{
  "id": 4260,
  "curve_key": "1421976309354013494962280247530685724619136:-1690741613903209643517012357975962115333449600099594829332959840",
  "ainvs": [
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    "1",
    "0",
    "-29624506444875281145047505156889285929565",
    "1956876867943529679986667245509071799032032313211123512714404"
  ],
  "rank_lower_bound": 26,
  "torsion": [],
  "naive_height": 291.18186473071074,
  "faltings_height": 22.079025795944553,
  "conductor": "4886783027910672419795090416419690625331967682390524060138371237024089995718528240155263527122564282137268",
  "bad_primes": [
    "2",
    "3",
    "7",
    "17",
    "19",
    "53",
    "193",
    "19053677491",
    "98063700001362749",
    "2684220103476677117874079",
    "3510773890401645166283691045154686287893234271"
  ],
  "discriminant": "9636881933818402648783263637967977915169408963573305335816523555453964261278867945723818143510532247613503906400924361552",
  "regulator": "88194201700180040915486499051.1163640391738168489234898881755818253483109700788060636398885",
  "points": [
    [
      "90829701228403989647",
      "124257710630847592898882337441"
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    [
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      "-411234111774782959054547564127"
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      "849473790054888256121",
      "-24285320277589204635166518392829"
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    [
      "-157621364256347471023",
      "1646301575222467612733870960931"
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    [
      "63857764810198878644",
      "570545526844000432167937131708"
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    [
      "94813063219603150841",
      "-20255989281505732231585939971"
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      "80357879445615256064",
      "-308571580431511063318021826022"
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      "415279269398015545890361103991"
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      "475001008101442711309128421917"
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      "-166550576326468997972294199879"
    ],
    [
      "488631603808501832789",
      "10205268297288461884614016954797"
    ],
    [
      "34388011827212712698081/64",
      "-6083199322619996950050195276351759/512"
    ],
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      "83677264583454036788",
      "-252740489320694985931310709300"
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    [
      "485032727434514065775",
      "-10084405941794426322935476722273"
    ],
    [
      "15943256345579691725483/169",
      "91481056921740714399834635919987/2197"
    ],
    [
      "118626115327449467897",
      "-334607023276474951946231149059"
    ],
    [
      "976358315603888844233/16",
      "-39262298315884005293675075371725/64"
    ],
    [
      "76017004857848338325",
      "379712185376585809836200857773"
    ],
    [
      "364579328652732464909083991/4713241",
      "3663486896018276853723974376247293028131/10232446211"
    ],
    [
      "208101934272216893619668/169",
      "-94050614094934858557943220685627948/2197"
    ],
    [
      "780532836961816048529",
      "21315702553388941379476153526307"
    ],
    [
      "92104444997353137863",
      "98342375642441753195160383535"
    ],
    [
      "83564466989298807713",
      "-254662783498086565275890576355"
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    [
      "94672450082350951697",
      "-28096058696792610050211418659"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 458/1105 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -1104083919542990740672T^8 - 10725368859924614083328T^7 + 27233182276536009979376T^6 + 206542082020468176713536T^5 - 397181427596358623750980T^4 + 4843779804480200729063344T^3 - 16606432570794981193216279T^2 - 25584496459329575271150212T - 11348709459926316525508132,\nA6 = 12350516786472668766297337795840T^12 + 221799272750803971404191627025920T^11 + 569212223298482978503626062159360T^10 - 11869075609185296079185311651020800T^9 - 53903362742072871161532361492760160T^8 + 383972047913208585082616093455327680T^7 + 1230371364926344316718891951621143520T^6 - 7765129801662673724018170759694598720T^5 - 1399242604874728526040920920131327735T^4 + 17367237161504277326036112974588085430T^3 + 57428692355319025444778734345548537226T^2 + 49825188772368199520084299618572523256T + 14830879968852803906439396097627134769.\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": "2026-10-15 20:57:27",
  "updated_at": "2026-10-15 20:57:27"
}