{
  "id": 4235,
  "curve_key": "119708455661944855294913891302246225:-41385631322943425260059368160404197384843039978209625",
  "ainvs": [
    "1",
    "0",
    "0",
    "-2493926159623851151977372735463463",
    "47900036253406741991315607254035780604713197945417"
  ],
  "rank_lower_bound": 22,
  "torsion": [],
  "naive_height": 242.31110195796956,
  "faltings_height": 17.95689551779175,
  "conductor": "3331430924370683245282024478207025284146188704187511096808570405072532150",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "23",
    "4007",
    "10133159",
    "89214652883359",
    "4261473342511522428524689791491525251"
  ],
  "discriminant": "1542464776091087046121923291078972795031204408049675787664672146050531971195974675289692572160000000",
  "regulator": "340664803994618037017.9603454556256824961912795795508690429825793307462629957218001",
  "points": [
    [
      "30602031805735222",
      "489032171040097576414789"
    ],
    [
      "27329072070803062",
      "393492189535572497118469"
    ],
    [
      "29654974200898606",
      "-147727644564549969050411"
    ],
    [
      "96726946759345462",
      "26676907111321890224550469"
    ],
    [
      "28018361374666222",
      "139735988882568341531989"
    ],
    [
      "29832798643317922",
      "-224292304360928760326111"
    ],
    [
      "-55940333126186378",
      "-3515088089462569311337211"
    ],
    [
      "30489961063029622",
      "452706080843962774515589"
    ],
    [
      "26607604723802662",
      "-616342286983713576937931"
    ],
    [
      "11751473334325648",
      "4496173275815234585954557"
    ],
    [
      "24254037537288118",
      "-1296108551754224462569595"
    ],
    [
      "32671689087427222",
      "-1137673096478350444926011"
    ],
    [
      "26224688528551072",
      "-730217109784475203672061"
    ],
    [
      "24124492709679922",
      "-1332506678519533781295311"
    ],
    [
      "15001855577371222",
      "3723273935653963709086789"
    ],
    [
      "1370165217550280278/49",
      "-56917200967190813335629773/343"
    ],
    [
      "28173078516553348",
      "-7805016586202744347355"
    ],
    [
      "36722522590856662",
      "2416340548574785699415269"
    ],
    [
      "2781430110486667318/289",
      "-24461193711288911404653963403/4913"
    ],
    [
      "17717765115390718",
      "3045518831174127419232205"
    ],
    [
      "12631188460870462",
      "4291159762675004786700469"
    ],
    [
      "80792722012168726",
      "19333404524551404553014469"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 1135/404 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -11140892170449903078832T^8 - 78517047092297850338880T^7 - 410980750922999091180480T^6 + 1172978174531038105951360T^5 + 202359376870041611948760T^4 + 727464198947794396860360T^3 - 533980972281075528757060T^2 - 2994527120513758550219760T - 1424568869019231533236800,\nA6 = 466667176236662985209696435215744T^12 + 4902108138265145170676233713437440T^11 + 30904617405388839778675659644720640T^10 - 2235477311686016201360264232122880T^9 - 1928619458298746783809833278130720T^8 - 1321657250248806493665223528336049184T^7 + 1152166039831051025589342359093195760T^6 + 3336273056288691191096244581228211360T^5 - 1565104306692700007697832976891694060T^4 - 3952505302344716290555441880536817840T^3 + 26850110070164475305157052575243376T^2 + 1903147075480838773866179023498043520T + 656146040532506595230072169941913600.\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": "2026-10-15 04:29:02",
  "updated_at": "2026-10-15 04:29:02"
}