{
  "id": 6179,
  "curve_key": "1096251161061460062001:-36163054398914823637409732374825",
  "ainvs": [
    "1",
    "0",
    "0",
    "-22838565855447084625",
    "41855387033877832055344377641"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 145.33854983009914,
  "faltings_height": 9.934884086086486,
  "conductor": "5240227668680445150085901505663732024266517078",
  "bad_primes": [
    "2",
    "3",
    "23",
    "487",
    "3163",
    "24651475359537885220952165832338600251"
  ],
  "discriminant": "5596953719326874216969573620134104832085337340321128251392",
  "regulator": "2528576445182533080.36221353485738014041907495305732707968510402851183037",
  "points": [
    [
      "-5450976316",
      "66201146520305"
    ],
    [
      "-2002216798",
      "282058647983699"
    ],
    [
      "2082945950",
      "57627866524271"
    ],
    [
      "16834437551/4",
      "1139283378733873/8"
    ],
    [
      "9256528106",
      "789665905186043"
    ],
    [
      "-529561885679488/116281",
      "8990743940732329366729/39651821"
    ],
    [
      "-1202601227578/961",
      "7795702536882810089/29791"
    ],
    [
      "-184344194950/49",
      "93639861588933197/343"
    ],
    [
      "-120577729726/169",
      "528135996297425567/2197"
    ],
    [
      "3762152016026/841",
      "4168176820700651527/24389"
    ],
    [
      "5221339598378/1681",
      "2048684017621989379/68921"
    ],
    [
      "5746777173386/2209",
      "713321979772332373/103823"
    ],
    [
      "8714733556538/3481",
      "3948665190150977617/205379"
    ],
    [
      "9681866778836/9409",
      "127264369976487023585/912673"
    ],
    [
      "12648541632674/4225",
      "4865815900687621963/274625"
    ],
    [
      "183386151643250/57121",
      "550080130906231407949/13651919"
    ],
    [
      "1874067773429018/635209",
      "6302752470645430525447/506261573"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,13,14,15,20,31,39,72,95,111: 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": "2026-10-30 14:40:40",
  "updated_at": "2026-10-30 14:40:40"
}