{
  "id": 6069,
  "curve_key": "11072901759259477234041:-1086088351700627622904628298128589",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-230685453317905775709",
    "1257046703414879260209833270465"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 152.2763633803609,
  "faltings_height": 10.644193422571279,
  "conductor": "74796929460358181130135996875568438477322157430",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "37",
    "103",
    "7146311",
    "2347345661258664947141613502279799"
  ],
  "discriminant": "103038890251472901697685300828111131547570191894990683895312500",
  "regulator": "48188017170914733113.7255820717139793444992906872271825056090036032731384",
  "points": [
    [
      "12093342911",
      "485717153265357"
    ],
    [
      "236338981411",
      "114663364254932857"
    ],
    [
      "-8615036290721641/1181569",
      "2051537850259205982686571/1284365503"
    ],
    [
      "-2138209100163539/234256",
      "182897506273889353191193/113379904"
    ],
    [
      "-63058526900629/3721",
      "124219776392148178612/226981"
    ],
    [
      "391772993131/7396",
      "709659274886528417867/636056"
    ],
    [
      "336712180324/81",
      "443392066413675431/729"
    ],
    [
      "29826266886689/1849",
      "104674419525191544249/79507"
    ],
    [
      "42038739892604/6241",
      "46239890525613712603/493039"
    ],
    [
      "71187424629256/121",
      "600428376402748361117/1331"
    ],
    [
      "159187658185621/961",
      "2000280063564330851212/29791"
    ],
    [
      "2449539032381701/229441",
      "11567922878090602766873/109902239"
    ],
    [
      "5139369888788239/3396649",
      "5976490190948053801855324/6260024107"
    ],
    [
      "27945611661303791/17956",
      "4671427856250156162284253/2406104"
    ],
    [
      "13518858085908214/5968249",
      "12594440621547341950024099/14580432307"
    ],
    [
      "26031095399032126/168921",
      "4180167802907900736568727/69426531"
    ],
    [
      "29928929423542136/1485961",
      "3960805981916095256933443/1811386459"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,1,21,39,65,66,75,96,98,113: 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": "2026-10-28 21:14:02",
  "updated_at": "2026-10-28 21:14:02"
}