{
  "id": 6021,
  "curve_key": "2294044416159506896:-3520214938995801723072337600",
  "ainvs": [
    "0",
    "1",
    "0",
    "-47792592003323060",
    "4074322830129091696892704"
  ],
  "rank_lower_bound": 16,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 126.85663912159947,
  "faltings_height": 8.447758311772919,
  "conductor": "288851801178904845552271754711772794800808",
  "bad_primes": [
    "2",
    "7",
    "29",
    "41",
    "22697933",
    "191125611813845590306777091939"
  ],
  "discriminant": "-184712851598402307068968650001058240501639266770688",
  "regulator": "252885490773130.4998324695894134792709378520277746620150241352337558445",
  "points": [
    [
      "-252667876",
      "139254060792"
    ],
    [
      "-40969956",
      "2442051110072"
    ],
    [
      "46001334",
      "1404686553382"
    ],
    [
      "90151608",
      "705998656160"
    ],
    [
      "147911307",
      "491147026324"
    ],
    [
      "192497358",
      "1416830828210"
    ],
    [
      "212343594",
      "1870936320022"
    ],
    [
      "414800744",
      "7457908159128"
    ],
    [
      "948225839",
      "28483970533998"
    ],
    [
      "-1926649266/25",
      "337726727149798/125"
    ],
    [
      "168396622/9",
      "48198129035210/27"
    ],
    [
      "956873794/9",
      "11918571540022/27"
    ],
    [
      "970907590/9",
      "11262379306654/27"
    ],
    [
      "1023474643/9",
      "8955244550728/27"
    ],
    [
      "1215092230/9",
      "7767769073246/27"
    ],
    [
      "1377543694/9",
      "15858684496522/27"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,5,7,18,32,36,42,57,59,72: 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 11:28:26",
  "updated_at": "2026-10-28 11:28:26"
}