{
  "id": 628,
  "curve_key": "617425053023481477243467764985745929583608313192225:-15381105923607590097058380533239219461936238054612455210227912667774033023025",
  "ainvs": [
    "1",
    "-1",
    "1",
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    "17802205930101377427150906610708284800466302835899765794079393280105836097"
  ],
  "rank_lower_bound": 27,
  "torsion": [],
  "naive_height": 350.8540436853045,
  "faltings_height": 27.04668843302755,
  "conductor": "626331835852237837959942160026415058213286411653252011129135977016421858574282246171665388209084791081551835278559332642950",
  "bad_primes": [
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    "5",
    "7",
    "13",
    "37",
    "61",
    "89",
    "149",
    "179",
    "4919",
    "526689608973452707",
    "1297327695885285412767490764778583",
    "7644533052528481157308027511138991115839138041559182477"
  ],
  "discriminant": "-698803764333922225881452682703627988473575385055139144321696385420459618811963213599318605839675657668786479665115883391213066301636816763473920000",
  "regulator": "35743860320941141662851642470301.598384221193797810458962096346551288551908088639280181999648",
  "points": [
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      "109292241610100662634669071/9",
      "1097533151962722049118285277817582562300/27"
    ],
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      "-13608087838410452272362192099221399076571742240337381540/2290420692235914211"
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      "1899645222030070993070647122789813287/1085478510769",
      "-912545665216743799264013548673706493719978385050879188/1130919897665322647"
    ],
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      "-149392249712752179858946689/49",
      "-1836876806687519387456827717703347474140/343"
    ],
    [
      "31131854726004058226229613519/14641",
      "-451385099131502081322873175296425234528820/1771561"
    ],
    [
      "3619513677230778891863526649723/2070721",
      "2418673712948680708775780088407794856628265260/2979767519"
    ],
    [
      "78380599592350844377619017364649895/24535149769",
      "11727998233765513746619321075056937079999595194388268/3843112254366853"
    ],
    [
      "4545075381747755621258644226857074873/3763751321521",
      "-14658183288143279789464880375175251929013446062925469240/7301824350052279319"
    ],
    [
      "-51945182919890832231503098220931/20151121",
      "526146099448064645708226705870192668737072679960/90458382169"
    ]
  ],
  "submitter": "Roy van Rijn",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Roy van Rijn",
      "at": "2026-09-07 09:26:36"
    }
  ],
  "commentary": "This curve was found prospectively as the specialization t = 4286/1881 of an elliptic K3 family with generic Mordell–Weil rank 17.\r\n\r\nWe found 27 independent rational points on the specialized curve, proving rank at least 27 over Q; the exact rank is not currently known. The submitted equation is a globally minimal integral Weierstrass model. In this presentation, the specialization has 10 independent directions beyond the 17 generic sections.",
  "created_at": "2026-09-07 08:27:08",
  "updated_at": "2026-09-07 09:26:36"
}