{
  "id": 5968,
  "curve_key": "84487889216578018528015328158424481:-23577110921888733655636139837965347166620732272411121",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-1760164358678708719333652669967177",
    "27288322826260108837768103371025961276261237251529"
  ],
  "rank_lower_bound": 22,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 241.2657488100426,
  "faltings_height": 18.03407957681568,
  "conductor": "2022780087364476965932436048653444994200721557816889611842167404345336970",
  "bad_primes": [
    "2",
    "5",
    "13",
    "17",
    "19",
    "23",
    "29",
    "37",
    "47",
    "61",
    "79",
    "421",
    "122509",
    "135479",
    "952129",
    "1745813",
    "2821513",
    "1189954989258699414085099"
  ],
  "discriminant": "27321516604345956554368929704304139960337809768843534469060624205002172796305140651162790148480000000",
  "regulator": "146006051290017832974.1541371680498824641279622664140922852461982013413701179264170",
  "points": [
    [
      "28103269209227287",
      "-133176978012471691306644"
    ],
    [
      "28200145188832487",
      "-278472161714686548948644"
    ],
    [
      "-844395883121001",
      "5364139848185159182205052"
    ],
    [
      "117940528543814833/9",
      "-68691807933012018111554638/27"
    ],
    [
      "402456193809516159/121",
      "-6167381184365243170815358412/1331"
    ],
    [
      "28112171628649287",
      "-152204778342892412080644"
    ],
    [
      "26160400091304237223/729",
      "63279573663233042478696064148/19683"
    ],
    [
      "-36868932874444713",
      "6485914952114529709119356"
    ],
    [
      "18376465072654907",
      "-1071613080081802055363864"
    ],
    [
      "129512858198964887",
      "-44404039866350051911060244"
    ],
    [
      "1176532039573287",
      "5021858385659630907747356"
    ],
    [
      "267169945370864247",
      "-136482809134711220244157444"
    ],
    [
      "3647815939837287",
      "-4573413071702493602020644"
    ],
    [
      "80613952810694603/4",
      "-174202857836287857981487/8"
    ],
    [
      "-45742165171527113",
      "3477589735220930385775356"
    ],
    [
      "2663574668651916343/9",
      "4305486648517665596441553332/27"
    ],
    [
      "32860631466393127",
      "-2220768744671960878880484"
    ],
    [
      "20073928146464787",
      "209647470816730314391856"
    ],
    [
      "213520120158358087",
      "-96881473144815826272592644"
    ],
    [
      "181088517709787323/9",
      "-3639018818638772694939488/27"
    ],
    [
      "35699107687977887",
      "3154030291813892198075356"
    ],
    [
      "29432336805281017",
      "-989293082432833391742944"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -7/13 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -2315727727754537200T^8 - 385085454700810899360T^7 - 21602016129394505916480T^6 + 522753273151467123362400T^5 - 5286101242963131414221040T^4 + 36372271295130380430902640T^3 - 119866073107198500927623880T^2 - 44611766420397375005288280T - 17644996097302241306504187,\nA6 = 1527906580671423711878454400T^12 + 405036291873933234226307839360T^11 + 29619810420503480598512683442496T^10 + 83447431068127636496045716863680T^9 + 10401708370692526999699168797492240T^8 - 680407910276562698898410450598391200T^7 + 10353906760921511571152027566046979840T^6 - 64341197016007520540432295631610298720T^5 + 151935569584040641348413346807219047840T^4 - 98223779992621049253987068203224001200T^3 + 461589258984786807406908653536129872360T^2 + 245414512415050160861358750620214278280T + 41992607521879070487127955356093746390.\nIt is a 2-neighbour of the fibration given in curve#4187 (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": "2026-10-27 04:44:02",
  "updated_at": "2026-10-27 04:44:02"
}