{
  "id": 6015,
  "curve_key": "53753550746587197681:-386124175113011924219532248265",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-1119865640553899952",
    "446902980734841322429600275"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 136.29282419736097,
  "faltings_height": 9.254419223658426,
  "conductor": "40220481138255114385295852764634938847335159754",
  "bad_primes": [
    "2",
    "17",
    "31",
    "83",
    "1361",
    "2399",
    "140812168004184810273002064451770823"
  ],
  "discriminant": "3603013766079317930654158634553132769528396232293814272",
  "regulator": "83409892295286.2514521048952909376134486400973690709957226976579166096473",
  "points": [
    [
      "-1218934251",
      "923751899465"
    ],
    [
      "-1180730347",
      "11094626236577"
    ],
    [
      "-1179695835",
      "11236338250689"
    ],
    [
      "3025613",
      "21059787859169"
    ],
    [
      "282695333",
      "12365709001369"
    ],
    [
      "359740855",
      "9518059176529"
    ],
    [
      "518156315",
      "2398746153595"
    ],
    [
      "534266781",
      "1047401819441"
    ],
    [
      "683917773",
      "951010827857"
    ],
    [
      "771548841",
      "6493104190461"
    ],
    [
      "1188157221",
      "28171537029057"
    ],
    [
      "1763152165",
      "62876223818689"
    ],
    [
      "2288394093",
      "99336417492737"
    ],
    [
      "7376964733",
      "627401465752369"
    ],
    [
      "15797482437/16",
      "1115329628756415/64"
    ],
    [
      "4829083633/9",
      "19093194858415/27"
    ],
    [
      "38763306509/49",
      "2568233456694823/343"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,2,14,32,36,39,41,67,69,72: 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 the sum of -a_p log(p)/p over 5 <= p <= 199 (with early abort on low partial sums); the sets scoring at least 31 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": "2026-10-28 06:03:28",
  "updated_at": "2026-10-28 06:03:28"
}