{
  "id": 6400,
  "curve_key": "45608043327055500371401252624:-9637952829817651058013091918861800100330432",
  "ainvs": [
    "0",
    "1",
    "0",
    "-950167569313656257737526096",
    "11155037997473816446473529613263393162980"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 197.96964480166838,
  "faltings_height": 14.364708959589771,
  "conductor": "1266010354850622690046273464492857040",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "31",
    "53",
    "83",
    "89",
    "97",
    "103",
    "109",
    "167",
    "179",
    "191",
    "193",
    "509",
    "1723",
    "3413"
  ],
  "discriminant": "1145176515428088219881658764884671042005727877663279912741610214075126432512640000",
  "regulator": "867416280.650313824853926115178193890653979463941188681252372",
  "points": [
    [
      "5551373030122",
      "77790643163312399100"
    ],
    [
      "19437415730344",
      "5472368843282126874"
    ],
    [
      "-32182451902304",
      "-91662784507661349546"
    ],
    [
      "579148913615512/121",
      "109083960587586464773650/1331"
    ],
    [
      "71265786264110008/289",
      "-18882775990651142266532550/4913"
    ],
    [
      "11042705570266",
      "44823873898722563964"
    ],
    [
      "18736630374129/64",
      "53397678060541687790313/512"
    ],
    [
      "26226815556299542/361",
      "3913722347779502484507600/6859"
    ],
    [
      "2988563255530255",
      "163369382427280667886930"
    ],
    [
      "39357502499872",
      "186344033046143380650"
    ],
    [
      "19288829905066",
      "1999837127260490364"
    ]
  ],
  "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=109/558. 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).\r\n",
  "created_at": "2026-11-02 01:28:13",
  "updated_at": "2026-11-02 01:28:13"
}