{
  "id": 806,
  "curve_key": "2334928:1807933184",
  "ainvs": [
    "0",
    "1",
    "0",
    "-48644",
    "-2108730"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "naive_height": 43.99047484047585,
  "faltings_height": 1.7162931235364358,
  "conductor": "9353416128",
  "bad_primes": [
    "2",
    "3",
    "7",
    "107",
    "193",
    "337"
  ],
  "discriminant": "5475199845431232",
  "regulator": "584.393501974103804655999204205864744894449557682",
  "points": [
    [
      "-4619/25",
      "-97296/125"
    ],
    [
      "1153",
      "38418"
    ],
    [
      "589",
      "-13188"
    ],
    [
      "-2783/16",
      "-67737/64"
    ],
    [
      "-537023/9409",
      "635587986/912673"
    ]
  ],
  "submitter": "benvchurch",
  "history": [],
  "commentary": "Found on 2026-09-19 by searching a second elliptic fibration of the D=26 K3 companion at moduli parameter j=-2. The source equation is Y^2=X^3+t^3(72900-3267t)X-t^5(43040889+405756t+729t^2). Setting u=X/t^2 gives a rational-2-torsion pencil; this curve is its fiber u=-60 (scaled parameter v=20). Candidates were selected by a Mestre-Nagao prime-sum sieve through 251 on a reduced-rational box |numerator(v)|<=256, denominator(v)<=8, followed by Magma descent and rational-point computations. In a fresh process with rigorous Minkowski class-group bounds, Magma verified the five submitted points, their independence modulo torsion, and unconditional rank bounds [5,5]. Thus the rank is exactly 5. Magma also verified global minimality, torsion Z/2, and conductor 9353416128. The exact map back to the source K3 is t=-(x+195), X=-60t^2, Y=27t^2y. The submitted points are independent witnesses; they are not claimed to be a saturated basis.",
  "created_at": "2026-09-19 19:11:10",
  "updated_at": "2026-09-19 19:11:10"
}