{
  "id": 6122,
  "curve_key": "758070059880416853297:-20869445595672903546901710151209",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-15793126247508684444",
    "24154450924865994000420817119"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 144.23192244764078,
  "faltings_height": 9.721299659627482,
  "conductor": "133189757005333373984927132272779327740156243097818",
  "bad_primes": [
    "2",
    "113",
    "2411",
    "151830629",
    "2226833419654303",
    "6397931882288571973"
  ],
  "discriminant": "61646612650404541482175553318191366285875836805338865664",
  "regulator": "119652716301597166823793.46205957175763553463496204566753775219499364698818",
  "points": [
    [
      "-841179993472485683/1452905689",
      "10076211657978856820928856785/55380406147613"
    ],
    [
      "-886571823533339/388129",
      "53148381012832838440203/241804367"
    ],
    [
      "259179362888893/124609",
      "766674502563305398829/43986977"
    ],
    [
      "508900288050637/26569",
      "11250481503440281075287/4330747"
    ],
    [
      "1696360727028281/942841",
      "36201074214254286222115/915498611"
    ],
    [
      "2356963826795821/177241",
      "109811694388565628570993/74618461"
    ],
    [
      "7912830677411581/3367225",
      "26529621699080357959199/6178857875"
    ],
    [
      "26419290284336261/11621281",
      "11984689609144941833845/39616946929"
    ],
    [
      "218962054867662509/94109401",
      "1878867607564552633628209/912955299101"
    ],
    [
      "412342250682365621/164583241",
      "37336777518301774342514857/2111438398789"
    ],
    [
      "4305434285939492719/2060615236",
      "1558905500826110142742714179/93539568022984"
    ],
    [
      "3733017571652531097/3101710249",
      "14338842936139142028442021265/172743548897557"
    ],
    [
      "6096851347162197619/2936447721",
      "2820625929013876923403453139/159123165553269"
    ],
    [
      "48420400931152622917/76862572081",
      "2562042440723411449339461227885/21309456346308521"
    ],
    [
      "98789146619795703669/46098237025",
      "121762009141530903318592457493/9897521980452625"
    ],
    [
      "312452527460365366089/134871828001",
      "33603801845612191063644357321/49531543961539249"
    ],
    [
      "187459415429267966880853/82836737957961",
      "1471216497875223896817275790467945/753936002585505344709"
    ],
    [
      "40023184945023819725569149/17287317786750025",
      "317660926137724701606365126063444217/2272958065312537790781125"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,3,5,19,44,45,68,83,90,113: 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 18, proved: 18 independent points listed, matching the 2-descent upper bound. Torsion trivial.",
  "created_at": "2026-10-29 03:14:15",
  "updated_at": "2026-10-29 03:14:15"
}