{
  "id": 6393,
  "curve_key": "414808961182200579170007458704:-242324034229797483881239098680285057256188608",
  "ainvs": [
    "0",
    "1",
    "0",
    "-8641853357962512066041822056",
    "280467632210410873874388895227789394920644"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 204.59284677174827,
  "faltings_height": 15.01957249041172,
  "conductor": "1886403763909308393938467715492012880",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "23",
    "59",
    "61",
    "83",
    "101",
    "107",
    "127",
    "131",
    "149",
    "227",
    "233",
    "503",
    "14249"
  ],
  "discriminant": "7322788127167554754078944674892130344488886932342036131835392444688498190568525440000",
  "regulator": "490404616.903962885568192129131608510926784254950646912483104",
  "points": [
    [
      "16574362207454",
      "376546888153394966700"
    ],
    [
      "-72563592983446",
      "724892940509600200800"
    ],
    [
      "72742171967054",
      "191703138521656307700"
    ],
    [
      "85864365665822",
      "414115520949751778388"
    ],
    [
      "-102965845017346",
      "280433692579682371500"
    ],
    [
      "27070021034954",
      "-257621842076141650800"
    ],
    [
      "22640304285341/4",
      "-3851112368044038064275/8"
    ],
    [
      "835617302793886/9",
      "14248230513870690914500/27"
    ],
    [
      "69113552761304",
      "115464231945780460050"
    ],
    [
      "136906479760304",
      "1289741315160914932050"
    ],
    [
      "61361937009737281730/97969",
      "475625325764955831009748160496/30664297"
    ]
  ],
  "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=1016/529. 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 01:15:50",
  "updated_at": "2026-11-02 01:15:50"
}