{
  "id": 408,
  "curve_key": "13290803560702940482893124521:-1628236367143163725361270759524647288786069",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-276891740847977926726940094",
    "1884532832341693905066312410598171652600"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "naive_height": 194.3921427029086,
  "faltings_height": 14.146083847913825,
  "conductor": "1921048791987278542375790503041156402647469228660080670360277605330",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "43",
    "4987",
    "18859754273231",
    "57997682476170649245198004209712540060550417"
  ],
  "discriminant": "-175574981472651644515284153152000581141671079737037803387236807293960702438312500",
  "regulator": "21879331590853938884.291277946765253852174072798582542275279886881693420907",
  "points": [
    [
      "-8027583276034",
      "-59916521839841622508"
    ],
    [
      "110579138173309526/12769",
      "-16833976176009319948919522/1442897"
    ],
    [
      "-39275422713709606494/2042041",
      "-28471732838972902310566194362/2918076589"
    ],
    [
      "799681980470396/121",
      "-24659002233759761630168/1331"
    ],
    [
      "15204738199492180121/654481",
      "-47329151186729263651405537007/529475129"
    ],
    [
      "-596097294527084154/63001",
      "-956322865641440068604067718/15813251"
    ],
    [
      "666957054379235011154/56055169",
      "-6952319984060723792978051121374/419685050303"
    ],
    [
      "-18587941837203319/961",
      "-58330309436108019299038/29791"
    ],
    [
      "185217128559293107676/16248961",
      "-947742666045528038062515348728/65499561791"
    ],
    [
      "-419780228754754/529",
      "558060458721497985538348/12167"
    ],
    [
      "60423170662936046241/564001",
      "-464347597727089192165161754358/423564751"
    ],
    [
      "5833837112380376983094/349577809",
      "285747900608833012595004204442766/6536056294873"
    ],
    [
      "4320424875300107714/552049",
      "5755235284857417756797778784/410172407"
    ],
    [
      "3648287888066411002799/83302129",
      "206490172176042496998518213697956/760298531383"
    ],
    [
      "18954401339362921599821/254689681",
      "2549593455208401910957316556125143/4064592619079"
    ],
    [
      "97310969184818314979/2365444",
      "891996379417223722451927434549/3638052872"
    ],
    [
      "10321488018550628245151/1061521561",
      "365194897622623942556799086317697/34585433978941"
    ],
    [
      "109680229741693103029/11370384",
      "404220412258421818055999737361/38340934848"
    ]
  ],
  "submitter": "Bhavik Mehta",
  "commentary": "Rank-18 curve from Mestre's quartic construction, specialized at T = 1861/5. The sextuple is [0, 113, 550, 753, 868, 1058], the canonical primitive representative from u = -3, v = -1/2 in the Mestre-Fermigier family, whose generic member has rank 12.",
  "created_at": "2026-08-28 20:29:18",
  "updated_at": "2026-08-28 20:29:18"
}