{
  "id": 4224,
  "curve_key": "71724979687900303034433102182062412161:-579633347210469793418092641179979701256714990939141771841",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1494270410164589646550689628792966920",
    "670871929641747445961232837555705146649381177854222400"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "naive_height": 261.4977072793767,
  "faltings_height": 19.726667940698608,
  "conductor": "1328015877675620242749067797948989434490391236328754978415175391077627125050756249555470",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19",
    "31",
    "53",
    "67",
    "232581224851787196031785080513655419432376166086234580579404532365359209088201"
  ],
  "discriminant": "19104388610819094744447973669190338515360068700909657468335218120407525920135618101876177483003332441600000000",
  "regulator": "2329259452135505285434879.4983795804048994361071904624381311560877669236424111280792975",
  "points": [
    [
      "1267015010591339640",
      "-900878651145691673543273520"
    ],
    [
      "16688542625836457760",
      "67997185304342941529932648680"
    ],
    [
      "127902420059191740",
      "694149470414175740829208380"
    ],
    [
      "222799888263979020240",
      "3325568742213022781725639565880"
    ],
    [
      "888591416928085800",
      "211431187924536862306190520"
    ],
    [
      "541799005995831240",
      "-142550784195979466329314120"
    ],
    [
      "897898411362337776",
      "230377857774505116253314552"
    ],
    [
      "-242040039575225760",
      "1009141058178345884844179880"
    ],
    [
      "487063929302038970640/361",
      "7229125277638777775309600266920/6859"
    ],
    [
      "1034367275607791040",
      "481594500801314800851097080"
    ],
    [
      "2683835840429292600",
      "-3999012057188668779263374320"
    ],
    [
      "550751298937878240",
      "-122304112356752762690364120"
    ],
    [
      "14488672876910714539440/11881",
      "-1053817765695704466748014070929480/1295029"
    ],
    [
      "-1098576195623541360",
      "-993279192338452343360672520"
    ],
    [
      "319635338092863120",
      "-475296124023075436629237000"
    ],
    [
      "1390441625610348240",
      "1131969857265142966553645880"
    ],
    [
      "934689923286175440",
      "301296944115390244346669880"
    ],
    [
      "1806646572917407440",
      "-1966747811864034781210117320"
    ],
    [
      "-51403930834645477980/49",
      "-357104488823679315414605637960/343"
    ],
    [
      "826067610485828640",
      "14209744854954133322363880"
    ],
    [
      "862978154402529990",
      "-155035632993137098000534620"
    ],
    [
      "2322942419139758952660/2809",
      "-3937856709391309965111343585740/148877"
    ],
    [
      "174771319116900240",
      "644247399074367803588165880"
    ],
    [
      "-675456903728248680",
      "1171330596755438589059023800"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 307/19 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 13:42:04",
  "updated_at": "2026-10-14 13:42:04"
}