{
  "id": 6443,
  "curve_key": "60432244184773548336:-470780628356531841305413087584",
  "ainvs": [
    "0",
    "0",
    "0",
    "-1259005087182782257",
    "544884986523763705214598481"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 136.64837947830452,
  "faltings_height": 9.18870611377725,
  "conductor": "513703381698555856869103997914550200450077860",
  "bad_primes": [
    "2",
    "5",
    "7",
    "1289849659093",
    "2844757792823385553109552181943"
  ],
  "discriminant": "-539613296012976767899939430809365326185278662063750000",
  "regulator": "43295939776222.3464244044368186951203005631071949232524525454529972371397",
  "points": [
    [
      "350387407",
      "12114577514095"
    ],
    [
      "8448245191112",
      "-24555555363206735875"
    ],
    [
      "-495958512845903/968256",
      "30952086348586524302825/952763904"
    ],
    [
      "-56911340303/81",
      "23986467677792375/729"
    ],
    [
      "-162996993475/169",
      "64503230180461177/2197"
    ],
    [
      "-1176202993907/1089",
      "912493954676954125/35937"
    ],
    [
      "-807826491119/900",
      "-832984699400083279/27000"
    ],
    [
      "14954128654853/26569",
      "-16529405849255896625/4330747"
    ],
    [
      "25897975556897/27556",
      "63345113658554956375/4574296"
    ],
    [
      "4746615613/9",
      "141799305941335/27"
    ],
    [
      "-7734951858657/80089",
      "584734659252232244875/22665187"
    ],
    [
      "26114871772993/54289",
      "89951638998467362375/12649337"
    ],
    [
      "367119678366577/793881",
      "5550129964225772067205/707347971"
    ],
    [
      "12180540809/25",
      "858136976874877/125"
    ],
    [
      "4837802528737/15376",
      "25573425466412476625/1906624"
    ],
    [
      "-557076423563/3481",
      "5595472887706365335/205379"
    ],
    [
      "2072024993/4",
      "45048842124265/8"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,14,123,126,130,132,150,163,166,190: 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); for the sets with S >= 31, or S >= 30 and one bad prime in that range, or S >= 29 and two or more bad primes, rational points were found by a point search on the quartic y^2 = r(x), and the curves were screened by conductor and by a GRH explicit-formula upper bound on the rank. Rank >= 17: the 17 listed points come from the point search and are independent (height matrix nonsingular at 57 and 115 digits). Torsion trivial.",
  "created_at": "2026-11-03 14:18:13",
  "updated_at": "2026-11-03 14:18:13"
}