{
  "id": 201,
  "curve_key": "97584912720148833729:-960629570668111379574769901217",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-2033019015003100703",
    "1111839781374124406036388487"
  ],
  "rank_lower_bound": 13,
  "naive_height": 138.0817637177321,
  "faltings_height": 9.328045196898401,
  "conductor": "38936103625318215160524810514628790",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19",
    "37",
    "41",
    "109",
    "463",
    "1295809",
    "48684511",
    "51807199"
  ],
  "discriminant": "3746479851109552777476494863795034246987040897069772800",
  "regulator": "88401680947.32886924606362766775259075928101595166417470536057740",
  "points": [
    [
      "59588989675",
      "-14542085792666722"
    ],
    [
      "38882274373",
      "-7661970975095272"
    ],
    [
      "19682641375",
      "-2754329599786054"
    ],
    [
      "9417396553",
      "-903979327498222"
    ],
    [
      "3767050411",
      "-216589785741346"
    ],
    [
      "30967318693/16",
      "-4258458933181603/64"
    ],
    [
      "47002945240745371/35772361",
      "-5697237047256759529124786/213954491141"
    ],
    [
      "1094757112585/961",
      "-493347650698187044/29791"
    ],
    [
      "121707573635009/112225",
      "-507973989441742763468/37595375"
    ],
    [
      "3615378856393/3481",
      "-2256266340234165578/205379"
    ],
    [
      "23288579411/25",
      "-641863748313274/125"
    ],
    [
      "108257172103/121",
      "-4013446770576302/1331"
    ],
    [
      "749728245355/841",
      "-68704246405359218/24389"
    ]
  ],
  "submitter": "Seewoo Lee",
  "commentary": "Rank ≥13. Mestre–Fermigier construction from the integer 6-tuple a=[348, -600, -216, 492, 876, -900] with shift t=939/1: let p6(x)=∏(x−a_i) and q(x)=p6(x−t)·p6(x+t); completing q to g(x)²−r(x) gives the genus-1 quartic model y²=r(x), whose x=a_i±t base points plus a few small-x extra points supply 13 independent rational points. The shift t was selected by a Nagao–Mestre prime-sum sieve; the witness points were found by an integer quartic-point search and certified independent via the Néron–Tate height-pairing matrix.",
  "created_at": "2026-06-25 16:03:49",
  "updated_at": "2026-07-01 22:45:38"
}