{
  "id": 427,
  "curve_key": "1268292534356458623086766433245825:-52132690208436444302974148897973840784875739250625",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-26422761132426221314307634025955",
    "60338761815319965289688140627358385040885056547"
  ],
  "rank_lower_bound": 21,
  "torsion": [],
  "naive_height": 228.9557533338518,
  "faltings_height": 17.06635150350187,
  "conductor": "88941907505430897549881539052676922760357137113333198823829960967920984550",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "37",
    "59",
    "73",
    "94065547",
    "1014246206813831009964763804797915611922643282349422786051"
  ],
  "discriminant": "-392178934915463317587385364218533001535084788286412387772961994010848738438549615708708864000000",
  "regulator": "382976288406273024674.48720510987172495067877611909979688105031901971683460956387",
  "points": [
    [
      "3970269019018939",
      "-134226622675063174573870"
    ],
    [
      "-5757989916959461",
      "146893765090808635810930"
    ],
    [
      "62634285181819",
      "-242247882946572957564910"
    ],
    [
      "1072849867984219",
      "-182279904964035407808910"
    ],
    [
      "9855100990107919",
      "-870113163592952809345810"
    ],
    [
      "83087503181307781/49",
      "-49002387210887323746704830/343"
    ],
    [
      "-2925741177921125",
      "335560264944516901694066"
    ],
    [
      "10660643972903899",
      "995103083101124930620850"
    ],
    [
      "4933685926223899",
      "223761641424416324020850"
    ],
    [
      "160872432696326299",
      "64491693079603774024219250"
    ],
    [
      "242505353506819",
      "-232261409413411107801910"
    ],
    [
      "6937576609184923",
      "-459275716753607799453454"
    ],
    [
      "6779609048639899",
      "-439106610303357658699150"
    ],
    [
      "1088327420659739",
      "-181304228057016689513870"
    ],
    [
      "-3744970816831205",
      "326754864737302521984626"
    ],
    [
      "5381533202006299",
      "-272025439503167657265550"
    ],
    [
      "5671410923746555",
      "304802886745993796283506"
    ],
    [
      "413099419529490499/121",
      "-132588981603691868443259210/1331"
    ],
    [
      "-3604746457565201",
      "-329765567531018289272050"
    ],
    [
      "-3058153940302565",
      "335474058501157034757746"
    ],
    [
      "3480589307627419",
      "-102652755326944083572110"
    ]
  ],
  "submitter": "Bhavik Mehta",
  "history": [],
  "commentary": "Found by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at t = -17. The 4 points beyond the seventeen generic sections came from searching the 1311 norm-4 quartic covers of the Mordell-Weil lattice; the claimed lower bound is rank >= 21.",
  "created_at": "2026-08-30 01:39:33",
  "updated_at": "2026-08-30 01:39:33"
}