{
  "id": 3518,
  "curve_key": "368242364840055164677535714942353:-7066038546295254037305402360855464967443216419769",
  "ainvs": [
    "1",
    "1",
    "1",
    "-7671715934167815930781994061299",
    "8178285354508392679962576458844594775376567537"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    4
  ],
  "naive_height": 224.9588823339518,
  "faltings_height": 16.424760412495235,
  "conductor": "27145429606258964067875985943433158218",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "17",
    "19",
    "23",
    "103",
    "1063",
    "6673",
    "43801",
    "76441",
    "1625287",
    "1683223"
  ],
  "discriminant": "3276721386201583895266720381163929043277538584375571439373626135094247611847844117389889472",
  "regulator": "879949790672.251315970506107851043949129922966222783444142151",
  "points": [
    [
      "1538865762039849",
      "4091995471313073867694"
    ],
    [
      "1619928061801999",
      "1272426754397506409594"
    ],
    [
      "39699269930220669/25",
      "45592653178469853882212/125"
    ],
    [
      "1032795906892023",
      "36832298467066294689538"
    ],
    [
      "-200168577914205",
      "-98518534079058408848954"
    ],
    [
      "1582877295233673",
      "894589483767100750318"
    ],
    [
      "2317104754481921",
      "53315963594447076854398"
    ],
    [
      "813599464909173",
      "49750765741963773993958"
    ],
    [
      "43925280402228791/25",
      "1386561391703091367406674/125"
    ],
    [
      "987829224002351285",
      "981795641366021819261814118"
    ],
    [
      "-57742117929904287476139/19333609",
      "-5671160357763549657125856551188498/85009878773"
    ]
  ],
  "submitter": "dujella",
  "history": [],
  "commentary": "It is the fiber at t = −94073/34016 of Elkies' K3 surface. This value of t lies on a rank-5 subfamily over Q(u), found by Dujella-Peral. The subfamily is defined by the condition 2(49t+22)(872t+791) = □, which gives an extra quadratic section. It is parametrized by t = (791 − 8624u²)/(19208u² − 872), and the curve is the fiber at u = 25/131. Found with the assistance of Claude, based on our old PARI/GP code.",
  "created_at": "2026-09-27 15:16:36",
  "updated_at": "2026-09-27 15:16:36"
}