{
  "id": 6018,
  "curve_key": "9875418537661083722497:-979387753088086944533354983478401",
  "ainvs": [
    "1",
    "0",
    "0",
    "-205737886201272577552",
    "1133550640131103954544980738304"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 151.93300693897382,
  "faltings_height": 10.460878044322797,
  "conductor": "12061362541463435473927866338570877306640433226",
  "bad_primes": [
    "2",
    "3",
    "7",
    "41",
    "1741321",
    "144196043",
    "2354068357",
    "1692832290971654689"
  ],
  "discriminant": "2250505237548991783441477703671291440686180883389281729511424",
  "regulator": "55813287788595495.2832570728677409751639432355059458064060864777860911919",
  "points": [
    [
      "-14811064096",
      "965243016343856"
    ],
    [
      "-7955332960",
      "1505591007596912"
    ],
    [
      "-26828608705/4",
      "11897559316811401/8"
    ],
    [
      "2951309264",
      "743006655131456"
    ],
    [
      "7934934704",
      "25348321209440"
    ],
    [
      "7975368608",
      "688677042800"
    ],
    [
      "8587287752",
      "7727686869296"
    ],
    [
      "8890479392",
      "84560558890736"
    ],
    [
      "9237537824",
      "145932636713456"
    ],
    [
      "9741156080",
      "231868512453872"
    ],
    [
      "10303655072",
      "328002680581616"
    ],
    [
      "132835245344",
      "48142524899702000"
    ],
    [
      "-10683550966874624203348/14230526441569",
      "60914340110946666399187497483922900/53682341425009076753"
    ],
    [
      "140131519109/16",
      "3766841276138309/64"
    ],
    [
      "1612587815840/121",
      "1159361886522545872/1331"
    ],
    [
      "9697468578848/961",
      "8685376714854160400/29791"
    ],
    [
      "54390705044188832/4355569",
      "6502380267767888675798800/9090072503"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,5,9,21,27,31,46,55,64,80: 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 11:27:53",
  "updated_at": "2026-10-28 11:27:53"
}