{
  "id": 4015,
  "curve_key": "48921039367626708536774748258845046961:255562637262561288994201657010707529392417517664123959959",
  "ainvs": [
    "1",
    "1",
    "1",
    "-1019188320158889761182807255392605145",
    "-295790089424260751575358162347115559511838112969284505"
  ],
  "rank_lower_bound": 16,
  "torsion": [
    2
  ],
  "naive_height": 260.34981271395276,
  "faltings_height": 19.716047597181724,
  "conductor": "2774700096374548868697941163846920764265826133256711902170",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "29",
    "43",
    "211",
    "349",
    "1279",
    "1321",
    "1381",
    "2549",
    "15767",
    "58601",
    "407521",
    "1204681",
    "19629975401"
  ],
  "discriminant": "29958854757518946016041896408200379479894420610475509031599914246970973637374994914558963432368517201239040000",
  "regulator": "10915521441441812653522960.05421257220538938348803226628944443771691060",
  "points": [
    [
      "28429770272040172193085631/6265009",
      "-147541140987321875197675625840194396840/15681317527"
    ],
    [
      "-64093919914267513720899107304950225/86372461229070241",
      "5782270536142978547179171811350353579876564860366344/25384168552109474171422961"
    ],
    [
      "-123943133331683611355020263197/305953903161",
      "38070123640451610153713715474013581638938108/169232588409347091"
    ],
    [
      "-1726043756526981581839680751/5189761600",
      "29884899433840694514131650318435069138827/373870425664000"
    ],
    [
      "-499706802304145844381848609537/657978923281",
      "107016615012543656152206082115942443240041752/533725525429692679"
    ],
    [
      "-1266911974346716422902190339503287/1567678580154241",
      "-494527194961343624678915696809384237772110926402/62070541856019185968961"
    ],
    [
      "16378426989024164740762542863/2704104001",
      "-2065345351454441998449428337390909957761112/140616112156001"
    ],
    [
      "25558100124031481522275353847/6751415889",
      "-3926399389125816871169604780039072812759456/554743589351463"
    ],
    [
      "170639349088023168197021156261587327/2985477910783729",
      "-70477530621429944582829614713908391508666804594671016/163125100914171151856183"
    ],
    [
      "4239557492926543045845358182338167/15547982406649",
      "276043683488089188813493801602136663682899496255816/61307140591780825357"
    ],
    [
      "-352834261705687076866323908296997/742246924035681",
      "-5765038868971586442622668369148454220031967384848/20221930328035216621329"
    ],
    [
      "25002092851774958036145126040467647041523857/1640987910341211675981609",
      "124735715793016179073692389358992193687668325651954248511779375626/2102122749432630180614424604456237227"
    ],
    [
      "276293357714041059797076984605119845047/190303286334120044089",
      "-2975747797838402614387833841168652469723971192156620734456/2625242535074527345173810616813"
    ],
    [
      "-6107668472347581437832465004383977901905/14923776794430496552641",
      "-418817393742697150210443294100366549912253490474118156632424/1823132014516101053919999215081439"
    ],
    [
      "8133147377762821604937066271743376127/237614528656240849",
      "-23184480842833620655546639188856740515270262608085383016/115826914481392627372848743"
    ],
    [
      "23928666780917165227534596614126526640309243/1431195873007202339534721",
      "116834416933658009392611045900439709728849791355247697410949795472/1712176818856354731217150727219811519"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3486 (source contributor: Steps Unbounded). Source equation and witness provenance are credited to that entry. Exact rank 16: 16 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.",
  "created_at": "2026-10-05 04:46:18",
  "updated_at": "2026-10-05 04:46:18"
}