{
  "id": 3487,
  "curve_key": "94975807512566250277856603768795121:-16889397653419964745486079135984491827809639150436169",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-1978662656511796880788679245183232",
    "19547913950717552283422700164968307960838375127331"
  ],
  "rank_lower_bound": 16,
  "torsion": [
    2
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  "naive_height": 241.61679081063238,
  "faltings_height": 18.17876079406083,
  "conductor": "11691134462264714370561833310976107653897746417708594365510",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "37",
    "53",
    "83",
    "107",
    "181",
    "239",
    "439",
    "617",
    "751",
    "827",
    "857",
    "1051",
    "1223",
    "1913",
    "3169",
    "11807",
    "36931",
    "948749"
  ],
  "discriminant": "330710880843178164195918151868871968794900314011642036913433405619191247033822171587664657574174720000",
  "regulator": "47880763636885620546779.34055916719517740013007707216025079195317261860",
  "points": [
    [
      "-1254529604465193264042220539/45428233321",
      "70576009063336172430424579940841457531051/9682528221804619"
    ],
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      "-519973316751840199190433699/65715835201",
      "99248434685329182798985947006572974448959/16846320069611551"
    ],
    [
      "-62380407838705440424065275/1278849121",
      "2549310623344297569964758384605057217/45732923416081"
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      "12116835140864693952549/7038409",
      "75033201528302536520705644162331173/18672899077"
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      "187461572711157771254589/18879025",
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      "551200904131273182932389/13564489",
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    [
      "1307860295629593573989491749/313442099881",
      "591575377153125275583731661721447840039019/175483380597276779"
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    [
      "7699849759858649604862762749/15091876801",
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      "12948728542313534425872794001/1585405838641",
      "3958433587950859890871054433834709676777121/1996230468202203689"
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      "66961445347559919321055765029/1233727797289",
      "11631194609081521313961021113113979192215093/1370342177466202837"
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    [
      "892607524959670089257944012089/21643029970849",
      "286445046697058797317050803660503027984481427/100687855531593513743"
    ],
    [
      "337936358954954371100312215622899/7303882834041049",
      "3246283855196604566384554867934588539011000774287/624209963802121498712093"
    ],
    [
      "81450890532247565317120483856452149/1017041105741424481",
      "19855133054403136806621959157837372920306168481900119/1025670251008512835753088879"
    ]
  ],
  "submitter": "Steps Unbounded",
  "history": [],
  "commentary": "Z/2Z curve from the Elkies-Klagsbrun rank-9 family y^2=x^3+2A(t,u)x^2+B(t,u)x (Elkies-Klagsbrun 2020), fibre u=11/5, t=-1621/3315. Found by sweeping t=a/b with the lossless conic-Hilbert prefilter of Breddin (Zenodo 10.5281/zenodo.22242109), screened with PARI ellrank (2-descent): 16 independent points, 2-Selmer upper bound 16.",
  "created_at": "2026-09-27 09:46:17",
  "updated_at": "2026-09-27 09:46:17"
}