{
  "id": 4231,
  "curve_key": "5870958504794417175529672096107841:-440870095406207744296252002095383181361680081553889",
  "ainvs": [
    "1",
    "0",
    "0",
    "-122311635516550357823534835335580",
    "510266314127555249409507227897867382022189742352"
  ],
  "rank_lower_bound": 22,
  "torsion": [],
  "naive_height": 233.26597793410417,
  "faltings_height": 17.334842059001286,
  "conductor": "90380223496560423965098889851226608711351320575453620625770728236549747310",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "17",
    "23",
    "41",
    "67",
    "73",
    "2179",
    "7963",
    "32707",
    "782367097",
    "2825273783",
    "417202551611",
    "434424634862545998787"
  ],
  "discriminant": "4626539043874319346593179481752922544446502769117791674117871396787367068409272295717697792000000",
  "regulator": "561786777273619703513.5206574155350600119056366180074795829726245215714345875612769",
  "points": [
    [
      "2008118142453944",
      "-522252730516739578388572"
    ],
    [
      "2891059597236744",
      "-425229603819768186484572"
    ],
    [
      "572448999045573144",
      "-433036722794298858483498972"
    ],
    [
      "-6147556390599336",
      "-1014816618679682224562652"
    ],
    [
      "11880658462894704",
      "-856784126513825066591892"
    ],
    [
      "5629181909297544",
      "-11297509933343049767772"
    ],
    [
      "-8880734812440936",
      "-946616389701893828748252"
    ],
    [
      "8540241019356294",
      "297630751221815301885978"
    ],
    [
      "5420654642352444",
      "80839142055463720129428"
    ],
    [
      "-12520993595766486",
      "-280619370182162001395802"
    ],
    [
      "-8654375966403816",
      "959478929948960415921348"
    ],
    [
      "17841496554718254",
      "2001831907096151916379488"
    ],
    [
      "20949118731496944",
      "2672413204283040428507628"
    ],
    [
      "8292868135044264",
      "-257422561462507045189212"
    ],
    [
      "140657036367128634/25",
      "-1797607041813274189071762/125"
    ],
    [
      "-551046235522536",
      "759933125078994524456388"
    ],
    [
      "-429221723440356",
      "750124022660156275163028"
    ],
    [
      "-323194190332900344/49",
      "-348117440868831067621961796/343"
    ],
    [
      "-1732211372712456",
      "-846722103806624992607772"
    ],
    [
      "-318578087513608776/121",
      "-1200888483627883398642066132/1331"
    ],
    [
      "-11258015062782006",
      "678512375685649647996678"
    ],
    [
      "79995498491672601444/10201",
      "-188162215190407269058098481272/1030301"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 50/61 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -10669947921935414766592T^8 + 11909462495223346810112T^7 + 29290850738695015599056T^6 + 749826724411797003953776T^5 - 2800296645908250177432680T^4 + 5291011042236720751525024T^3 - 9053743075112346775820704T^2 - 1373686135035664689321352T - 153062929487822447776267,\nA6 = 424084459520579325699737587892224T^12 - 702971076900016054991835746922496T^11 - 1428460164091780099364248773693184T^10 - 45531551300070380060674898437602560T^9 + 178145138683306119166957105019549520T^8 - 224307849011465835658368095576866752T^7 + 1890363249575504635685922631864051728T^6 - 8402714629932209203714457518206796848T^5 + 10932033646871752694840038266436614840T^4 - 1045636958253350245306227479236779680T^3 + 3911537622199302231442442603656239344T^2 + 397823992391227625022128206594583384T + 16543056563137220502197778370669126.\nIt is a 2-neighbour of the fibration given in curve#4205 (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 19:37:53",
  "updated_at": "2026-10-14 19:37:53"
}