{
  "id": 6453,
  "curve_key": "4564962119426842805150802414400:-9307581231358645749166854876061772094372928000",
  "ainvs": [
    "0",
    "1",
    "0",
    "-95103377488059225107308383633",
    "10772663462220623101150623049774237487914863"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 211.78788901736812,
  "faltings_height": 15.584105414879232,
  "conductor": "190274465488636094225424596624908315200",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "37",
    "53",
    "71",
    "73",
    "89",
    "97",
    "139",
    "151",
    "2221",
    "6263",
    "7109",
    "12791"
  ],
  "discriminant": "4917607384809166461910357876710211747881908179575551021902299207823486030723641600000000",
  "regulator": "36268786223.5449256167372560541796007521598109587942793326072",
  "points": [
    [
      "-200395591844457",
      "4667268591088421766000"
    ],
    [
      "-197856735650457",
      "4673751458871541032000"
    ],
    [
      "297144779196018",
      "2957971521387600766125"
    ],
    [
      "1159912600332393",
      "38223085552889016780000"
    ],
    [
      "1313782444480413",
      "46405257835767725594700"
    ],
    [
      "5443384262705967",
      "400977451911077089443648"
    ],
    [
      "12343712609293482/49",
      "574079754841995705152625/343"
    ],
    [
      "42165733687384457/289",
      "258003224470778859072000/4913"
    ],
    [
      "234324473503237983/841",
      "59264815627685668328328000/24389"
    ],
    [
      "302497794978666933/8281",
      "2042630990152602443456179500/753571"
    ],
    [
      "5367904757067148429983/40436881",
      "179478088457898734120685672240000/257138126279"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Z/2xZ/2 X400a family y^2=x(x+A)(x+B), with\r\nA=q(121q-99p)(26p-23q)(75p-44q),\r\nB=p(21q-74p)(25p-36q)(p+77q),\r\nat T=p/q=-71/306.\r\n\r\nFamily equations as posted by wgxli with curve #4252:\r\nhttps://elliptic-rank.icarm.cloud/curve/4252\r\n\r\nSection formulas from the Layr-Labs elliptic-rank-challenge-public repository, submission/research/x400a-family.gp, commit 7482bf9:\r\nhttps://github.com/Layr-Labs/elliptic-rank-challenge-public/blob/7482bf9/submission/research/x400a-family.gp\r\n\r\nRank bounds [11,11]. The eleven displayed points were checked exactly on the global minimal model, and the torsion subgroup was computed as Z/2xZ/2.\r\n\r\nThe minimal discriminant was fully factored, and every listed bad-reduction prime was proved prime. The conductor is 190274465488636094225424596624908315200.\r\n",
  "created_at": "2026-11-03 17:59:47",
  "updated_at": "2026-11-03 17:59:47"
}