{
  "id": 4208,
  "curve_key": "6931765691608470900338005816210258021681:-574076429741478368653403743945586046292750504061008458298921",
  "ainvs": [
    "1",
    "0",
    "0",
    "-144411785241843143757041787837713708785",
    "664440312200785148892368165981682106414633675158209573225"
  ],
  "rank_lower_bound": 25,
  "torsion": [],
  "naive_height": 275.21079959121045,
  "faltings_height": 20.772273949694796,
  "conductor": "863147432773276692280622020482356041379384990774069866239356534650083835203112312990133085330",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "31",
    "61",
    "52452600344437098527",
    "82239645115100520642843359",
    "45807144898958519315103658828515673779361"
  ],
  "discriminant": "2027353082094439742535445592333122824694671927678035010023665980654437494687808362129147158280051198221219840000000",
  "regulator": "93370544687827192244336032.67233129867816260691267172826172787770717691283962017220191176",
  "points": [
    [
      "6518504828838445670",
      "-261846355093603520235621085"
    ],
    [
      "6521403228909248522",
      "140112866095844676854878907"
    ],
    [
      "1100694534711209551130/169",
      "-886055472937333979616345528745/2197"
    ],
    [
      "7444408190697983270",
      "-1394016071811700548542094685"
    ],
    [
      "7906716430888042820",
      "-4112768389225964087508394735"
    ],
    [
      "24670103763709899722",
      "110074327621000100661647710907"
    ],
    [
      "17128123375728143810",
      "56708550521470270934247072275"
    ],
    [
      "-13505709575677739830",
      "-12301459745021616605812638085"
    ],
    [
      "527021466422190417970/81",
      "-382855189220759159973544281965/729"
    ],
    [
      "6409576756331062940",
      "1464391947233102061475641545"
    ],
    [
      "245487414263358890",
      "25079948774216185597315575515"
    ],
    [
      "-10266831504664286710",
      "-32632611864906668562138524485"
    ],
    [
      "9693830276783967170",
      "-13246492212127289256759600085"
    ],
    [
      "5468080180246888970",
      "-6187095185178737236577334085"
    ],
    [
      "5535507373108609970",
      "-5887779878972538032777485885"
    ],
    [
      "7371554771905528970",
      "685481726803210986879065915"
    ],
    [
      "1237788308881452170",
      "-22081339019364814896683910085"
    ],
    [
      "-5877265521707800630",
      "36196308426441596696451670715"
    ],
    [
      "2035455418969608170",
      "19466114492783500358718737915"
    ],
    [
      "7421226453928034282",
      "1203679855833546483876015611"
    ],
    [
      "6191054726626323242",
      "2770733706722989827175836251"
    ],
    [
      "7348228367868820820",
      "218758868182483881263853515"
    ],
    [
      "41903494902381703370",
      "-261135117149177066561721630085"
    ],
    [
      "3758793486003192710",
      "-13218640450619903093512612585"
    ],
    [
      "7368528353609485730",
      "643251986445568762955323115"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -6/1891 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -26975048530559638402192T^8 - 312966956619947949551760T^7 - 842243888708948190021348T^6 + 562167338991061514848920T^5 - 461942736201433628752680T^4 + 1431271445622423050083968T^3 + 603334350434130915358656T^2 - 986867998885806893128512T - 418274582761882236107952,\nA6 = 1451452485240104576307296743782976T^12 + 24581324346135835035118126720145920T^11 + 152392747348176550954751684612771616T^10 + 397210221029004103236543130531121600T^9 + 10829685735288357984444464355358836T^8 - 1893933432491868927718338035329167456T^7 + 859289861319319080984756807841283568T^6 + 1744608022036113544067265254248327200T^5 - 669413043714196611286442553109280544T^4 - 1068656424150865477675382650153889280T^3 + 65017381339639250150552216405922816T^2 + 368098108547413859417253532055609088T + 103576617923784908883415898755916160.\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 00:18:47",
  "updated_at": "2026-10-14 00:18:47"
}