{
  "id": 6130,
  "curve_key": "20017036780253111361:-89299534579322524249121758305",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-417021599588606487",
    "103355942904397210370672175"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 133.32934627155157,
  "faltings_height": 8.924309639580859,
  "conductor": "2046819555713424945668705479118862619827345878",
  "bad_primes": [
    "2",
    "11",
    "17",
    "5472779560731082742429693794435461550340497"
  ],
  "discriminant": "26652014049742757487742217085414868043493918909079552",
  "regulator": "316975927372837026749.903161297866962283105628342513281352075549799550034",
  "points": [
    [
      "456957130305",
      "308896105560821754"
    ],
    [
      "-346582105905/961",
      "428463274063444754/29791"
    ],
    [
      "10153687119/25",
      "123721074552118/125"
    ],
    [
      "762222083863/7396",
      "4986939883064969777/636056"
    ],
    [
      "3393401421875/7921",
      "1285799596596936206/704969"
    ],
    [
      "18125491757851/361",
      "77161023812795187658/6859"
    ],
    [
      "19816003770237/3721",
      "87590129193752316000/226981"
    ],
    [
      "21161344652491/19321",
      "83228807613506801818/2685619"
    ],
    [
      "50951863197595/167281",
      "146632435585166593390/68417929"
    ],
    [
      "193910262794765/52441",
      "2661514826306119736546/12008989"
    ],
    [
      "1407978328375753/1149184",
      "46610654601257464436995/1231925248"
    ],
    [
      "400689125489251/231361",
      "7527654781607032202142/111284641"
    ],
    [
      "3180272958899347/7789681",
      "23315833512561493471122/21740999671"
    ],
    [
      "3406616726597747/2217121",
      "183510528148814549858830/3301293169"
    ],
    [
      "8319396160217223/20693401",
      "77617317063987303449078/94134281149"
    ],
    [
      "15969774081473459/47128225",
      "315972045335046636533918/323535264625"
    ],
    [
      "1076514456328940311/2766654801",
      "6854938445491334852396098/145523275877799"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,2,31,38,43,68,75,83,125,137: 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": "2026-10-29 12:55:56",
  "updated_at": "2026-10-29 12:55:56"
}