{
  "id": 6121,
  "curve_key": "2910937120413884727130576:-4971010230851149848571566186722656960",
  "ainvs": [
    "0",
    "1",
    "0",
    "-60644523341955931815220",
    "5753484063464912298436438516620224"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 168.99337286600664,
  "faltings_height": 11.852763040872341,
  "conductor": "12812290006126708208219509600625580071112139117656",
  "bad_primes": [
    "2",
    "3",
    "7",
    "41",
    "103",
    "587087",
    "55772862889277",
    "551532355724953405051771"
  ],
  "discriminant": "-26016874788140069728912815710527686485545853826622963559548468516608",
  "regulator": "1120114749907382356777.2168829263665795794898612643494017833201518380188989",
  "points": [
    [
      "107443415702",
      "21862422841705614"
    ],
    [
      "-5965716966559/64",
      "52704901855722766671/512"
    ],
    [
      "2329046438369/16",
      "204064857834599097/64"
    ],
    [
      "4995690805616/25",
      "5022397094695402464/125"
    ],
    [
      "25077929631251/169",
      "10288704977791077096/2197"
    ],
    [
      "135973302581291/625",
      "835180363361526508536/15625"
    ],
    [
      "688722489807506/6241",
      "9922189865775253207974/493039"
    ],
    [
      "2866616322061940/22801",
      "37126617298997300495568/3442951"
    ],
    [
      "4041664140897376/27225",
      "21203426910054001422824/4492125"
    ],
    [
      "6655638529177456/26569",
      "343236446596044789270336/4330747"
    ],
    [
      "8431703193422516/10609",
      "740782603631545523574624/1092727"
    ],
    [
      "13939628213063714/22201",
      "1534583365180518932055378/3307949"
    ],
    [
      "35529268168582804/22201",
      "6621977305518633185597232/3307949"
    ],
    [
      "45266276751753029/376996",
      "3297246852909083227056897/231475544"
    ],
    [
      "185395739408581856/3481",
      "79826114326438531955933064/205379"
    ],
    [
      "293668626751092257/2298256",
      "33181317681957927552221991/3484156096"
    ],
    [
      "536016705898109156/4541161",
      "149855970683735259341498856/9677214091"
    ],
    [
      "253518154460556719846/1677312025",
      "435818959664229900342030627306/68694313983875"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,2,24,30,43,74,77,81,114,127: 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 18, proved: 18 independent points listed, matching the 2-descent upper bound. Torsion trivial.",
  "created_at": "2026-10-29 03:14:07",
  "updated_at": "2026-10-29 03:14:07"
}