{
  "id": 5971,
  "curve_key": "256827007886459583671731572127825:-3130244183677584504723210825565165287396395448025",
  "ainvs": [
    "1",
    "0",
    "0",
    "-5350562664301241326494407752663",
    "3622967805182389027179049763745127059952589417"
  ],
  "rank_lower_bound": 23,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 223.8778665810136,
  "faltings_height": 16.6740129051857,
  "conductor": "42462656859705214487368244037209023330788587592623444561992701603383470131697815150",
  "bad_primes": [
    "2",
    "3",
    "5",
    "19",
    "61",
    "347",
    "292292513",
    "3996185426561705062200990191",
    "602614630677817741469201907929666439239"
  ],
  "discriminant": "4133049508222893213435278258425610470437878361385466937790212346108761346457425846602430080000",
  "regulator": "333431942141516808309305.403835880982703623851678565164843005352255528541419414916176",
  "points": [
    [
      "339700374737822",
      "42948571920081271667549"
    ],
    [
      "13009057013295722",
      "-1461373435401486751411651"
    ],
    [
      "-645354924680018",
      "82505760297230764266469"
    ],
    [
      "5302593975713222",
      "-352628430025039628326651"
    ],
    [
      "5022164062820252",
      "-321591744571400566331041"
    ],
    [
      "22824986172440518/9",
      "2154125463248837819833303/27"
    ],
    [
      "-2060354450405698",
      "76815977161811281565309"
    ],
    [
      "-1432459708415548",
      "91367996731453959660359"
    ],
    [
      "14895114232199486/25",
      "3178488856542344645413969/125"
    ],
    [
      "421851326444966",
      "-37959161092800179215771"
    ],
    [
      "746274586288286",
      "6752658823095312480005"
    ],
    [
      "2031002349424166",
      "-33671759629035862759195"
    ],
    [
      "637386142497662",
      "-21714937582153128328891"
    ],
    [
      "33746214765025718/49",
      "-5580451333145011713828733/343"
    ],
    [
      "3628694128550402",
      "-178851772945559518519411"
    ],
    [
      "749742153022708",
      "-5732841395371276743275"
    ],
    [
      "10377238689957242",
      "1032275861160629323297769"
    ],
    [
      "-1976986567723558",
      "80460885830291047976669"
    ],
    [
      "319827825473116742",
      "-180868540273136292559940731"
    ],
    [
      "66650508241291678/9",
      "-16426686039999508973966297/27"
    ],
    [
      "29544973078776947/4",
      "-4846908509811266575546385/8"
    ],
    [
      "-81309898427164642/169",
      "171392469529067555012389553/2197"
    ],
    [
      "277262026280539382/121",
      "77540795543482242482510239/1331"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 153/79 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -46118133600050365068267T^8 - 175585131457438249904328T^7 + 186310120046915943350856T^6 + 1086331850638516901792016T^5 - 496083140846252073481680T^4 + 514411161151166512216704T^3 - 1349221054433071325320224T^2 - 2378315976590397135297312T - 727839380732795443417392,\nA6 = 3720542197990934008634945538033126T^12 + 21526619776657745210072107363777176T^11 + 8750301169726091012404314376074744T^10 - 195259865254986340553776941743082000T^9 - 376011441894779917411915234538303040T^8 + 641327438884246873021760128611712704T^7 + 2168837359823326715713321889328303264T^6 - 1791411665482428423973793516575869984T^5 - 3162380047574807481299569084055523120T^4 + 550294990071515361307367747441559360T^3 + 2282676589946398330859127503834660544T^2 + 1241084125645116952889139651480184704T + 235518724223176451772618983340821376.\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 10:32:34",
  "updated_at": "2026-10-27 10:32:34"
}