{
  "id": 5736,
  "curve_key": "379385251261422566369777679825:-229279642030998178102784430082657767601568025",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-7903859401279636799370368330",
    "265369956054398015435665632504868555093897"
  ],
  "rank_lower_bound": 21,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 204.3250490812045,
  "faltings_height": 14.920448135569657,
  "conductor": "295467857760801570733226526810048978697727929518698431717750472646806905950",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "37",
    "1365062867917771174558681112543538825122328156704543459079466263094511"
  ],
  "discriminant": "1178800456316783615727333244011142989725919013066548182851100279274725771542318080000",
  "regulator": "844932653463054376097.48939975356902421880771838009177704096893619658343093646968",
  "points": [
    [
      "57906197130709",
      "43062566306094027755"
    ],
    [
      "44292688044169",
      "46712314907333025455"
    ],
    [
      "4829039171939",
      "476775123563452536445"
    ],
    [
      "87426423992743",
      "-492541554216824008015"
    ],
    [
      "-14953928463671",
      "-616619572974767161105"
    ],
    [
      "45461619477329",
      "-2431429052951153225"
    ],
    [
      "147111183849713",
      "1512071356941457670615"
    ],
    [
      "57074793168319",
      "-13482665592844282825"
    ],
    [
      "57215168094433",
      "-21153799745944623529"
    ],
    [
      "73903934622433",
      "-291361553675964398905"
    ],
    [
      "94760688440449",
      "-606058415550290796265"
    ],
    [
      "116649848623729",
      "-964708448748215759305"
    ],
    [
      "1543566000095881/25",
      "14107417411487707532539/125"
    ],
    [
      "28745201993929",
      "-248844739729115717905"
    ],
    [
      "-2107311012451",
      "-531052244916317547985"
    ],
    [
      "58476711857569",
      "-56043529435432410745"
    ],
    [
      "1677173512529",
      "-502114061744697917705"
    ],
    [
      "-31682054708111",
      "-695686348495983510985"
    ],
    [
      "38774999324053",
      "131133678790672160171"
    ],
    [
      "-99673783710431",
      "-250862714990753752825"
    ],
    [
      "354951087214141/9",
      "3306193700913260743945/27"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 86/83 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -4765105671341170713012T^8 + 114715794415427693698302T^7 - 1289703173484205490556069T^6 + 1970946774680673720492576T^5 - 1710136570699445082168780T^4 - 705937567588433468644896T^3 + 1908320361802866590386896T^2 + 127404060867858778875648T - 648856125950076308077632,\nA6 = 96897205978949562584426677136484T^12 - 5182597562294583468083790262057896T^11 + 84877162983356922665937799396845291T^10 - 478870362976518748392317900380853010T^9 + 1861233683275843787028761356431736485T^8 - 1364843279709253439363789384039551872T^7 - 1311792976812619745745993240617168352T^6 + 735145326496711370457296224143481152T^5 + 1094740667609718961081479717092760480T^4 + 53782848467549070290540339428638720T^3 - 759905051149062814344760081603028736T^2 - 65476590517227188924250720852312576T + 200491211946380337902432377627289856.\nIt is a 2-neighbour of the fibration given 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": "2026-10-24 17:50:25",
  "updated_at": "2026-10-24 17:50:25"
}