{
  "id": 439,
  "curve_key": "3997649423357404379381988980131702081:-11511791491249191109208393817634001565033894938729303521",
  "ainvs": [
    "1",
    "0",
    "0",
    "-83284362986612591237124770419410460",
    "13323832744501378591680462595599415504584388273763600"
  ],
  "rank_lower_bound": 21,
  "torsion": [],
  "naive_height": 253.56593375760713,
  "faltings_height": 19.15618427964129,
  "conductor": "4479899643408242486142354247621158610090019978552603894717305621336633370665189642410",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "17",
    "19",
    "29",
    "1145843",
    "23115300343175592012955584317",
    "46299734573614272920775317733182071773759047"
  ],
  "discriminant": "-39718810606077930167476934805655304641592918506960890175061918369101870306860126560331166758723567360000000",
  "regulator": "11804621917922556586224.516047569157520774637925201678865666370015413517068129017",
  "points": [
    [
      "329798104056396770",
      "147403828399081166378066990"
    ],
    [
      "424928882919214520",
      "-233796912715477087246295260"
    ],
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      "24476695543403690",
      "-106301321488297860080019280"
    ],
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      "-152374516666820680",
      "-149921368610676511470148060"
    ],
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      "43470204711521720",
      "-98922132462493294323594460"
    ],
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      "192955439915201966",
      "-66616368506507756325344398"
    ],
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      "101424898593814460",
      "76942079631161937961470740"
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      "-11662518825397480",
      "119555643644393067208440740"
    ],
    [
      "2925049295655794120",
      "4979576424018922912674159140"
    ],
    [
      "-258382605425594440",
      "-132638737960657090307470300"
    ],
    [
      "1373414583542027000",
      "-1577836281627999080523318940"
    ],
    [
      "67490324139288387980/1849",
      "8081800470536829881179691405180/79507"
    ],
    [
      "1973813411064263624/25",
      "-10636370328559798070548768892/125"
    ],
    [
      "-109196171190889690",
      "145313910542961325479542240"
    ],
    [
      "279542233094883800",
      "109026808874265836016048260"
    ],
    [
      "4238657985224151920",
      "8707064841694210311608184740"
    ],
    [
      "205346435383761620",
      "-69861014805627787403608360"
    ],
    [
      "415172138240621192",
      "224296315195107401444458532"
    ],
    [
      "110837536643613080",
      "-73854138477841865377696060"
    ],
    [
      "118352924598540920",
      "71587033087488666961824740"
    ],
    [
      "-27181594296393808",
      "-124769995123970045786416468"
    ]
  ],
  "submitter": "Bhavik Mehta",
  "history": [],
  "commentary": "Found by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at t = -15/19. 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 04:30:19",
  "updated_at": "2026-08-30 04:30:19"
}