{
  "id": 222,
  "curve_key": "159888926055372110393121:-76439655304583283704599313650092081",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-3331019292820252299857",
    "88471823270026370222046861281089"
  ],
  "rank_lower_bound": 18,
  "naive_height": 160.64361935761244,
  "faltings_height": 11.38352331175443,
  "conductor": "66208178266486068165130805597508803777331470494813390770",
  "bad_primes": [
    "2",
    "3",
    "5",
    "37",
    "1601",
    "20646107",
    "548313117529",
    "1097006657722059559605800613523"
  ],
  "discriminant": "-1015940660555052781009392764803757490793791575413533348544972800000",
  "regulator": "13449739871232258.441561791518281871515000729231548101061803269736297924462",
  "points": [
    [
      "41800029847",
      "4719079210983476"
    ],
    [
      "45876571447",
      "5675420192525876"
    ],
    [
      "30812028847",
      "3884404658379476"
    ],
    [
      "-12479014553",
      "11317972352032676"
    ],
    [
      "20181196247",
      "5428367253417076"
    ],
    [
      "32644665487",
      "-3810579273384364"
    ],
    [
      "7360873847",
      "-8021938656133324"
    ],
    [
      "135390399127",
      "-46035550207283404"
    ],
    [
      "150332668567",
      "54637052958893876"
    ],
    [
      "41235033187",
      "-4607646049543564"
    ],
    [
      "-66023960453",
      "4537618321160276"
    ],
    [
      "-19076706553",
      "12044688521663876"
    ],
    [
      "56388122263",
      "-8940650106097612"
    ],
    [
      "30824886247",
      "-3883638204463324"
    ],
    [
      "-133558553",
      "9429565645552676"
    ],
    [
      "-65429995013",
      "5129270282761136"
    ],
    [
      "-62531015753",
      "7229109483649076"
    ],
    [
      "94911552247",
      "-25046047487098924"
    ]
  ],
  "submitter": "RoyManami",
  "commentary": "Rank-18 naive-height record: h=160.644 (beats prior r18 height record 168.785). Found via a NEW 3-parameter sub-family of Mestre's locus 12*p5=5*p2*p3: the six roots are the union of two depth-2 cubics x^3+px+q, x^3+rx+s with (p-r)(q-s)=0 (here equal product), a slice disjoint from Mestre's (u,v) 2-parameter family. Sextuple {0,54,90,129,585,600}, T=2745/8; certified by injecting the 12 Mestre base points + Neron-Tate height-pairing independence (18 indep).",
  "created_at": "2026-06-25 23:05:55",
  "updated_at": "2026-07-01 22:31:41"
}