{
  "id": 6426,
  "curve_key": "125661575602789318817130121:-1414884315235667250576617282381587052581",
  "ainvs": [
    "1",
    "0",
    "1",
    "-2617949491724777475356878",
    "1637597587078100414598626271300186756"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 180.29573279700716,
  "faltings_height": 12.855222304150622,
  "conductor": "18803473705399809452684642393719310",
  "bad_primes": [
    "2",
    "5",
    "7",
    "11",
    "13",
    "17",
    "23",
    "59",
    "79",
    "127",
    "743",
    "1956109",
    "70686336211"
  ],
  "discriminant": "-10183361519044788759810796109559689008388605940813061450553746859059812500",
  "regulator": "134214846.7869414997632882781082761983149149628100474186676",
  "points": [
    [
      "901878515980",
      "100495881588304572"
    ],
    [
      "3660496280155/4",
      "725377736631817551/8"
    ],
    [
      "1298660566775",
      "654205651793771577"
    ],
    [
      "892288723755",
      "109783289648944697"
    ],
    [
      "10776318265570/9",
      "12652717725688158319/27"
    ],
    [
      "8262094989460/9",
      "2405813124126473444/27"
    ],
    [
      "1279265236821",
      "618132335798316839"
    ],
    [
      "50879827753469/25",
      "-272125932753749283057/125"
    ],
    [
      "4627519841659/4",
      "3172670237641810187/8"
    ],
    [
      "1102691920550",
      "302656744102969272"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Z/3 K3 family\r\ny^2+(7t^2+309)xy-91(t^2-1)(t^2-25)(t^2-121)y=x^3,\r\nat t=308/87.\r\n\r\nFamily construction from the Layr-Labs elliptic-rank-challenge-public repository, submission/board/3-r12-z3k3.ec, commit c8f82607a219df846ab80dd9e14ee09a2904d709:\r\nhttps://github.com/Layr-Labs/elliptic-rank-challenge-public/blob/c8f82607a219df846ab80dd9e14ee09a2904d709/submission/board/3-r12-z3k3.ec\r\n\r\nThis specialization was obtained in the rational-parameter search using the family sections to seed point recovery. The displayed model was independently confirmed globally minimal, and all ten displayed rational points were checked exactly on it. A separate rank computation returned bounds [10,10]; the torsion subgroup is Z/3Z.\r\n\r\nThe minimal discriminant was fully factored, and every listed bad-reduction prime was proved prime. Attribution for the family construction remains with the cited source.",
  "created_at": "2026-11-02 19:38:42",
  "updated_at": "2026-11-02 19:38:42"
}