{
  "id": 5997,
  "curve_key": "59793976997745885446716565764561:-462301142111714957297928215802580870548969628441",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1245707854119705946806595120095",
    "535070766333003318989540184240454514437640025"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 219.50537317981264,
  "faltings_height": 15.998601189978206,
  "conductor": "161629801809854228923433025145794886883310",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "31",
    "37",
    "71",
    "109",
    "149",
    "331",
    "853",
    "240043",
    "483139",
    "594630419"
  ],
  "discriminant": "34859386028472206375655464503865538368668059475459230124791779354656748474411478528000000",
  "regulator": "2011275737849.40250258929017207206351769323663651105534133778",
  "points": [
    [
      "11353498438244625958354830/17442749041",
      "190986835850760761809126115648493915/2303681308593911"
    ],
    [
      "695607607404390",
      "2265064790810337915405"
    ],
    [
      "8187856952948467561955190/12584576761",
      "-12256153373586471323697585004214295/1411750405625741"
    ],
    [
      "11374534100640678830010/17447329",
      "13664012034027916868331114945765/72877493233"
    ],
    [
      "242341403113543654810101510/346218090409",
      "501818303959900542444062683633304791935/203715763050926827"
    ],
    [
      "2314942798943070",
      "100284666551866758314205"
    ],
    [
      "26927489064117714060/38809",
      "16705395685861380392377767465/7645373"
    ],
    [
      "1963234032524527071406770/2966871961",
      "115454902126046634092867808140291025/161602548843709"
    ],
    [
      "625909045086447068815634065461537510/956408580033082205929",
      "10281188113696952302362213743464135222453428103793985/29577754188726259882445821849717"
    ],
    [
      "47100569385025848150/72361",
      "-1643901524928780720224342895/19465109"
    ],
    [
      "5927806054558507914377190/9087618241",
      "-185703911300301910738931693407276755/866313559296289"
    ]
  ],
  "submitter": "Mahesh Panchpor",
  "history": [],
  "commentary": "t = 709/1079\r\n\r\nFamily y^2+(7t^2+309)xy-91(t^2-1)(t^2-25)(t^2-121)y=x^3 (Z/3Z K3 family, parameter t=709/1079). Family construction from the Layr Labs Elliptic Rank Challenge public repository, submission/board/3-r12-z3k3.ec (commit c8f82607a219df846ab80dd9e14ee09a2904d709, 2026-10-17). Not itself a repository curve: this t-value is not in that file.",
  "created_at": "2026-10-27 17:50:30",
  "updated_at": "2026-10-27 17:50:30"
}