Elliptic curve data - 770.a1

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• 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': '770b', 'Clabel': '770b4', 'Cnumber': 4, 'abc_quality': 0.982542860656489, 'absD': 99207416000000, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 9240, 'ainvs': [1, 0, 1, -15649, 580116], 'analytic_rank': 0, 'bad_primes': [2, 5, 7, 11], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 770, 'degree': 3456, 'elladic_images': ['2.3.0.1', '3.8.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3975185569129732631545928801', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 6, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [423783056881319689, 99207416000000], 'lmfdb_iso': '770.a', 'lmfdb_label': '770.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -15649, 580116], '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', '6.24.0-6.a.1.2', '56.6.0.a.1', '168.48.0.?', '220.6.0.?', '660.48.0.?', '3080.12.0.?', '9240.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 7], [3, 2, 7], [5, 6, 154], [7, 8, 110], [11, 12, 70]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.3975185569129732631545928801', 'prec': 100}, 'szpiro_ratio': 6.106772987568272, '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, -2, 1, -1, 2, 1, -1, 1, 1, -1, -2, 2, -1, 2, 1, -6, -1, 2, -1], 'aplist': [-1, -2, -1, 1, -1, 2, -6, 2, -6, 0, 8, -4, 12, -4, 12, 0, 0, 2, 8, 12, 2, 14, 12, 6, 8], 'class_deg': 6, 'class_size': 4, 'conductor': 770, 'isogeny_matrix': [[1, 3, 6, 2], [3, 1, 2, 6], [6, 2, 1, 3], [2, 6, 3, 1]], 'lmfdb_iso': '770.a', 'trace_hash': 1186186856457122509}
• 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': '0.061112606167870027162972754187', 'prec': 107}, 'conductor': 770, 'gens': [], 'heights': [], 'lmfdb_label': '770.a1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.56315565348231471143745894664', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.56315565348231471143745894664176622922', 'prec': 133}, 'tamagawa_product': 4, 'torsion_generators': [[167, -171, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': [2, 1], '5': [0, 0], '7': [1, 0], '11': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '770.a1'}
• ec_torsion_growth •

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

  
  
  • id: 35749
    {'degree': 2, 'field': [-14, 0, 1], 'lmfdb_label': '770.a1', 'torsion': [2, 2]}
  • id: 35750
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '770.a1', 'torsion': [6]}
  • id: 35751
    {'degree': 3, 'field': [-7, 0, 0, 1], 'lmfdb_label': '770.a1', 'torsion': [6]}
  • id: 35753
    {'degree': 4, 'field': [196, 0, 14, 0, 1], 'lmfdb_label': '770.a1', 'torsion': [2, 6]}
  • id: 35752
    {'degree': 4, 'field': [224, 0, 29, 0, 1], 'lmfdb_label': '770.a1', 'torsion': [4]}
  • id: 35755
    {'degree': 6, 'field': [-56, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '770.a1', 'torsion': [2, 6]}
  • id: 35754
    {'degree': 6, 'field': [64, -24, -15, 7, 6, -3, 1], 'lmfdb_label': '770.a1', 'torsion': [3, 6]}
  • id: 35756
    {'degree': 8, 'field': [1603, -420, 238, 392, -265, 80, -22, -4, 1], 'lmfdb_label': '770.a1', 'torsion': [2, 4]}
  • id: 35758
    {'degree': 8, 'field': [50176, 0, -6496, 0, 617, 0, -29, 0, 1], 'lmfdb_label': '770.a1', 'torsion': [12]}
  • id: 35757
    {'degree': 8, 'field': [93494, 50316, 24246, 4480, 831, -28, 10, 0, 1], 'lmfdb_label': '770.a1', 'torsion': [2, 4]}
  • id: 35759
    {'degree': 12, 'field': [3025, 330, 861, -2290, 930, 210, 29, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '770.a1', 'torsion': [6, 6]}
  • id: 35760
    {'degree': 12, 'field': [8605184, 0, 0, 0, 0, 0, -91, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '770.a1', 'torsion': [12]}
  • id: 35762
    {'degree': 16, 'field': [15076075, -6312180, 20839994, -8131648, 11340581, -3240440, 2873430, -532588, 368082, -36908, 24538, -1136, 985, -72, 38, -4, 1], 'lmfdb_label': '770.a1', 'torsion': [2, 12]}
  • id: 35761
    {'degree': 16, 'field': [2998219536, 0, -104474448, 0, 43555320, 0, -582048, 0, 97609, 0, -5267, 0, -740, 0, 13, 0, 1], 'lmfdb_label': '770.a1', 'torsion': [8]}
  • id: 35763
    {'degree': 16, 'field': [4538582161, 4821464592, 1872514996, 175484736, -88027050, -27579216, -3371744, -516096, 201387, 157584, 24544, -2016, -538, 0, -12, 0, 1], 'lmfdb_label': '770.a1', 'torsion': [2, 12]}
  • id: 35764
    {'degree': 18, 'field': [3176523, 0, 0, 9507960, 0, 0, 9551227, 0, 0, 1355200, 0, 0, 169401, 0, 0, -440, 0, 0, 1], 'lmfdb_label': '770.a1', '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: 9731
    {'conductor': 770, 'conductor_valuation': 1, 'discriminant_valuation': 9, 'j_denominator_valuation': 9, 'kodaira_symbol': 13, 'lmfdb_label': '770.a1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 9732
    {'conductor': 770, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '770.a1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 9733
    {'conductor': 770, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '770.a1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 9734
    {'conductor': 770, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '770.a1', 'prime': 11, '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: 1669481
    {'adelic_gens': [[2521, 12, 5886, 73], [10, 3, 4593, 9232], [6610, 3, 5253, 9232], [11, 2, 9190, 9231], [1, 0, 12, 1], [9229, 12, 9228, 13], [6161, 12, 1540, 1], [1, 6, 6, 37], [3697, 12, 3702, 73], [1, 12, 0, 1], [6546, 5017, 1925, 386]], 'adelic_image': '9240.96.1.?', 'conductor': 770, 'lmfdb_label': '770.a1', 'prime': 0}
  • id: 3490
    {'conductor': 770, 'elladic_image': '2.3.0.1', 'lmfdb_label': '770.a1', 'modell_image': '2B', 'prime': 2}
  • id: 3491
    {'conductor': 770, 'elladic_image': '3.8.0.2', 'lmfdb_label': '770.a1', 'modell_image': '3B.1.2', 'prime': 3}
• lmfdb_iso 770.a does not appear in ec_padic