{
  "id": 3684,
  "curve_key": "1306942071457482407119725582704353:-47240918488225701179987786544624832968806277230545",
  "ainvs": [
    "1",
    "0",
    "0",
    "-27227959822030883481660949639674",
    "54676988991001966689322545553705118390298499044"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    4
  ],
  "naive_height": 228.75899454210503,
  "faltings_height": 16.77224529377197,
  "conductor": "50602109704855750262657748221866866",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "23",
    "29",
    "43",
    "59",
    "67",
    "313",
    "521",
    "569",
    "2609",
    "6379",
    "8563",
    "8831"
  ],
  "discriminant": "393638554341388480856201081603859227851495402245666016601959648504636572362676511999141085184",
  "regulator": "383326188492.4446298013039714687597560562369248519140361279",
  "points": [
    [
      "-5776925883678636",
      "138485680604688976341942"
    ],
    [
      "-6124932541025889/4",
      "2436772945638885831649977/8"
    ],
    [
      "3447519905706132",
      "42227787609941215094454"
    ],
    [
      "324391752127437780/529",
      "2378358595273334431475868666/12167"
    ],
    [
      "1914033903030140448/361",
      "1671146208230278509236958834/6859"
    ],
    [
      "47630973783088585524/15625",
      "3527103343742079513168493518/1953125"
    ],
    [
      "108634665333670341204/36481",
      "11166811115984622165701488074/6967871"
    ],
    [
      "2331989675564255450580/877969",
      "27223925396339184547938035821446/822656953"
    ],
    [
      "828899126583462980667732/162384049",
      "456633535074678115030754188319657562/2069259936407"
    ],
    [
      "1406962787432949478072308/419881081",
      "280679220988339525465586039679882306/8603783230771"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = 797/1707 of the Elkies-Klagsbrun Z/4 fibration E1: y^2 + a*xy + a*c*y = x^3 + c*x^2, a = (8t-1)(32t+7), c = 8(t+1)(15t-8)(31t-7) (arXiv:2003.00077, eq. (5)), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:32:40",
  "updated_at": "2026-09-29 19:32:40"
}