{
  "id": 6447,
  "curve_key": "9252377255102354107441:-880294228809157720165029638025385",
  "ainvs": [
    "1",
    "0",
    "0",
    "-192757859481299043905",
    "1018859061105647169308305679241"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 151.73750241579575,
  "faltings_height": 10.513658669009908,
  "conductor": "476374753687193055372372517588509157743651102",
  "bad_primes": [
    "2",
    "3",
    "11",
    "37",
    "43",
    "61",
    "29243463533",
    "4904099656411",
    "518581108686019"
  ],
  "discriminant": "9922201523464135751507534061798767835849696838714640881631232",
  "regulator": "11183103279591.0673230806933802363925841887727436024687034576916198965504",
  "points": [
    [
      "-13965478556",
      "993517632802561"
    ],
    [
      "80332381208146/25",
      "-719999234472481896721/125"
    ],
    [
      "-1548640268534/529",
      "-15187137400261677523/12167"
    ],
    [
      "11259318418690/841",
      "-22324649284198953049/24389"
    ],
    [
      "135836333360374/15625",
      "23721609110775983807/1953125"
    ],
    [
      "103689937844266/14161",
      "-8224910664220970131/1685159"
    ],
    [
      "732270732571/100",
      "2859101764384351/1000"
    ],
    [
      "239853304949938/25281",
      "843763042434648326477/4019679"
    ],
    [
      "311911095720970/32041",
      "1461375065488947706841/5735339"
    ],
    [
      "3726173298648586/609961",
      "125403903066123323227111/476379541"
    ],
    [
      "339887184228/49",
      "42764446056223767/343"
    ],
    [
      "-12098410223066/3025",
      "218567596293608189413/166375"
    ],
    [
      "628291779950781706/98465929",
      "215621760112241652083985017/977077413467"
    ],
    [
      "22010447144284/61009",
      "14682742004693285889133/15069223"
    ],
    [
      "631603744348/121",
      "523867367174455643/1331"
    ],
    [
      "3191471134",
      "660441140356675"
    ],
    [
      "481233001786/361",
      "-5996320484797626023/6859"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,1,23,29,100,119,122,159,179,198: 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, proved: the 17 listed points come from the point search and are independent, and the 2-descent upper bound (ellrank) is 17. Torsion trivial.",
  "created_at": "2026-11-03 14:23:40",
  "updated_at": "2026-11-03 14:23:40"
}