{
  "id": 4592,
  "curve_key": "135025708502455243656601609:-1567243714173071073394956154918127058277",
  "ainvs": [
    "1",
    "0",
    "1",
    "-2813035593801150909512534",
    "1813939483996375619018752861172039532"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 180.50252227655076,
  "faltings_height": 12.819572454590393,
  "conductor": "228807620212586562666564901674588770",
  "bad_primes": [
    "2",
    "5",
    "7",
    "11",
    "13",
    "19",
    "23",
    "37",
    "41",
    "97",
    "443",
    "1979",
    "2239",
    "181089821480563"
  ],
  "discriminant": "3199085908104098429442921705210829177457785712821495290514784216766901100",
  "regulator": "1076385297768.110838392372628937943472859482195587382950393",
  "points": [
    [
      "4973823189938838926226/4903500625",
      "-22266633471846518756928979939976/343367631265625"
    ],
    [
      "2787785780499459/484",
      "141543491604973942880777/10648"
    ],
    [
      "449762956782322957323479511/85344912009361",
      "9104572264110081867169195412295929579159/788436011817151080391"
    ],
    [
      "3073547841476406285354573099/2970197353233289",
      "-17042191300703447205039688805106764024123/161874321145892638821413"
    ],
    [
      "379465977588359/289",
      "-3044748820842022792073/4913"
    ],
    [
      "4540566996473558982634236/3213977661049",
      "4679189947893590185997262779831978515/5761880949689222093"
    ],
    [
      "219502493834821/81",
      "2736551122577168598991/729"
    ],
    [
      "7954151321166269/7225",
      "139170772233920545180883/614125"
    ],
    [
      "725673451010356/729",
      "-209347357934073617540/19683"
    ],
    [
      "544359508553965140126559806/546480809471041",
      "190888374954904712161492207930862796081/12775043082867053013089"
    ]
  ],
  "submitter": "Maksym Voznyy",
  "history": [],
  "commentary": "t = 4/447 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": "2026-10-18 15:20:44",
  "updated_at": "2026-10-18 15:20:44"
}