{
  "id": 6456,
  "curve_key": "80570148729399865035975524800:-15700347639377703176242075636403162200960000",
  "ainvs": [
    "0",
    "1",
    "0",
    "-1678544765195830521582823433",
    "18171698656686596939062151894922391606263"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 199.6767771857749,
  "faltings_height": 14.670209055646202,
  "conductor": "16492761487975778066271897405280161600",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "29",
    "43",
    "47",
    "61",
    "67",
    "83",
    "109",
    "113",
    "127",
    "149",
    "181",
    "223",
    "241",
    "271",
    "281"
  ],
  "discriminant": "160025544932199927450311330216051547754170543357206105737180807237887269273664000000",
  "regulator": "195681649.910594470722839983605954940555232356141818614176082",
  "points": [
    [
      "-44187411567782",
      "77878866289597047675"
    ],
    [
      "-27596560253927",
      "208511496593345700300"
    ],
    [
      "11395068297823",
      "22895162719752061200"
    ],
    [
      "42433665809767",
      "152812396051778167848"
    ],
    [
      "64805665365343",
      "426100520804007310800"
    ],
    [
      "326513121175423",
      "5854906988368505289600"
    ],
    [
      "-16277882495393603/484",
      "2036609095391361880354875/10648"
    ],
    [
      "628094071573087/9",
      "13252721708265554576600/27"
    ],
    [
      "4097950438964011/25",
      "254563360094545367604816/125"
    ],
    [
      "1073788841632458826/16129",
      "919490848274264451032181747/2048383"
    ],
    [
      "3233723529344599207/76729",
      "3172925473887232380347830800/21253933"
    ]
  ],
  "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=-473/669.\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 16492761487975778066271897405280161600.",
  "created_at": "2026-11-03 18:26:50",
  "updated_at": "2026-11-03 18:26:50"
}