{
  "id": 607,
  "curve_key": "39881120247808063691861413350051013364310736:-251346197826431230349268920067375055143449126580726783346734625984",
  "ainvs": [
    "0",
    "1",
    "0",
    "-830856671829334660247112778126062778423140",
    "290909951187999109200265779335518757825576340394243607947394400"
  ],
  "rank_lower_bound": 23,
  "torsion": [],
  "naive_height": 301.18343082274686,
  "faltings_height": 22.898418015143104,
  "conductor": "30850735333146160393655147247586815539031998716975145138749640447746073755426064682136055267761829160",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "37",
    "47",
    "67",
    "103",
    "10141",
    "152151799",
    "1238346295113173",
    "1035343180402295367665723832883252361400522861121753731089879"
  ],
  "discriminant": "148240876780830806794728997651430140140180140071341641121381593487446266320743344635443446881389656011769841682992221380000000",
  "regulator": "17672199467394920619640243.5627574016023183012566686329374987157758203187867877097486",
  "points": [
    [
      "504656244572404018908",
      "371145125927674321124470621416"
    ],
    [
      "548618321122343062950",
      "-459382723665638824449378104670"
    ],
    [
      "2153535977123291626770",
      "-92136426394528380828543029090550"
    ],
    [
      "186030903017223152130",
      "11949183994941765503746397150490"
    ],
    [
      "-561688998977060049030",
      "24091143514991144910715723026750"
    ],
    [
      "1270544443189769540970",
      "-35864859549228223769440161863250"
    ],
    [
      "79332039964713783270",
      "15016513524907494782669848020450"
    ],
    [
      "2998765899105493924205/4",
      "-75632105514975639540182512510725/8"
    ],
    [
      "1360516349970382737855",
      "40973626582645710089745887888610"
    ],
    [
      "1771137644821035136095",
      "66145904472642630306112353980250"
    ],
    [
      "1732040641035850815030",
      "-63623056773077661238922387439090"
    ],
    [
      "16950911503675301000021210/19321",
      "-41367577756200176652266657468870655510/2685619"
    ],
    [
      "1199050607024022272970",
      "31915084534094569973137808267250"
    ],
    [
      "11088866342341872638530/9",
      "-910669644657168629253997792560850/27"
    ],
    [
      "18835191593260255877736/25",
      "-1202781715135435100480878338794784/125"
    ],
    [
      "-473203544661046560030",
      "24043996778287393742179556247750"
    ],
    [
      "4565736311935291581720",
      "-302778036744886510482016079829000"
    ],
    [
      "-893749504337131779160",
      "-17876553163036370281912515526080"
    ],
    [
      "288667423275522610470",
      "8667354270921298760628840054750"
    ],
    [
      "-1031402285398826763630",
      "7117674386056303993386153708150"
    ],
    [
      "2613123393960944685270",
      "-126345822953294533048652201741550"
    ],
    [
      "1964521219587948433470",
      "-78996435542742080277909875144250"
    ],
    [
      "546265184353792173720",
      "-224714225882098796209587039000"
    ]
  ],
  "submitter": "Bhavik Mehta",
  "history": [],
  "commentary": "Found by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at t = -1335/338. 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 15:46:44",
  "updated_at": "2026-09-06 15:46:44"
}