a3', 'torsion': [4, 4]}
  • id: 320669
    {'degree': 16, 'field': [230410654, -275427773, 16381232, 218018029, -213373059, 110974705, -29517665, 555122, 1948701, -692431, 57674, 19489, -3109, 63, -13, -4, 1], 'lmfdb_label': '6150.a3', 'torsion': [2, 6]}
  • id: 320671
    {'degree': 16, 'field': [2301591024, -2573154864, 221712516, 950721156, -382772232, -12016920, 34097982, -12255582, -20597, 984904, -123434, -26600, 5884, 244, -104, -2, 1], 'lmfdb_label': '6150.a3', 'torsion': [12]}
• 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: 122617
    {'conductor': 6150, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '6150.a3', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 122618
    {'conductor': 6150, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '6150.a3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 122619
    {'conductor': 6150, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '6150.a3', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 122620
    {'conductor': 6150, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '6150.a3', 'prime': 41, '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: 1704266
    {'adelic_gens': [[7, 6, 1634, 1635], [131, 1110, 210, 371], [1, 0, 8, 1], [516, 985, 15, 6], [983, 0, 0, 1639], [1633, 8, 1632, 9], [1521, 1520, 710, 871], [1, 8, 0, 1], [1, 4, 4, 17]], 'adelic_image': '1640.48.0.?', 'conductor': 6150, 'lmfdb_label': '6150.a3', 'prime': 0}
  • id: 30244
    {'conductor': 6150, 'elladic_image': '8.12.0.11', 'lmfdb_label': '6150.a3', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 239010
    {'lmfdb_iso': '6150.a', 'p': 7, 'prec': 20, 'unit': 9765241314540466, 'val': 2}
  • id: 239008
    {'lmfdb_iso': '6150.a', 'p': 11, 'prec': 20, 'unit': 27563239895960245377, 'val': 2}
  • id: 239014
    {'lmfdb_iso': '6150.a', 'p': 13, 'prec': 20, 'unit': 58393471529661108696, 'val': 3}
  • id: 239016
    {'lmfdb_iso': '6150.a', 'p': 17, 'prec': 20, 'unit': 37226356486236336791667, 'val': 2}
  • id: 239017
    {'lmfdb_iso': '6150.a', 'p': 19, 'prec': 20, 'unit': 1867557121582896877843976, 'val': 2}
  • id: 239013
    {'lmfdb_iso': '6150.a', 'p': 29, 'prec': 20, 'unit': 574998580649938030848409178, 'val': 2}
  • id: 239025
    {'lmfdb_iso': '6150.a', 'p': 31, 'prec': 20, 'unit': 17502176214357314390728105131, 'val': 2}
  • id: 239009
    {'lmfdb_iso': '6150.a', 'p': 37, 'prec': 20, 'unit': 227305040568688795218404542485, 'val': 2}
  • id: 239012
    {'lmfdb_iso': '6150.a', 'p': 43, 'prec': 20, 'unit': 9380359037811327660364898438982, 'val': 2}
  • id: 239023
    {'lmfdb_iso': '6150.a', 'p': 47, 'prec': 20, 'unit': 14595455334368549910651711534701, 'val': 2}
  • id: 239018
    {'lmfdb_iso': '6150.a', 'p': 53, 'prec': 20, 'unit': 150929056535594997561826749462489, 'val': 2}
  • id: 239019
    {'lmfdb_iso': '6150.a', 'p': 59, 'prec': 20, 'unit': 800747760383174540333821747937534, 'val': 2}
  • id: 239024
    {'lmfdb_iso': '6150.a', 'p': 61, 'prec': 20, 'unit': 318443200064874671755196971522021, 'val': 2}
  • id: 239007
    {'lmfdb_iso': '6150.a', 'p': 67, 'prec': 20, 'unit': 46905878773763560863125061922735717, 'val': 2}
  • id: 239022
    {'lmfdb_iso': '6150.a', 'p': 71, 'prec': 20, 'unit': 126845908994645253010224567678271727, 'val': 2}
  • id: 239011
    {'lmfdb_iso': '6150.a', 'p': 73, 'prec': 20, 'unit': 209676863806928078205554762781848471, 'val': 2}
  • id: 239015
    {'lmfdb_iso': '6150.a', 'p': 79, 'prec': 20, 'unit': 762737790736752148429336736805714008, 'val': 2}
  • id: 239020
    {'lmfdb_iso': '6150.a', 'p': 83, 'prec': 20, 'unit': 434188826875296875868550393503481610, 'val': 2}
  • id: 239021
    {'lmfdb_iso': '6150.a', 'p': 89, 'prec': 20, 'unit': 9335715114447518139083084811877243151, 'val': 2}
  • id: 239006
    {'lmfdb_iso': '6150.a', 'p': 97, 'prec': 20, 'unit': 27955360183991852150259899493461849346, 'val': 2}