{
  "id": 3717,
  "curve_key": "18303864395985607242911881:-78309430780363746618731789997840461221",
  "ainvs": [
    "1",
    "0",
    "1",
    "-381330508249700150893998",
    "90635915255018855118215059707148256"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    6
  ],
  "naive_height": 174.5074633157728,
  "faltings_height": 12.080430758629078,
  "conductor": "447060738391164495290",
  "bad_primes": [
    "2",
    "5",
    "7",
    "11",
    "31",
    "41",
    "43",
    "59",
    "61",
    "73",
    "109",
    "409",
    "907"
  ],
  "discriminant": "1917523281786781390971332623201098397040724314837167577694272000000",
  "regulator": "19096556.50190866289388076085736561219199829862410368",
  "points": [
    [
      "142212243658061/400",
      "8127223157255448899/8000"
    ],
    [
      "2046212739609181/5625",
      "3171397777536389808071/421875"
    ],
    [
      "3117555472318266/9025",
      "9780986299017744216476/857375"
    ],
    [
      "88911667482176845/249001",
      "67731950524310263539423/124251499"
    ],
    [
      "103907538642461605/247009",
      "8383639402834992869533421/122763473"
    ],
    [
      "1707255230699357645/4791721",
      "1911699047366521595207713/10489077269"
    ],
    [
      "6314317910825566645/17631601",
      "122030791666362883136340923/74035092599"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -2076829/55327 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 01:49:04",
  "updated_at": "2026-09-30 01:49:04"
}