Elliptic curve data - 107648.s1

Formats: - HTML - YAML - JSON - 2025-10-31T06:28:00.473992

• 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': '107648r', 'Clabel': '107648r1', 'Cnumber': 1, 'abc_quality': 0.6526962078695199, 'absD': 4098018614976512, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 8, 'ainvs': [0, 0, 0, -97556, 11316496], 'analytic_rank': 2, 'bad_primes': [2, 29], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 107648, 'degree': 389760, 'elladic_images': ['8.2.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7622616123342195297143385938', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 18, 'isogeny_degrees': [1], 'jinv': [25056, 1], 'lmfdb_iso': '107648.s', 'lmfdb_label': '107648.s1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -116, 464], 'min_quad_twist_disc': 29, 'modell_images': [], 'modm_images': ['8.2.0.b.1'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 4, 'optimality': 1, 'potential_good_reduction': True, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '3.6411488492120977636909536957', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 841], [29, 310, 128]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.2335117199300372402765108927', 'prec': 103}, 'szpiro_ratio': 3.976840608818407, '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, 0, 0, -2, 0, -1, 0, -3, 0, -2, 0, 0, 0, 0, 0, 5, 0, 2, 0], 'aplist': [0, 0, -2, -1, -2, 0, 5, 2, -7, 0, -3, -8, 6, -8, 3, -6, 12, -4, -16, -5, 7, -1, 6, 11, 1], 'class_deg': 1, 'class_size': 1, 'conductor': 107648, 'isogeny_matrix': [[1]], 'lmfdb_iso': '107648.s', 'trace_hash': 1818994448827244711}
• 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': '0.029465852612277440443813712606', 'prec': 107}, 'conductor': 107648, 'gens': [[0, 3364, 1], [71485, 9433497, 23]], 'heights': [{'__RealLiteral__': 0, 'data': '0.52375591799502301830588944516', 'prec': 103}, {'__RealLiteral__': 0, 'data': '7.0065520750349274284674759475', 'prec': 100}], 'lmfdb_label': '107648.s1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.43523684097337076022630356655', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '0.99999999999999999999999999999', 'prec': 103}, 'special_value': {'__RealLiteral__': 0, 'data': '9.5085727358693864633677643728323409108', 'prec': 130}, 'tamagawa_product': 6, 'torsion_generators': [], 'xcoord_integral_points': [0, 96]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [8, 2, 0], '5': [4, 0], '7': [2, 0], '11': [2, 0], '13': [2, 2, 0], '17': [2, 0], '19': [4, 0], '23': [2, 0], '29': 'a', '31': [2, 0], '37': [2, 0], '41': [2, 0], '43': [2, 0], '47': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '107648.s1'}
• ec_torsion_growth •

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

  
  
  • id: 4969020
    {'degree': 3, 'field': [15, -19, -1, 1], 'lmfdb_label': '107648.s1', 'torsion': [2]}
  • id: 4969021
    {'degree': 6, 'field': [-2, 0, 85, 0, -20, 0, 1], 'lmfdb_label': '107648.s1', 'torsion': [2, 2]}
  • id: 4969022
    {'degree': 8, 'field': [-4332, 0, 1872, 0, -228, 0, 0, 0, 1], 'lmfdb_label': '107648.s1', 'torsion': [3]}
  • id: 4969023
    {'degree': 12, 'field': [72, 0, -116, 0, -2223, 0, 580, 0, -86, 0, 0, 0, 1], 'lmfdb_label': '107648.s1', 'torsion': [4]}
• 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: 2646401
    {'conductor': 107648, 'conductor_valuation': 7, 'discriminant_valuation': 13, 'j_denominator_valuation': 0, 'kodaira_symbol': -6, 'lmfdb_label': '107648.s1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2646402
    {'conductor': 107648, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '107648.s1', 'prime': 29, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
• ec_galrep •

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

  
  
