{
  "id": 3488,
  "curve_key": "68809530968347615017440703384694401:-2759737775863620713696002678544141110331334732799425",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-1433531895173908646196681320514467",
    "3194140944286598406642236152903250797239004587875"
  ],
  "rank_lower_bound": 16,
  "torsion": [
    2
  ],
  "naive_height": 240.64995100699466,
  "faltings_height": 18.12096741088182,
  "conductor": "838256123569356158476120539959505376633930110489000273931854",
  "bad_primes": [
    "2",
    "3",
    "11",
    "23",
    "29",
    "43",
    "67",
    "71",
    "89",
    "139",
    "199",
    "443",
    "499",
    "1579",
    "1777",
    "3547",
    "5381",
    "28109",
    "32933",
    "37537",
    "70313",
    "435769"
  ],
  "discriminant": "184131875554992201997692952405763209609933169191617009997844541112566444653561646552768590063748513792",
  "regulator": "21142833061760751175450.68075425453854663113900149660906566837800598836",
  "points": [
    [
      "-489872323568834203588099537947/25260565428121",
      "618085550511808721916249113080237827648605846/126959323975516436669"
    ],
    [
      "-196804680242789310024490313613/5342445145129",
      "30277896782420925037576198996022580519037178/12348383462432252117"
    ],
    [
      "-192451538759528391534735421149/5029052928025",
      "15995221527906642721530104430938449020843286/11277927789007103875"
    ],
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      "-131261542629828056605022216829/5955049448209",
      "71315329460188121199044419994506399701348970/14532089303316078073"
    ],
    [
      "-2211905557494967498340927541/121958100625",
      "205267201325802795899531620319336752733602/42590817690765625"
    ],
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      "-53829714873983456912592161/2639390625",
      "663569004244075824489765421279005876062/135598693359375"
    ],
    [
      "-1984175308043758987891605/7164437449",
      "1149182230107944206721316697045439507230/606419478995707"
    ],
    [
      "-3417277138243208330477/114921",
      "172159789463453030053321705415846/38958219"
    ],
    [
      "2670041495568279276603/58081",
      "82151565019589559362009146943314/13997521"
    ],
    [
      "8466622243978127913795/13697401",
      "77019708956088551664154817490477194/50694081101"
    ],
    [
      "88499228762503556458599/2319529",
      "7101313109247607422064081836407354/3532642667"
    ],
    [
      "921729424784234335750123/15437041",
      "692793113651409585159397995521727426/60652134089"
    ],
    [
      "1683717592394279479168389/40998409",
      "967597361720882568360327617062241722/262512812827"
    ],
    [
      "11379207641570642334462123/129937201",
      "34713763354578033380817747640445738366/1481154154199"
    ],
    [
      "22758324081466955004745945/345625281",
      "89566178643780177313308197999172000760/6425519599071"
    ],
    [
      "16516673743929045374803029339/16480654129",
      "2121164853409254018722912241148568460965506/2115736935118633"
    ]
  ],
  "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=-529/1848. 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 10:22:17",
  "updated_at": "2026-09-27 10:22:17"
}