{
  "id": 6067,
  "curve_key": "806351104698331620001:-22008074004989103800894358348145",
  "ainvs": [
    "1",
    "0",
    "0",
    "-16798981347881908750",
    "25472307874744880953526459396"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 144.41715280595088,
  "faltings_height": 9.962023039525802,
  "conductor": "5527800195841822656759390610258034728913162118",
  "bad_primes": [
    "2",
    "3",
    "43",
    "67",
    "169151",
    "1890528629892876709227099661969414463"
  ],
  "discriminant": "23111032099180805348620775988120207401547603783808399982592",
  "regulator": "152468871943541239898.522281345425290425773708643245196752478775938187167",
  "points": [
    [
      "-436218119866321548916/389636875681",
      "50361689954103731583877018444354/243214844531961329"
    ],
    [
      "-1267948607638036/273529",
      "8744475030393375178886/143055667"
    ],
    [
      "-336052983475300/332929",
      "39086909599366401551138/192100033"
    ],
    [
      "69998821638974/10609",
      "490963159256871608516/1092727"
    ],
    [
      "319999575413756/112225",
      "1032985361167764447166/37595375"
    ],
    [
      "453974529852476/286225",
      "8128549905356545651694/153130375"
    ],
    [
      "667990368829772/380689",
      "8781794279623902784642/234885113"
    ],
    [
      "911025671123564/635209",
      "33309601858874142387034/506261573"
    ],
    [
      "1383924393067628/703921",
      "3929887655313873559486/590589719"
    ],
    [
      "2747510517508124/290521",
      "132171183050533362445030/156590819"
    ],
    [
      "3697563425833600/870489",
      "142430541367453808972218/812166237"
    ],
    [
      "8587408447706540/19918369",
      "12028816994088408711351982/88895680847"
    ],
    [
      "15460413538727144/9102289",
      "1177656160122732514425298/27461605913"
    ],
    [
      "26740265741980712/7360369",
      "2222917063003598209611698/19968681097"
    ],
    [
      "741443731468461308/180123241",
      "390314449995315755871492394/2417434017461"
    ],
    [
      "772523629314482684/236083225",
      "269983945319623981854838522/3627418752125"
    ],
    [
      "56585941632960702968/15262378681",
      "224309635516288191694060364654/1885529524629421"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,17,27,44,62,86,99,113,117,137: 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 21:13:38",
  "updated_at": "2026-10-28 21:13:38"
}