{
  "id": 4225,
  "curve_key": "57937279998600203455971456814419825:-14490624414657208325805078213927015848590855106495625",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-1207026666637504238666072016967080",
    "16771556035482880308475507184754550232016679133547"
  ],
  "rank_lower_bound": 23,
  "torsion": [],
  "naive_height": 240.21068318179886,
  "faltings_height": 17.942744037862425,
  "conductor": "432634656575362589579070369184686409693027916184207096152588384540341013487139150",
  "bad_primes": [
    "2",
    "5",
    "7",
    "13",
    "23",
    "29",
    "151",
    "23509",
    "175294403",
    "587530212168689",
    "389919287788835426706086699226136196124383663"
  ],
  "discriminant": "-8969028904260421044394593515425750923399144281146323244274051703131292140928254003846697826304000000",
  "regulator": "65499564227554616205782.2181839134614846617048236024388628859986680173578326625109246",
  "points": [
    [
      "17004825668196269",
      "1078639428254540867167865"
    ],
    [
      "17700365641176665",
      "-975868524389178964106527"
    ],
    [
      "102472574450902349",
      "-31130545554285624043451975"
    ],
    [
      "21824230955068669",
      "907713745868819464965865"
    ],
    [
      "44522189580945749",
      "7161361541751478417893025"
    ],
    [
      "87981914423836269",
      "24323382972850911770831865"
    ],
    [
      "19848813471369485",
      "795897613096317262279993"
    ],
    [
      "34197468676509013",
      "3935366021431245392796321"
    ],
    [
      "66203642599144289",
      "-15067428979061276511505295"
    ],
    [
      "10355260681186454349",
      "33322617900744033461371229625"
    ],
    [
      "16472368076479099",
      "1165574058165964330096275"
    ],
    [
      "22182507497877539",
      "954925803746689922945755"
    ],
    [
      "20024886861791869",
      "-794282710200824353378535"
    ],
    [
      "-37286019294254611",
      "-3152775012253100739013895"
    ],
    [
      "50131629246674669",
      "-9069242731171508992066535"
    ],
    [
      "9624390279919484141/289",
      "-18057309283150806554963744855/4913"
    ],
    [
      "-3463652833636211",
      "-4572824541623819819895495"
    ],
    [
      "1484089323894909409/81",
      "-654888624363616554339304555/729"
    ],
    [
      "5861000163903669",
      "-3146189071272752746929535"
    ],
    [
      "21336181796212249",
      "-855068604925835612239775"
    ],
    [
      "4229397145339556899/121",
      "-5533914724475629864114590135/1331"
    ],
    [
      "-253714308232866059/9",
      "143875182550265553120227075/27"
    ],
    [
      "30879840773990349",
      "2990766898340767132060025"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 243/47 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -48788204994959095721152T^8 + 292967918358775673142176T^7 - 257383034328976566251548T^6 - 697546673797396881668416T^5 + 120168749817393327515900T^4 - 1757567929634520292525024T^3 - 413537200758726229861444T^2 + 1707114327506779370979968T - 562162388405818919328652,\nA6 = 4093740998135849949800603694210304T^12 - 39254200079660475614530561864102528T^11 + 106574491886043297526892628627228560T^10 + 93605566178607331448553679365937280T^9 - 784525015208748993169852391016411996T^8 + 155163719535379155266150397777650688T^7 + 2578710394897183836702469318351911360T^6 - 11129400918516684422195231027746944T^5 - 2571149805127224053198426441759406936T^4 + 885351238544731577742776581975479680T^3 + 1010399979603017167929810575585795728T^2 - 806575307806361814743442724032893696T + 165741056816888627629082643287877460.\nIt is a 2-neighbour of the fibration given in curve#4191 (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": "2026-10-14 13:47:08",
  "updated_at": "2026-10-14 13:47:08"
}