{
  "id": 6024,
  "curve_key": "32301436193162260761:-183300398387535892430514831741",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-672946587357547099",
    "212153239042699485300630793"
  ],
  "rank_lower_bound": 16,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 134.76493010195256,
  "faltings_height": 9.019858366763497,
  "conductor": "2460778281652252664436701822393680259927870",
  "bad_primes": [
    "2",
    "5",
    "17",
    "37",
    "73",
    "9517601",
    "563081793671021241489752794511"
  ],
  "discriminant": "60026764315520320471249394963764390013026128607187500",
  "regulator": "27214739041927.58212120825677255890469167164750383239623054167584390795",
  "points": [
    [
      "-446327623",
      "20581663871709"
    ],
    [
      "-117017818",
      "17008810240659"
    ],
    [
      "173165432",
      "10040567646909"
    ],
    [
      "327650587",
      "5180260186659"
    ],
    [
      "390004632",
      "3003480475709"
    ],
    [
      "454193232",
      "448830690109"
    ],
    [
      "488730177",
      "25228375114"
    ],
    [
      "490488232",
      "285903370109"
    ],
    [
      "493430507",
      "487807744834"
    ],
    [
      "498654182",
      "760644692659"
    ],
    [
      "520731572",
      "1711753372119"
    ],
    [
      "559619497",
      "3288713051309"
    ],
    [
      "576061557",
      "3956836159409"
    ],
    [
      "713005907",
      "9736914812034"
    ],
    [
      "752329372",
      "11475415376309"
    ],
    [
      "8745843782",
      "814424484933559"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,6,12,26,34,53,55,58,66,76: with p(x) = prod (x - a_i), write p = q^2 - r with q a monic quintic and deg r <= 4; the genus-one curve y^2 = r(x) carries the ten points (a_i, q(a_i)), and the curve submitted is the minimal Weierstrass model of its Jacobian. Found by enumerating integer ten-root sets 0 = a_1 < ... < a_10 and scoring each by S = sum of -a_p log(p)/p over the good primes 5 <= p <= 199 (with early abort on low partial sums); the sets with S >= 31, or S >= 30 and one bad prime in that range, or S >= 29 and two or more bad primes, were screened by exact conductor and by a GRH explicit-formula upper bound on the rank, and the survivors were certified with ellrank. Rank 16, proved: 16 independent points listed, matching the 2-descent upper bound. Torsion trivial.",
  "created_at": "2026-10-28 11:29:00",
  "updated_at": "2026-10-28 11:29:00"
}