{
  "id": 4274,
  "curve_key": "69885594012627498671119117333621507201:-584830964920452933876548153864430891796597158262523469505",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1455949875263072888981648277783781400",
    "676887690880153858532083058848946346979072317432975936"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "naive_height": 261.4218357566053,
  "faltings_height": 19.559750730373437,
  "conductor": "5500829082348913334217047404382743088488241899479066241289896407758721932164790308655994186",
  "bad_primes": [
    "2",
    "3",
    "17",
    "19",
    "23",
    "59",
    "83",
    "251269642339847",
    "942198604500147520764311",
    "106447130856764071772177688995129232648180811"
  ],
  "discriminant": "-408725930731533853382497009861051123524424125397615167055338039840094902916176546130077216123842160699998208",
  "regulator": "12514726908117829930387793.052267157394625951682399992759399364657924414320962207963398",
  "points": [
    [
      "695635339761463408",
      "-26483515431820779728459096"
    ],
    [
      "764434110277975066",
      "-103025651002432241060107772"
    ],
    [
      "-1180925369321652560",
      "865653135618883438334872936"
    ],
    [
      "-712249781820870032",
      "1162997650572810649008510184"
    ],
    [
      "728099626688072548",
      "-52895232235642725757438172"
    ],
    [
      "666502832526304144",
      "-50703840973414317574551320"
    ],
    [
      "-656117537491155440",
      "-1161770094276406898062073624"
    ],
    [
      "-2182102455238917501/4",
      "9152217489413579790111443703/8"
    ],
    [
      "751289945011676008",
      "-84277621446844084554942296"
    ],
    [
      "717054993205049200",
      "39726523239745884361554856"
    ],
    [
      "698596276414543648",
      "26593060068359888297319928"
    ],
    [
      "635346882079646200",
      "-91226071219683572740106144"
    ],
    [
      "707781622800015520",
      "-30979749301103414835098504"
    ],
    [
      "658936198169788336",
      "60147141149661785736842728"
    ],
    [
      "12414194722011054064/25",
      "34540137838369775896240921928/125"
    ],
    [
      "-511415056363904346901904/395641",
      "-157208258707076968876081129248983608/248858189"
    ],
    [
      "13576932321644246086/25",
      "-26915887529463567672983442556/125"
    ],
    [
      "271791311963495140",
      "-548862941980686041451619976"
    ],
    [
      "709715720191429762",
      "32533556992829676774908164"
    ],
    [
      "31703839565242043920",
      "-178384716599488609484264468216"
    ],
    [
      "83695593328297596592/289",
      "-2597522444197128307934866031896/4913"
    ],
    [
      "29479361345436948880/49",
      "-46921592741224986778008867272/343"
    ],
    [
      "-1165515581604181088",
      "-889130260747057664867163416"
    ],
    [
      "7060187998740983920",
      "18501933306410795273496111784"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 605/1052 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -25598589065575488253872T^8 - 219912513106757586234048T^7 - 324549648424331055742464T^6 + 1523547434916270832355136T^5 - 2849165156820063127691880T^4 + 3746564993881929295112904T^3 - 973581348748449447744444T^2 - 862126587120769476566112T - 118556909623229874930432,\nA6 = 1625048868702522016795790220948864T^12 + 18521876511799709835187838396715264T^11 + 69457772033476867393403462775818496T^10 + 74100738882710387630246485913752320T^9 - 324420440712638126863027033199077920T^8 - 1791949805594601002560679464033967520T^7 + 4689003940396889037978292829416265040T^6 - 2864400878761409044683373393741992480T^5 - 91393345783003551423720760724759820T^4 - 338626380479684457921000808774737600T^3 + 374448354510478802333765563563322320T^2 + 177989462843015858245005305484080640T + 17806843321561611911434592141844480.\nIt is a 2-neighbour of the fibration given 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": "2026-10-16 04:26:21",
  "updated_at": "2026-10-16 04:26:21"
}