{
  "id": 6385,
  "curve_key": "682498188094586454279577249:-10704504050780823919377264523497401765393",
  "ainvs": [
    "1",
    "1",
    "1",
    "-14218712251970551130824526",
    "12389472280990399517322401765150815898"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 185.36340631231866,
  "faltings_height": 13.488507386213378,
  "conductor": "16334391992898237107214324401202491115",
  "bad_primes": [
    "3",
    "5",
    "7",
    "11",
    "19",
    "47",
    "61",
    "109",
    "127",
    "163",
    "167",
    "367",
    "443",
    "463",
    "619",
    "1301",
    "1567",
    "7253"
  ],
  "discriminant": "117664251543947196560280847013585040596442512818419075008341516024809388962225",
  "regulator": "3966245035.41239331220504948779332146255565929032253401976279",
  "points": [
    [
      "-290381469522416/81",
      "3031220638090564345873/729"
    ],
    [
      "1171616914103/4",
      "22978082908797488287/8"
    ],
    [
      "285021352442347863/51076",
      "119301331401147978120559483/11543176"
    ],
    [
      "-190414672197591/64",
      "2726452632817614364703/512"
    ],
    [
      "112876407191931",
      "1198572068641703603194"
    ],
    [
      "-3487642781898",
      "-4422303958848836462"
    ],
    [
      "1907428224122664/529",
      "34412663918867640144218/12167"
    ],
    [
      "-11062540169801/4",
      "-44224597866597263573/8"
    ],
    [
      "-1179768336206394/289",
      "7618028212377332440946/4913"
    ],
    [
      "11186130725152",
      "35398472810626016438"
    ],
    [
      "3298998366816",
      "-1177392985786217546"
    ]
  ],
  "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=-2672/61. 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 [11,11]; torsion Z/2xZ/2 (elltors).",
  "created_at": "2026-11-02 01:03:52",
  "updated_at": "2026-11-02 01:03:52"
}