{
  "id": 5863,
  "curve_key": "4549649213558012873410304770430082961:-9700610499394560302644385526270177108318534102994874041",
  "ainvs": [
    "1",
    "0",
    "0",
    "-94784358615791934862714682717293395",
    "11227558448373333675717490400385599303475783503877025"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 253.22434044556545,
  "faltings_height": 18.84185694081795,
  "conductor": "55148200243517392566407009102465537396292625010",
  "bad_primes": [
    "2",
    "5",
    "13",
    "19",
    "29",
    "41",
    "107",
    "173",
    "383",
    "587",
    "823",
    "1553",
    "2161",
    "5233",
    "67399",
    "1295839",
    "3574411"
  ],
  "discriminant": "42098466258700710262503271270882020257211004135959985864481610114136483484857981490292131954624000000000",
  "regulator": "715849892610414.58104536736162492758989838911477986168970746369",
  "points": [
    [
      "6132556362321162514064978748585/300444304384",
      "15184944278517949334999296892074807550554183685/164681935673393152"
    ],
    [
      "27739341339538449593746422968303032750/153586825821789131209",
      "-421744573394170402458654570803138226752301461549507965/1903403867389945671733298770427"
    ],
    [
      "521570308694111811659278910/845820889",
      "10644808352781598790162512964640097460235/24599008914787"
    ],
    [
      "35255902483027223116739983766/149765130025",
      "2566021724642668588722252582294664829458651/57958356494024875"
    ],
    [
      "1657028294770063076696129185774462120091206047041728600510/5972344293254415773538330163789439097529",
      "-36597485125473910618893709193737629552513702854561227304016364712250432484474669643365/461548404401335819716453702448145221688958953807746492483667"
    ],
    [
      "31399825078319062580834421140/12230811649",
      "-5525753272932802648785869327999245110979815/1352642152697857"
    ],
    [
      "8705178964447362091942142538240/43296281560081",
      "-4918841485909364058025133238034398533076828745/284889142998798939271"
    ],
    [
      "111311673818677941045613816796008841425053734/95556234635129767780720609",
      "-1136944400534899366423173909201726987648295679925076464861715854369/934089611857290925555131538235628431023"
    ],
    [
      "367858741277573760095430994510/1875193368129",
      "34725667135184574681771355671751553536059865/2567846668868385633"
    ],
    [
      "11852453075028085233186460/65561409",
      "411237019557667620437152792821321065/530850728673"
    ],
    [
      "88325561041162244961309467374510/486920668905841",
      "-17985505584103626804591913629432128916377917505/10744527330942912235639"
    ],
    [
      "86059550195608561933099310/86359849",
      "-764050884014916513445310614483500106915/802542076757"
    ]
  ],
  "submitter": "Maksym Voznyy",
  "history": [],
  "commentary": "Voznyy (2026), T = -1411/2470 for the rank-5 fibration of X163 given by y^2 + (9T^2 - 6T + 244)xy + (13T - 90)(22T - 15)(5T + 6)(4T + 15)y = x^3 mentioned in the curve#4645",
  "created_at": "2026-10-25 15:48:14",
  "updated_at": "2026-10-25 15:48:14"
}