{
  "id": 4604,
  "curve_key": "915061931793387971111044561:-27665898333757217511759858595638813148441",
  "ainvs": [
    "1",
    "0",
    "0",
    "-19063790245695582731480095",
    "32020715664069264952386769113058040025"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 186.24310193958655,
  "faltings_height": 13.271121854230556,
  "conductor": "1176541376429733882533000620110890",
  "bad_primes": [
    "2",
    "5",
    "7",
    "13",
    "19",
    "37",
    "67",
    "79",
    "97",
    "433",
    "457",
    "661",
    "1559",
    "4339",
    "7321"
  ],
  "discriminant": "471358479271697853963600730303399961710479562011918423699731000000000000000",
  "regulator": "1053146660864.171020281398895784677263328353963317945387372",
  "points": [
    [
      "2942557545672384191115190585590/21160560517956601",
      "5045170358890773081019422752797251104000366295/3078156887536876972730099"
    ],
    [
      "981348855047847770/344569",
      "184015364780745838633686195/202262003"
    ],
    [
      "3599515975205160866710/1161650889",
      "65063362157818887697554370916735/39592547249787"
    ],
    [
      "172116887306660969590/7284601",
      "-2221956291985248352941398673705/19661138099"
    ],
    [
      "54317919490518440/121",
      "-12658849437663529990356945/1331"
    ],
    [
      "1005168660600100222334127590/111370051346401",
      "28673020349859581791133463676932687122205/1175310537238890379601"
    ],
    [
      "26282213221886219861215/8728417476",
      "-1129530395941547213410477977561295/815461131112776"
    ],
    [
      "174339113943915112520542990/67425135660961",
      "-67878300845958775474640529820211672595/553646735375271501041"
    ],
    [
      "767411257204962086189750/288176786041",
      "-57606441158653807090306085632772055/154699350459315661"
    ],
    [
      "2950140279090",
      "-1206607333923420795"
    ]
  ],
  "submitter": "Maksym Voznyy",
  "history": [],
  "commentary": "t = 115/273 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 23:17:01",
  "updated_at": "2026-10-18 23:17:01"
}