{
  "id": 600,
  "curve_key": "12833430397115245567535999636808258021841:-1448544095739318404851992679926671628284551767516732980718361",
  "ainvs": [
    "1",
    "0",
    "0",
    "-267363133273234282656999992433505375455",
    "1676555666364951857445303859179396712885703435256389576025"
  ],
  "rank_lower_bound": 23,
  "torsion": [],
  "naive_height": 277.0586164283292,
  "faltings_height": 20.91111291140009,
  "conductor": "228001852874781479760816970618209987557663751437348824206835929566733219877581322524771870",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "73",
    "1709",
    "3314683491850541",
    "17410932364273432099",
    "4771574992486411657388928663090308317459423"
  ],
  "discriminant": "8881171505845574880320624088491350678064646227084932972708101647246459807244607224779794011557733857450397696000000",
  "regulator": "852515066835138080736132.952866188449696683482796215903373554294354789551981497515062",
  "points": [
    [
      "5274144479892974310",
      "20326156549867454601635704845"
    ],
    [
      "-18063643653731137110",
      "-24739187830301371417800989355"
    ],
    [
      "16007500505497530150",
      "38710505857333175175918296205"
    ],
    [
      "12722882135809060710",
      "-18286633763407101533044125555"
    ],
    [
      "24503850479942519310",
      "99187646730311960646952510845"
    ],
    [
      "-15015532175124588690",
      "48017291875482051281736421845"
    ],
    [
      "10364605141976808360",
      "-4342865398751400163825018155"
    ],
    [
      "4745750367116116710",
      "22684828930721846721950738445"
    ],
    [
      "4685453327651317560",
      "-22949948944855114696287639405"
    ],
    [
      "10003371778091249910",
      "1742044486325572801280329245"
    ],
    [
      "-13783374406172250",
      "-40990740782695233939348697395"
    ],
    [
      "30703415650923251830/9",
      "765654823124791742937868000895/27"
    ],
    [
      "4473664910399593260",
      "23874611753709251425594975095"
    ],
    [
      "20921560930903431150",
      "72391393339869252977857910205"
    ],
    [
      "10570006271552686310",
      "5608918424495036705490456845"
    ],
    [
      "37690208379725880330",
      "-212462884087850060697895862175"
    ],
    [
      "15280012238821485207030/1369",
      "-461095811273208270915286542147015/50653"
    ],
    [
      "18052647267607397366310/961",
      "-1706984017961632282770721843282605/29791"
    ],
    [
      "14918185821122049510",
      "31749942579900791581665381645"
    ],
    [
      "16270794333695552310",
      "-40420970275931139941445301155"
    ],
    [
      "8310887794442798280",
      "5345165931146410845471955875"
    ],
    [
      "10055506774400062470",
      "2197385238335067264272106285"
    ],
    [
      "12936914509935444435/4",
      "-232643653036143524536290487965/8"
    ]
  ],
  "submitter": "Bhavik Mehta",
  "history": [],
  "commentary": "Found by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at t = 28/117. The 6 points beyond the seventeen generic sections come from the surface's rational quadratic sections: writing x_tau = a/c^2 and y_tau = b/c^3 for a trace of height 10, the slope of the bisection is forced to be kappa/c with kappa = -b*a^(-1) mod c^2 of degree 5, so each section's point on this fibre is obtained by one polynomial evaluation and one square test rather than by any search. Claimed lower bound: rank >= 23.",
  "created_at": "2026-09-06 15:45:21",
  "updated_at": "2026-09-06 15:45:21"
}