{
  "id": 6123,
  "curve_key": "5576275837874130027856:-429841238988689295786830947925440",
  "ainvs": [
    "0",
    "1",
    "0",
    "-116172413289044375580",
    "497501433975962547175446953424"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 150.28193743735872,
  "faltings_height": 10.439956639006914,
  "conductor": "7767535589308845848132270205771462688836499272",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "31",
    "16389695458611531389013247172084077515649"
  ],
  "discriminant": "-6579871306915912852402074324636225017391611245834473672284928",
  "regulator": "14146575926716997303.9669080931398975669680761443256454104557144366652353",
  "points": [
    [
      "132816330999",
      "48249058008107502"
    ],
    [
      "-134195912668897182/16024009",
      "60276625626508970085682002/64144108027"
    ],
    [
      "-517147773254514/43681",
      "4217621861798319138606/9129329"
    ],
    [
      "-336069704268801/34969",
      "5573049322301087629842/6539203"
    ],
    [
      "-4322999627739/5476",
      "310920941681574706161/405224"
    ],
    [
      "-1505063254626/121",
      "178869001412728458/1331"
    ],
    [
      "3222311341446/529",
      "1532824286231436534/12167"
    ],
    [
      "8644534667630/1369",
      "6348456344990076954/50653"
    ],
    [
      "15584648941989/3364",
      "47284898269394333457/195112"
    ],
    [
      "15621789680442/361",
      "59993687545512121674/6859"
    ],
    [
      "78180799894950/5329",
      "543344221460702850006/389017"
    ],
    [
      "93774572310939/19321",
      "588326405487254578452/2685619"
    ],
    [
      "208057568970267/19321",
      "1889906955629467912956/2685619"
    ],
    [
      "2865303805156146/410881",
      "42869571983239264978806/263374721"
    ],
    [
      "4495127821774704/201601",
      "271443435237693166747572/90518849"
    ],
    [
      "21560566217646726/3530641",
      "833919242405237273649546/6634074439"
    ],
    [
      "240163182251355600/13756681",
      "99334676387901587417680428/51023529829"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,8,61,72,92,114,115,117,130,139: 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 17, proved: 17 independent points listed, matching the 2-descent upper bound. Torsion trivial.",
  "created_at": "2026-10-29 03:14:23",
  "updated_at": "2026-10-29 03:14:23"
}