{
  "id": 4177,
  "curve_key": "1258864448429691556729:-38442397584106747436956782707917",
  "ainvs": [
    "1",
    "0",
    "1",
    "-26226342675618574099",
    "44493515720160243940176209922"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "naive_height": 145.75349110824047,
  "faltings_height": 10.13663442282369,
  "conductor": "990433349479246683456268348048692288078629191071270710",
  "bad_primes": [
    "2",
    "5",
    "11",
    "41",
    "67",
    "8707",
    "378347134263144107",
    "994981297502993806984589287"
  ],
  "discriminant": "299279245212143970339980606729873348688719382666005870440700",
  "regulator": "30819873128172819.8799654030780724146344001361794390765454160960733710017",
  "points": [
    [
      "4144962871",
      "83662340450254"
    ],
    [
      "4998326841",
      "-195655861648786"
    ],
    [
      "1847165842653/361",
      "1443063624711797886/6859"
    ],
    [
      "449277978350061/312481",
      "-17255213929143676452784/174676879"
    ],
    [
      "1806714132957816/72361",
      "-75274792687022960608674/19465109"
    ],
    [
      "-19683442502426/5329",
      "-117332796151589979432/389017"
    ],
    [
      "1419245171244209/134689",
      "-47877168019603983942168/49430863"
    ],
    [
      "-5660538457",
      "-107586605678238"
    ],
    [
      "3142280721308371/320356",
      "-155023028560612128894151/181321496"
    ],
    [
      "701705236452001/1666681",
      "393977404782721055052954/2151685171"
    ],
    [
      "1174612756",
      "123726329966289"
    ],
    [
      "75018453305689/81",
      "649748530288799565400/729"
    ],
    [
      "-13349991530/9",
      "7643078625652456/27"
    ],
    [
      "544935598",
      "174251468515504"
    ],
    [
      "-4455113084149902489/7238436241",
      "151353992964082012973950853506/615838916948039"
    ],
    [
      "45925937095/81",
      "125856940910347214/729"
    ],
    [
      "111603909314059759/55756089",
      "-1739118607466305901417498/416330716563"
    ]
  ],
  "submitter": "Andrii Prokhorenkov",
  "history": [],
  "commentary": "Mestre construction: sextuple [-803, -792, 315, 365, 427, 488], T = 517; y^2 = r(x) with p(x-T)p(x+T) = g(x)^2 - r(x), p(x) = prod(x - a_i), on the locus sum a_i = 0, 12 p5 = 5 p2 p3. Found by a discriminant-first sweep + Nagao-sum rescoring + ratpoints search on the quartic.",
  "created_at": "2026-10-11 22:58:56",
  "updated_at": "2026-10-11 22:58:56"
}