Elliptic curve data - 3344.d2

Formats: - HTML - YAML - JSON - 2026-01-21T23:37:59.619580

• 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': '3344e', 'Clabel': '3344e2', 'Cnumber': 2, 'abc_quality': 1.1357429264760874, 'absD': 2119699214336, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 132, 'ainvs': [0, -1, 0, 3083, 22781], 'analytic_rank': 0, 'bad_primes': [2, 11, 19], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 3344, 'degree': 5184, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0540368513631198214082108798', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 3, 'isogeny_degrees': [1, 3], 'jinv': [790939860992, 517504691], 'lmfdb_iso': '3344.d', 'lmfdb_label': '3344.d2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, 193, -308], 'min_quad_twist_disc': -4, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '12.8.0-3.a.1.2', '22.2.0.a.1', '66.8.0.a.1', '132.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 11], [3, 2, 176], [11, 12, 304], [19, 20, 176]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.36088967080317451199097875834', 'prec': 103}, 'szpiro_ratio': 4.401058895196286, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, -3, 0, 4, 0, -2, 0, -1, 0, 2, 0, 3, 0, 0, 0, -1, 0], 'aplist': [0, -1, -3, 4, -1, 2, 0, -1, -3, -6, 7, -7, 0, 10, 0, 6, -3, -10, -11, -15, 8, 16, 0, 9, -1], 'class_deg': 3, 'class_size': 2, 'conductor': 3344, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '3344.d', 'trace_hash': 1070167729251218893}
• 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': '0.12147173187618154189132172069', 'prec': 103}, 'conductor': 3344, 'gens': [], 'heights': [], 'lmfdb_label': '3344.d2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.51611531214296183889457911609', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0322306242859236777891582321752159728', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '5': [0, 0], '7': [0, 0], '11': [0, 0], '13': [0, 0], '17': [0, 0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0, 0], '43': [0, 0], '47': [0, 0, 0]}, 'iwp0': 0, 'lmfdb_label': '3344.d2'}
• ec_torsion_growth •

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

  
  
  • id: 174502
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '3344.d2', 'torsion': [3]}
  • id: 174503
    {'degree': 3, 'field': [1, 1, -1, 1], 'lmfdb_label': '3344.d2', 'torsion': [2]}
  • id: 174506
    {'degree': 6, 'field': [-2, -4, -4, -6, 6, -2, 1], 'lmfdb_label': '3344.d2', 'torsion': [6]}
  • id: 174504
    {'degree': 6, 'field': [1, -1, 2, -3, 2, -1, 1], 'lmfdb_label': '3344.d2', 'torsion': [2, 2]}
  • id: 174505
    {'degree': 6, 'field': [121, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '3344.d2', 'torsion': [3]}
  • id: 174509
    {'degree': 12, 'field': [121, -154, 247, -240, 290, -310, 305, -226, 130, -60, 23, -6, 1], 'lmfdb_label': '3344.d2', 'torsion': [2, 6]}
  • id: 174507
    {'degree': 12, 'field': [286, -644, -8, 924, -706, -32, 404, -304, 140, -42, 14, -4, 1], 'lmfdb_label': '3344.d2', 'torsion': [4]}
  • id: 174508
    {'degree': 12, 'field': [20736, 0, 9072, 0, 3537, 0, 477, 0, 72, 0, -3, 0, 1], 'lmfdb_label': '3344.d2', 'torsion': [3, 3]}
  • id: 174510
    {'degree': 18, 'field': [-26449376448, 0, -9535858992, 0, 3729813384, 0, 952956433, 0, -186677469, 0, 12780339, 0, -481012, 0, 10971, 0, -150, 0, 1], 'lmfdb_label': '3344.d2', 'torsion': [9]}
  • id: 174511
    {'degree': 18, 'field': [1771561, 0, 0, 0, 0, 0, 35211, 0, 0, 0, 0, 0, 275, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '3344.d2', 'torsion': [6]}
• 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: 60871
    {'conductor': 3344, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '3344.d2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 60872
    {'conductor': 3344, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '3344.d2', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 60873
    {'conductor': 3344, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '3344.d2', 'prime': 19, '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: 1685741
    {'adelic_gens': [[1, 0, 6, 1], [4, 3, 9, 7], [3, 4, 8, 11], [118, 75, 89, 125], [71, 126, 72, 125], [65, 0, 0, 131], [1, 6, 0, 1], [13, 6, 39, 19], [127, 6, 126, 7]], 'adelic_image': '132.16.0.?', 'conductor': 3344, 'lmfdb_label': '3344.d2', 'prime': 0}
  • id: 16765
    {'conductor': 3344, 'elladic_image': '3.4.0.1', 'lmfdb_label': '3344.d2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 3344.d does not appear in ec_padic