{
  "id": 4276,
  "curve_key": "314390646507007314751135397093094261625:-6883659525850710209994988746003322611717303099148798552525",
  "ainvs": [
    "1",
    "0",
    "1",
    "-6549805135562652390648654106106130451",
    "7967198525290173853615049509540291249526157411468931898"
  ],
  "rank_lower_bound": 25,
  "torsion": [],
  "naive_height": 266.35300143804034,
  "faltings_height": 20.19987378908999,
  "conductor": "26976009553634069537301594434056775454262504651639756129924480206364431273292626306665719285050",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "43",
    "61",
    "73",
    "89",
    "101",
    "3948210856508020405740130399",
    "185062123304701313626594575556403822101399862455505701"
  ],
  "discriminant": "-9438618116657891653374869872278198630193924973163805731183384978513795370133670941362839957752576147240677057500",
  "regulator": "162557287250877821015725031.0001738248656792595605405710156566359589904126634855783639839",
  "points": [
    [
      "1663744331937481033",
      "-1294340323609095414100531846"
    ],
    [
      "16728807864203049217",
      "67675727133322107851488122956"
    ],
    [
      "-161780403085327853",
      "3003763369278011652430300166"
    ],
    [
      "7884553925325979027",
      "-21130016304508404921694374154"
    ],
    [
      "900276279036872197",
      "1673390537828720275528781516"
    ],
    [
      "5516883123394890283/4",
      "-9983005886215585540125696917/8"
    ],
    [
      "4859442717289890772",
      "-9533654485541827201839156334"
    ],
    [
      "413927854296865537",
      "-2308023525536281038942758734"
    ],
    [
      "2311576914412639762",
      "2275625656873806000398062841"
    ],
    [
      "4152452492619897952",
      "7236684869078707078611075446"
    ],
    [
      "-2253381261564782318",
      "-3359218890776460142918692364"
    ],
    [
      "15905995135817423932",
      "-62673867252513812663804784694"
    ],
    [
      "-1774201043652296462",
      "-3742066072079766472378608391"
    ],
    [
      "28959138611523305437",
      "155255732221698938485343075996"
    ],
    [
      "14238603967807636357",
      "52928356969229102261329356236"
    ],
    [
      "1789023257053659688",
      "-1405489305218087922298571698"
    ],
    [
      "-2951607003313958933",
      "-1259085593637378926406815974"
    ],
    [
      "469387041416085768922/49",
      "9847488797733619596975542335007/343"
    ],
    [
      "707367508053490743451/625",
      "22118978529318758228172988723874/15625"
    ],
    [
      "1075444440949620121",
      "-1472102353051999192548147958"
    ],
    [
      "398303906231874817",
      "-2328427554779914197849804724"
    ],
    [
      "-287989905561195623",
      "3135217843844246382216737546"
    ],
    [
      "481229081510796793",
      "-2219613825695209590409511908"
    ],
    [
      "4878890180961028627",
      "9599292657403598235199591046"
    ],
    [
      "-1029446068433577764",
      "3690380024459610290701808042"
    ]
  ],
  "submitter": "apkorte",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Daniel Błażewicz",
      "at": "2026-10-16 06:08:11"
    }
  ],
  "commentary": "Specialization at T = -30/1871 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -43748288271748043306667T^8 + 231005568889113088943880T^7 - 41811485832351502958160T^6 - 845807620575605275473120T^5 - 1273696848822391714464840T^4 - 2479538071066771770038640T^3 - 723198327599392266394800T^2 + 1473487148401141809248640T - 304202213366895598996800,\nA6 = 3496542619563277295766359856805926T^12 - 28800862572418754868158883533967960T^11 + 61983572330491650413223232787176320T^10 + 92074250730656596945854018024980640T^9 - 554403246688053294582105340433199720T^8 + 21665370800800153534189468438161072T^7 + 2696996106708736152461893481712643920T^6 + 2003709311601233451889158133572553920T^5 - 1216187330113512252280500336077191920T^4 - 278472048982945948218206647760751360T^3 + 596780792582732967834659478701644416T^2 - 397452607403627859574187730447221760T + 82758424296652691415712452035078400.\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": "2026-10-16 06:05:46",
  "updated_at": "2026-10-16 06:08:11"
}