{
  "id": 394,
  "curve_key": "17030548304384374425924194339428561:-2210280087650863568842730182317291621396271850726809",
  "ainvs": [
    "1",
    "0",
    "0",
    "-354803089674674467206754048738095",
    "2558194545892203175112161719607326368645810580537"
  ],
  "rank_lower_bound": 21,
  "torsion": [],
  "naive_height": 236.46095027802525,
  "faltings_height": 17.5448733118206,
  "conductor": "1593562111507190066539814084004447718921281851572777685020200143306222910",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "23",
    "29",
    "89",
    "43207",
    "226549",
    "22823593909227592035983291",
    "44013936637595415741483513793"
  ],
  "discriminant": "31362810004008297563332830974145357962340308661810559854716023966067971553607881810277592152000000",
  "regulator": "351640015835560137294.39337380230310483256740118707430013952530013327207162781358",
  "points": [
    [
      "-21518735422155486",
      "-478256579137186088822007"
    ],
    [
      "-16162051516824546",
      "-2017627317695268505559667"
    ],
    [
      "1038924778080097686/49",
      "-733011743810123946757418901/343"
    ],
    [
      "-14545633423847586",
      "-2154421321999041799859307"
    ],
    [
      "-10943447218123569/4",
      "14984597983246077098605569/8"
    ],
    [
      "10125440811318864",
      "61344439585521052023093"
    ],
    [
      "789701034488124",
      "-1509469661698186222233897"
    ],
    [
      "228385634227786349/16",
      "-40580603327174753093901823/64"
    ],
    [
      "-21627184418104416",
      "340283723703987370480203"
    ],
    [
      "8007779902166814",
      "-480109043182118745601707"
    ],
    [
      "12800689418722964",
      "337581497100471707837693"
    ],
    [
      "9953363946011664",
      "113068979322481106243643"
    ],
    [
      "11790929866630764",
      "118246915756400740772493"
    ],
    [
      "945820846806594",
      "-1491127257554750266981227"
    ],
    [
      "16992684482716974",
      "-1198247797994777274230547"
    ],
    [
      "20859855244894382",
      "-2057638595340369190119955"
    ],
    [
      "13765446221801214",
      "531556029601305747519693"
    ],
    [
      "-2970309185321538",
      "-1893637547361814114859787"
    ],
    [
      "-21725671106393538",
      "109128648895082432309325"
    ],
    [
      "11620482431468214",
      "-66260339865015976889907"
    ],
    [
      "67111185729163791/4",
      "9219933694407166168945929/8"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "Rank-21 conductor record from Elkies's rank-17 K3 fibration (arXiv:2608.25406), specialized at t=3/8. Four extra independent directions were found by an exhaustive search of the 1,311 norm-4 half-lattice quartic covers using ratpoints; independence and conductor are supplied for exact server verification.",
  "created_at": "2026-08-27 23:04:27",
  "updated_at": "2026-08-27 23:04:27"
}