Elliptic curve data - 70980.x1

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '70980bb', 'Clabel': '70980bb2', 'Cnumber': 2, 'abc_quality': 0.7640124772477683, 'absD': 885830400, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 5460, 'ainvs': [0, 1, 0, -420, -3132], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 70980, 'degree': 29952, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.45086984296055834153711960602', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 23, 'isogeny_degrees': [1, 2], 'jinv': [14602768, 1575], 'lmfdb_iso': '70980.x', 'lmfdb_label': '70980.x1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -420, -3132], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '364.6.0.?', '420.6.0.?', '780.6.0.?', '5460.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 5, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.2072282831155120678147203512', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 91], [3, 4, 23660], [5, 6, 14196], [7, 8, 10140], [13, 50, 420]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.65246561677812271542107366868', 'prec': 107}, 'szpiro_ratio': 2.6621610321720546, '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, -1, 0, 1, 0, -4, 0, 0, 0, 1, 0, -2, 0, 6, 0], 'aplist': [0, 1, 1, -1, -4, 0, -2, 6, -4, -6, -2, 2, 6, 10, -2, -2, 8, 10, -4, 0, 6, -4, -6, -10, -14], 'class_deg': 2, 'class_size': 2, 'conductor': 70980, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '70980.x', 'trace_hash': 2169062354669170284}
• 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': '0.40586297111395555392795763410', 'prec': 103}, 'conductor': 70980, 'gens': [[-12, 18, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.2072282831155120678147203512', 'prec': 100}], 'lmfdb_label': '70980.x1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.0617589337471526904374564827', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.6907124880207912114411642955532514802', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [[-9, 0, 1]], 'xcoord_integral_points': [-12, -9, 56]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [4, 0], '7': [1, 0], '11': [1, 0], '13': 'a', '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': '70980.x1'}
• ec_torsion_growth •

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

  
  
  • id: 3373096
    {'degree': 2, 'field': [-91, 0, 1], 'lmfdb_label': '70980.x1', 'torsion': [2, 2]}
  • id: 3373097
    {'degree': 4, 'field': [91, 0, 13, 0, 1], 'lmfdb_label': '70980.x1', 'torsion': [4]}
  • id: 3373100
    {'degree': 8, 'field': [-32448, 0, -25012, 0, 624, 0, 0, 0, 1], 'lmfdb_label': '70980.x1', 'torsion': [6]}
  • id: 3373099
    {'degree': 8, 'field': [6084, 0, 14872, 0, -2080, 0, -52, 0, 1], 'lmfdb_label': '70980.x1', 'torsion': [2, 4]}
  • id: 3373098
    {'degree': 8, 'field': [2556801, 0, 5070, 0, 4303, 0, 130, 0, 1], 'lmfdb_label': '70980.x1', 'torsion': [2, 4]}
  • id: 3373101
    {'degree': 16, 'field': [314885025, 0, 0, 0, 58593990, 0, -5536440, 0, 489931, 0, 131144, 0, 6006, 0, 104, 0, 1], 'lmfdb_label': '70980.x1', 'torsion': [8]}
  • id: 3373102
    {'degree': 16, 'field': [13013105625, 0, -64467889200, 0, -6831571500, 0, -47455200, 0, -1812018, 0, -343408, 0, -6396, 0, 0, 0, 1], 'lmfdb_label': '70980.x1', 'torsion': [2, 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: 1721735
    {'conductor': 70980, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '70980.x1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 1721736
    {'conductor': 70980, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '70980.x1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1721737
    {'conductor': 70980, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '70980.x1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1721738
    {'conductor': 70980, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '70980.x1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1721739
    {'conductor': 70980, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '70980.x1', 'prime': 13, 'reduction_type': 0, '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: 2133867
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [3277, 4, 1094, 9], [1, 2, 2, 5], [1, 4, 0, 1], [4096, 1369, 1365, 4096], [5457, 4, 5456, 5], [4682, 1, 3119, 0], [3641, 4, 1822, 9], [424, 1, 1259, 0]], 'adelic_image': '5460.12.0.?', 'conductor': 70980, 'lmfdb_label': '70980.x1', 'prime': 0}
  • id: 295603
    {'conductor': 70980, 'elladic_image': '2.3.0.1', 'lmfdb_label': '70980.x1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 3644082
    {'lmfdb_iso': '70980.x', 'p': 11, 'prec': 20, 'unit': 35818657914299361397, 'val': 1}
  • id: 3644083
    {'lmfdb_iso': '70980.x', 'p': 17, 'prec': 20, 'unit': 68517397801650351702075, 'val': 1}
  • id: 3644084
    {'lmfdb_iso': '70980.x', 'p': 19, 'prec': 20, 'unit': 150613712953352619811845, 'val': 1}
  • id: 3644088
    {'lmfdb_iso': '70980.x', 'p': 23, 'prec': 20, 'unit': 14694950009441229729030281, 'val': 1}
  • id: 3644080
    {'lmfdb_iso': '70980.x', 'p': 29, 'prec': 20, 'unit': 2484241470887679457020377620, 'val': 1}
  • id: 3644092
    {'lmfdb_iso': '70980.x', 'p': 31, 'prec': 20, 'unit': 15321957589078899357924719377, 'val': 1}
  • id: 3644077
    {'lmfdb_iso': '70980.x', 'p': 37, 'prec': 20, 'unit': 432840270522256337262841543164, 'val': 1}
  • id: 3644078
    {'lmfdb_iso': '70980.x', 'p': 41, 'prec': 20, 'unit': 4181123708724082806944912494797, 'val': 1}
  • id: 3644079
    {'lmfdb_iso': '70980.x', 'p': 43, 'prec': 20, 'unit': 9619549468006505954224529948164, 'val': 1}
  • id: 3644090
    {'lmfdb_iso': '70980.x', 'p': 47, 'prec': 20, 'unit': 22559140024974370849850300697380, 'val': 1}
  • id: 3644085
    {'lmfdb_iso': '70980.x', 'p': 53, 'prec': 20, 'unit': 383014601480540639834288176049105, 'val': 1}
  • id: 3644086
    {'lmfdb_iso': '70980.x', 'p': 59, 'prec': 20, 'unit': 3595455551945776158259422251348665, 'val': 1}
  • id: 3644091
    {'lmfdb_iso': '70980.x', 'p': 61, 'prec': 20, 'unit': 99580276101166336212450815082528, 'val': 2}
  • id: 3644076
    {'lmfdb_iso': '70980.x', 'p': 67, 'prec': 20, 'unit': 19684671932395109411793944505761184, 'val': 1}
  • id: 3644087
    {'lmfdb_iso': '70980.x', 'p': 73, 'prec': 20, 'unit': 55490752739206658168966692217570150, 'val': 1}
  • id: 3644081
    {'lmfdb_iso': '70980.x', 'p': 79, 'prec': 20, 'unit': 204494020851421309400001331612969502, 'val': 1}
  • id: 3644075
    {'lmfdb_iso': '70980.x', 'p': 83, 'prec': 20, 'unit': 1676263521939319375274938189740761779, 'val': 1}
  • id: 3644089
    {'lmfdb_iso': '70980.x', 'p': 89, 'prec': 20, 'unit': 9300842739572569786758081606887215705, 'val': 1}
  • id: 3644074
    {'lmfdb_iso': '70980.x', 'p': 97, 'prec': 20, 'unit': 28653541520085598864054287064217672084, 'val': 1}