{
  "id": 5969,
  "curve_key": "3673867249614433979312499347969143081:-7065077107623406482033705516700983364025248863268600021",
  "ainvs": [
    "1",
    "0",
    "1",
    "-76538901033634041235677069749357148",
    "8177172578267831570049658150786264346130208149670006"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 252.58951790357122,
  "faltings_height": 18.86796568879168,
  "conductor": "1815662763075819492679731665574431988241426419467083404483983040651142994921569249869810",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "19",
    "23",
    "79",
    "54711148930777111562285234059",
    "2464825716641823703871398562214754348798891574462747"
  ],
  "discriminant": "-189828716701432934131785730945332228485587635587959637570795003883299453986144144939171150077944098687500",
  "regulator": "3225389867147631730355414.5798089736484467711063422242917815463985962299334570944012118",
  "points": [
    [
      "127501501587803315",
      "-22160615421223438777126593"
    ],
    [
      "172060455443857550",
      "-10083146169011353923098178"
    ],
    [
      "226191908839523396855/1849",
      "-2018801382308449929090437164011/79507"
    ],
    [
      "77842976495795405",
      "51873388869220968746813877"
    ],
    [
      "-144527872649418208",
      "-127358685120847847132411406"
    ],
    [
      "658812915774933320",
      "493659662631328678484765877"
    ],
    [
      "1575303139066157200/9",
      "-322598647808508557812301681/27"
    ],
    [
      "238184322053847245",
      "-58816875284474660444629323"
    ],
    [
      "265072853328584975",
      "80707900878346901943059127"
    ],
    [
      "173271463016152070",
      "10830250815043074368859627"
    ],
    [
      "157556334187039760",
      "5400194654962000396148562"
    ],
    [
      "-220995035684142085",
      "119577406477813075565947557"
    ],
    [
      "1265543988254036315/4",
      "-1000211362368390270666387429/8"
    ],
    [
      "-282532199819164565",
      "85140477675995511948378677"
    ],
    [
      "1522983502905663095",
      "1850442530297171284147952727"
    ],
    [
      "206227546451739395",
      "34110984987826957275631677"
    ],
    [
      "16059850101772194235/9",
      "63628081225768512649559752229/27"
    ],
    [
      "175650153255836770",
      "12346372010302743234461927"
    ],
    [
      "633128521450633655/4",
      "42264935839056845468028141/8"
    ],
    [
      "193938323562051605",
      "-25055316398119266976453983"
    ],
    [
      "908133447776955020",
      "-829224376404076772981564823"
    ],
    [
      "216828573202181233398245/3024121",
      "-290813243109644356460460540658069137/5258946419"
    ],
    [
      "2738493734750830037/16",
      "610477818882903552343778541/64"
    ],
    [
      "2433693202872601795/9",
      "2299465328844265453727003909/27"
    ]
  ],
  "submitter": "apkorte",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Daniel Błażewicz",
      "at": "2026-10-27 05:21:26"
    }
  ],
  "commentary": "Specialization at T = 399/62 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -2315727727754537200T^8 - 385085454700810899360T^7 - 21602016129394505916480T^6 + 522753273151467123362400T^5 - 5286101242963131414221040T^4 + 36372271295130380430902640T^3 - 119866073107198500927623880T^2 - 44611766420397375005288280T - 17644996097302241306504187,\nA6 = 1527906580671423711878454400T^12 + 405036291873933234226307839360T^11 + 29619810420503480598512683442496T^10 + 83447431068127636496045716863680T^9 + 10401708370692526999699168797492240T^8 - 680407910276562698898410450598391200T^7 + 10353906760921511571152027566046979840T^6 - 64341197016007520540432295631610298720T^5 + 151935569584040641348413346807219047840T^4 - 98223779992621049253987068203224001200T^3 + 461589258984786807406908653536129872360T^2 + 245414512415050160861358750620214278280T + 41992607521879070487127955356093746390.\nIt is a 2-neighbour of the fibration given in curve#4187 (itself a 2-neighbour of the fibration in curve#3900): its Mordell-Weil lattice (rank 17, no reducible fibres) is a root-free Kneser 2-neighbour of that fibration's, realised by the pencil |O + P - F| for a section P of height 12. Constructed and searched by Claude (Anthropic): a Mestre-Nagao sieve over the fibration, then a 2-covering point search seeded with its generic sections.",
  "created_at": "2026-10-27 05:20:23",
  "updated_at": "2026-10-27 05:21:25"
}