{
  "id": 6406,
  "curve_key": "49712443710302708632553636863081:-352485198508451835127199571524457622600853380021",
  "ainvs": [
    "1",
    "0",
    "1",
    "-1035675910631306429844867434648",
    "407968979755152500646451395914808650197220006"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 218.96267563211165,
  "faltings_height": 16.087407412960314,
  "conductor": "112820662312116398359576655670828686730",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "41",
    "59",
    "61",
    "71",
    "131",
    "251",
    "10905968613524806738099"
  ],
  "discriminant": "-804460546842247741910810801304477899361793151691618389579896823729635368338756512125000000",
  "regulator": "6911677354711.98676681476904433142904097189859439211185204380",
  "points": [
    [
      "4131497694694271509050105/4315570249",
      "4860139951332034625513943868417911839/283502756367557"
    ],
    [
      "-79677410926751172015/108241",
      "-989117646784370539306147777597/35611289"
    ],
    [
      "51470304076478452620/398161",
      "-4175774897216667494785387517018/251239591"
    ],
    [
      "-1374725445406057959900855/3266236801",
      "5177539941433511841761040502266980077/186668699413951"
    ],
    [
      "40948909883796720",
      "8283819849288207566561602"
    ],
    [
      "70303549365487148659173315684345/97123303487762161",
      "-185519609684555592367315795974027309494043614107/30268100596420241470703159"
    ],
    [
      "4454995235101622993145/4405801",
      "-183703236644259603045044576473327/9247776299"
    ],
    [
      "118915474644765442020/203401",
      "-139233444289302388347614086373/91733851"
    ],
    [
      "138064500711922372545/121",
      "-1622268993413912144729484808663/1331"
    ],
    [
      "-69620361116215",
      "-21902868752921324838573"
    ],
    [
      "25962240084748946789655/40780996",
      "671610166292726165181258534470537/260427440456"
    ]
  ],
  "submitter": "Maksym Voznyy",
  "history": [],
  "commentary": "Voznyy (2026), t = 1369/446 for y^2 + (7t^2+309) x y - 91 (t^2-1)(t^2-25)(t^2-121) y = x^3 from https://github.com/Layr-Labs/elliptic-rank-challenge-public/blob/main/submission/board/3-r12-z3k3.ec",
  "created_at": "2026-11-02 01:58:49",
  "updated_at": "2026-11-02 01:58:49"
}