{
  "id": 4223,
  "curve_key": "1034679641752006243844990619443129298561:-33172617573113338796492563360620007162693107125078985973185",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-21555825869833463413437304571731860387",
    "38394233302214512501329423320027818587957829759922532195"
  ],
  "rank_lower_bound": 25,
  "torsion": [],
  "naive_height": 269.50473144208536,
  "faltings_height": 20.277549231117955,
  "conductor": "225844906993455043280757412501037785360724212266388761170205156457263736701803479546704613860962",
  "bad_primes": [
    "2",
    "7",
    "11",
    "17",
    "23",
    "41",
    "61",
    "375153763410287",
    "363410221733252303361812769117415788340837473984904761318875507501320219"
  ],
  "discriminant": "4204924587257814326043938015887585060405620797220188369386915901580497262671926319100156972114317655183522660352",
  "regulator": "261644586440324123616609946.9582890492175211076080094143524120036565483176614791957351500",
  "points": [
    [
      "1272644010324870043",
      "3608676189813566941942401714"
    ],
    [
      "1418509846090341403",
      "3266705569507858933022757682"
    ],
    [
      "838039272904286215",
      "4573638362719196687763766594"
    ],
    [
      "2419858463279571163",
      "-634182227863182671602035086"
    ],
    [
      "1470269769785137923",
      "-3143187287645142127525930638"
    ],
    [
      "-3896388589116350005",
      "7951713237557132920727940274"
    ],
    [
      "607480781632668736079/169",
      "-5958428668846297824012100808578/2197"
    ],
    [
      "-4585809883793799269",
      "-6388048628065673520996661838"
    ],
    [
      "62890173834756427971/25",
      "37019602549044033016131551466/125"
    ],
    [
      "1978708513665175691",
      "1867819479260609508917817026"
    ],
    [
      "2915125093602444507",
      "573501744872502898971183282"
    ],
    [
      "3609060915840914835",
      "2758100881165355551428446714"
    ],
    [
      "5615934486090476331",
      "9718925533112536483653878306"
    ],
    [
      "-14032560210618746139/25",
      "-886678546923591476746162066956/125"
    ],
    [
      "-112223708495899349",
      "6388418791712969944577831602"
    ],
    [
      "201876958245704807947/81",
      "-283930262723331041190483057182/729"
    ],
    [
      "2443797257736757083",
      "-557563286688102607612444686"
    ],
    [
      "2829525246665022507",
      "-235078601700900287386541790"
    ],
    [
      "2810688294137588123",
      "-108974179325904914743038286"
    ],
    [
      "6532304768138264340099/2809",
      "-136642445803854236428371967497206/148877"
    ],
    [
      "-5160221943533149353",
      "-3495891023318840572997429310"
    ],
    [
      "4717954500649975291",
      "6458500094729073752901350226"
    ],
    [
      "9813035258844124475",
      "27781628287717700740795389970"
    ],
    [
      "188336448004443907",
      "5860133619050016633367091082"
    ],
    [
      "2939879932310901275",
      "657087571856514008376962354"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 961/909 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 13:26:51",
  "updated_at": "2026-10-14 13:26:51"
}