{
  "id": 4648,
  "curve_key": "15066665211904256853437533163787967489:-58463855779134033539165088958728394127261916871557990913",
  "ainvs": [
    "1",
    "0",
    "0",
    "-313888858581338684446615274245582656",
    "67666499744368094347876262894527788017483353154949120"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 256.81664414820204,
  "faltings_height": 19.134639679988023,
  "conductor": "1106047551364870575551927475736261117099622365890",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "23",
    "43",
    "59",
    "73",
    "89",
    "109",
    "127",
    "1289",
    "2171633",
    "2237479",
    "58975978981919"
  ],
  "discriminant": "1259764479403997562246662608225222522097850368584823467951971228293094692329002518163555103650903962419200",
  "regulator": "364714331073933.66657491437850955307879987582847132822971091211",
  "points": [
    [
      "650599613942904483022737/984064",
      "-376974044679649629115433428903192617/976191488"
    ],
    [
      "481126945684807406088/121",
      "10453782132639111609461975651496/1331"
    ],
    [
      "284031498749102923948272/49729",
      "150671071466077926748762588080050352/11089567"
    ],
    [
      "3662209634231511998145217832712535603925697799353168/714639621885563024360921823590521",
      "-220350560825669955030638522258895966379365980615782716251871093716581820708544/19104278333001859672156393542483008547297170202931"
    ],
    [
      "450898711655277327367398304/1040643081",
      "3828639445462990172295468580991862521920/33570105149979"
    ],
    [
      "8004128039784513964237638968254080/1832055975165529",
      "710476157460054388830377153990816202388116919364160/78416618014309983829667"
    ],
    [
      "143719823200445644277864772/436684609",
      "-28307241196913633865724889691992706132/9125398274273"
    ],
    [
      "839655732851925314128119702144/2534225205625",
      "25166153271883411498154115881255876329908672/4034296460464578125"
    ],
    [
      "137126491963413489539985587182760754/402809957826418321",
      "4141667576787812280412805430831199125288335415961950/255652649075471713776466631"
    ],
    [
      "531468856199556223177823352/1422572089",
      "-2705876712953817052745925009200040083712/53655151480813"
    ],
    [
      "478927492685746370944944774784/1086712427025",
      "138421806488401393766602513089534946312604992/1132848803114346375"
    ],
    [
      "106334254766271866880736858824/323409453481",
      "-455641638304494894200412275008580250965760/183920045509563371"
    ]
  ],
  "submitter": "Maksym Voznyy",
  "history": [],
  "commentary": "t = 2743/5141 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": "2026-10-20 13:15:09",
  "updated_at": "2026-10-20 13:15:09"
}