{
  "id": 6392,
  "curve_key": "174619046075448395571248358595556368:-51188070163325104169423300710500005824677901897393600",
  "ainvs": [
    "0",
    "1",
    "0",
    "-3637896793238508241067674137407424",
    "59245451577922573057533592890983370830078414726916"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 243.4437443709348,
  "faltings_height": 18.315140775888267,
  "conductor": "2774737613430508387442347675631879178546556272",
  "bad_primes": [
    "2",
    "3",
    "11",
    "23",
    "31",
    "53",
    "59",
    "61",
    "73",
    "89",
    "101",
    "113",
    "149",
    "211",
    "337",
    "2099",
    "2521",
    "2963",
    "3469",
    "39317"
  ],
  "discriminant": "1564949344296111487865026593217573450342657457776982755146521439642631825224557564524904033666853356544",
  "regulator": "129942025575.43783111422017406573806076624377609293635247172473",
  "points": [
    [
      "12673118384303712",
      "3895812900074902692361410"
    ],
    [
      "93768727566871758",
      "23293625727772273242510240"
    ],
    [
      "-31014544927079346",
      "11926450117677234344187840"
    ],
    [
      "17825085260813462",
      "251516856959253633966240"
    ],
    [
      "3751007055139979160",
      "-7263834043943602747961715474"
    ],
    [
      "-42332569629742992",
      "11721136450765835758184190"
    ],
    [
      "14450334434544750",
      "3113524032254112393843696"
    ],
    [
      "742398441247180244904/51529",
      "-36661417646867154379740910126554/11697083"
    ],
    [
      "5296251622133374989/4",
      "12176077520494416906589231701/8"
    ],
    [
      "14181005664738105576/1369",
      "-241191367072032849063938011530/50653"
    ],
    [
      "13939109820998862",
      "3353320850781389612208480"
    ],
    [
      "-1609494072421570176/25",
      "644860851162506251733338182/125"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Z/2xZ/2 X400a family y^2=x(x+A)(x+B), A=q(121q-99p)(26p-23q)(75p-44q), B=p(21q-74p)(25p-36q)(p+77q), at T=p/q=-2024/2963. Family equations as posted by wgxli with curve #4252; section formulas from the Layr Labs Elliptic Rank Challenge repository (submission/research/x400a-family.gp, commit 7482bf9). T selected by our Mestre-Nagao sieve; PARI/GP 2.19 ellrank seeded with the family sections, bounds [12,12]; torsion Z/2xZ/2 (elltors).",
  "created_at": "2026-11-02 01:15:12",
  "updated_at": "2026-11-02 01:15:12"
}