{
  "id": 6482,
  "curve_key": "2220276093321:-3024645444274882725",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-46255751944",
    "3500758605922804"
  ],
  "rank_lower_bound": 13,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 85.28595801132208,
  "faltings_height": 5.073290537510932,
  "conductor": "42538594273565336395730892886",
  "bad_primes": [
    "2",
    "11",
    "101",
    "81611",
    "21325424994279436853"
  ],
  "discriminant": "1039728321234483952184454483919612",
  "regulator": "407926153.2356973433102338243231169466264247314377479729786368853",
  "points": [
    [
      "154421",
      "6261600"
    ],
    [
      "21417438083/361",
      "-3134560225074347/6859"
    ],
    [
      "379752125/2209",
      "-2613683643496/103823"
    ],
    [
      "3000885/16",
      "-2420127707/64"
    ],
    [
      "78263222/841",
      "-36582006090/24389"
    ],
    [
      "-535662/121",
      "-81018164170/1331"
    ],
    [
      "703763642/1681",
      "16514437613658/68921"
    ],
    [
      "1737431",
      "2272423399"
    ],
    [
      "97093231/49",
      "950941149969/343"
    ],
    [
      "-165547",
      "81454080"
    ],
    [
      "-113330",
      "85422572"
    ],
    [
      "153310",
      "3481878"
    ],
    [
      "177752",
      "29825910"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,19,47,48,58,66,82,101,105,134: 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 13, proved: 13 independent points listed, matching the 2-descent upper bound. Torsion trivial.",
  "created_at": "2026-11-04 02:12:00",
  "updated_at": "2026-11-04 02:12:00"
}