{
  "id": 3719,
  "curve_key": "9088520562319502346536529:-27399320395047713798087053301888480217",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-189344178381656298886178",
    "31712176383204412199788762803759137"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    6
  ],
  "naive_height": 172.40716311714075,
  "faltings_height": 11.787436688160737,
  "conductor": "1693477477526556829770",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "19",
    "37",
    "43",
    "61",
    "67",
    "97",
    "103",
    "271",
    "4327"
  ],
  "discriminant": "694031916904332139240570697877480993938759864943604300161945600",
  "regulator": "1989258.346585550007553568637719820727099851379880463",
  "points": [
    [
      "-62762872737",
      "208203601991477023"
    ],
    [
      "12309612294897/49",
      "2334218148590089/343"
    ],
    [
      "23052923744937/289",
      "642761138977130558519/4913"
    ],
    [
      "8094611808468487/33124",
      "35704465284930450150689/6028568"
    ],
    [
      "3697564874076033/14641",
      "2035069667637663602503/1771561"
    ],
    [
      "70823250272805297/271441",
      "1197207014817343925044295/141420761"
    ],
    [
      "3894516757287338977/15499969",
      "1724423215946297923198239/61023377953"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -1737309/17308 of the universal curve with a 6-torsion point, y^2 + txy + (t+2)y = x^3 (as searched in arXiv:2003.00077, Sec. 13), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-30 01:49:26",
  "updated_at": "2026-09-30 01:49:26"
}