{
  "id": 5860,
  "curve_key": "146418652145817806228934436961860401:-58843184744826832458036677272504546252808611862180649",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-3050388586371204296436134103372092",
    "68105537899105130922361819361903558197932382164991"
  ],
  "rank_lower_bound": 22,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 243.01343152494348,
  "faltings_height": 18.18780643385072,
  "conductor": "5482964318949809323506534297906311454985709025939332441422020958716999870",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "29",
    "31",
    "53",
    "61",
    "3533",
    "501299",
    "19516397507",
    "463263129281127072835382699302210927197049"
  ],
  "discriminant": "-187231239596558651158985340741408448221817390546917881155267876252246254153741612633666583314432000000",
  "regulator": "202021601423944573140.2219872813764486081984152259663107810825255795924273839011463",
  "points": [
    [
      "22280172491336821",
      "3346993752882960252677189"
    ],
    [
      "38514004792877941",
      "-2784202011290630736939451"
    ],
    [
      "24254092314882421",
      "2896354245067963701470789"
    ],
    [
      "38009048625970021",
      "2659770229364895518214389"
    ],
    [
      "33842145807916661",
      "1906027775968250797769029"
    ],
    [
      "39189222653279221",
      "2958005957532022303973189"
    ],
    [
      "3044091488468410309/529",
      "86670427334203004397834014563/12167"
    ],
    [
      "-59284641212065579",
      "-6370310709279556376265211"
    ],
    [
      "-63908993392154179",
      "-1423201175548020025233811"
    ],
    [
      "53126819437405621",
      "-7483071649880788856798011"
    ],
    [
      "38788054211112421",
      "2853776014128007131290789"
    ],
    [
      "3924995362671829",
      "7496215290240195914493221"
    ],
    [
      "-63723338948447579",
      "1930652759207177162900789"
    ],
    [
      "33551302154999921",
      "-1878667076165577609784211"
    ],
    [
      "87050530589074421",
      "-21499271137904781589009211"
    ],
    [
      "149117781550021789/9",
      "126966512871637593861263303/27"
    ],
    [
      "-3955263040445579",
      "8950349189614086745310789"
    ],
    [
      "-62875604089516619",
      "3366277256398750472574149"
    ],
    [
      "23315814419144539",
      "-3107789365632988257453571"
    ],
    [
      "358837120424869789/9",
      "-84807212918864651961760697/27"
    ],
    [
      "14934160374016021",
      "5087366559113391336403589"
    ],
    [
      "30213074567020021",
      "-1877050135585160999735611"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -3/41 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -77688200046122639977675T^8 - 345051545551894951495160T^7 - 26575925672984725510240T^6 + 1397379174658735482223200T^5 + 924444105192629673167160T^4 - 552617251497682425745200T^3 - 3294538182497011117811760T^2 - 2836363778933196694377600T - 685235941086191704065792,\nA6 = 8343511083085250123050296186761350T^12 + 55798071641305709411620408773693480T^11 + 63992696069821126283929842778614576T^10 - 287548516348103372029428932872522080T^9 - 549777946830148798846989863404282920T^8 + 702321721822785932402284527824455920T^7 + 1394771712241954046774251387009862160T^6 - 1833587512252380081925577530665112512T^5 - 1898687314820271014676246427139553840T^4 + 2184401546825882198833306353761222400T^3 + 3375300416127856002328341391809073920T^2 + 1517503055739234059908068559049779200T + 234697979821554858808091582382514176.\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": "2026-10-25 15:31:57",
  "updated_at": "2026-10-25 15:31:57"
}