  • id: 2370118
    {'adelic_gens': [[7, 2, 0, 1], [1, 0, 2, 1], [1, 1, 7, 0], [1, 2, 0, 1], [5, 2, 5, 3], [7, 2, 6, 3]], 'adelic_image': '8.2.0.?', 'conductor': 107648, 'lmfdb_label': '107648.s1', 'prime': 0}
  • id: 428859
    {'conductor': 107648, 'elladic_image': '8.2.0.2', 'lmfdb_label': '107648.s1', 'modell_image': '2G', 'prime': 2}
• ec_padic •

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

  
  
  • id: 5613821
    {'lmfdb_iso': '107648.s', 'p': 5, 'prec': 20, 'unit': 2433384237973, 'val': 3}
  • id: 5613822
    {'lmfdb_iso': '107648.s', 'p': 7, 'prec': 20, 'unit': 4991741272881568, 'val': 2}
  • id: 5613827
    {'lmfdb_iso': '107648.s', 'p': 11, 'prec': 20, 'unit': 32475986041571823801, 'val': 2}
  • id: 5613828
    {'lmfdb_iso': '107648.s', 'p': 17, 'prec': 20, 'unit': 80253481947555471448244, 'val': 2}
  • id: 5613829
    {'lmfdb_iso': '107648.s', 'p': 19, 'prec': 20, 'unit': 51497848616858416517496, 'val': 3}
  • id: 5613833
    {'lmfdb_iso': '107648.s', 'p': 23, 'prec': 20, 'unit': 35298053751151394892223799, 'val': 2}
  • id: 5613823
    {'lmfdb_iso': '107648.s', 'p': 31, 'prec': 20, 'unit': 5805275790515085511260214086, 'val': 2}
  • id: 5613838
    {'lmfdb_iso': '107648.s', 'p': 37, 'prec': 20, 'unit': 171410014246746741725689828562, 'val': 2}
  • id: 5613824
    {'lmfdb_iso': '107648.s', 'p': 41, 'prec': 20, 'unit': 2176686911662932937055272952942, 'val': 2}
  • id: 5613825
    {'lmfdb_iso': '107648.s', 'p': 43, 'prec': 20, 'unit': 7467019874384320416787617582346, 'val': 2}
  • id: 5613836
    {'lmfdb_iso': '107648.s', 'p': 47, 'prec': 20, 'unit': 13015160810607932641790556381727, 'val': 2}
  • id: 5613830
    {'lmfdb_iso': '107648.s', 'p': 53, 'prec': 20, 'unit': 219851370427683279711545238990852, 'val': 2}
  • id: 5613831
    {'lmfdb_iso': '107648.s', 'p': 59, 'prec': 20, 'unit': 923679156113571374354349202234956, 'val': 2}
  • id: 5613837
    {'lmfdb_iso': '107648.s', 'p': 61, 'prec': 20, 'unit': 3740245825039574173324263231909468, 'val': 2}
  • id: 5613820
    {'lmfdb_iso': '107648.s', 'p': 67, 'prec': 20, 'unit': 3047347442999020725831072244214830, 'val': 2}
  • id: 5613835
    {'lmfdb_iso': '107648.s', 'p': 71, 'prec': 20, 'unit': 4050367020894734370455190840767571, 'val': 2}
  • id: 5613832
    {'lmfdb_iso': '107648.s', 'p': 73, 'prec': 20, 'unit': 7999135034751639009676402173826567, 'val': 2}
  • id: 5613826
    {'lmfdb_iso': '107648.s', 'p': 79, 'prec': 20, 'unit': 137427556572162261145790695908984124, 'val': 2}
  • id: 5613819
    {'lmfdb_iso': '107648.s', 'p': 83, 'prec': 20, 'unit': 2450101287333399203606594286940225581, 'val': 2}
  • id: 5613834
    {'lmfdb_iso': '107648.s', 'p': 89, 'prec': 20, 'unit': 6395106933968203157931146328525985498, 'val': 2}
  • id: 5613818
    {'lmfdb_iso': '107648.s', 'p': 97, 'prec': 20, 'unit': 246367688685525869436768983205564353, 'val': 0}