{
  "id": 5975,
  "curve_key": "14050021018665059751823696:-75420467148596125638106356770430585280",
  "ainvs": [
    "0",
    "1",
    "0",
    "-292708771222188744829660",
    "87292207347814612861104590754536624"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 174.43228406711688,
  "faltings_height": 12.56114114228451,
  "conductor": "219967660802230675544908382319674196047258614835447558971128",
  "bad_primes": [
    "2",
    "3",
    "11",
    "13",
    "37",
    "59",
    "57259",
    "6818783",
    "24708833",
    "603370003",
    "5043955467318181838389571"
  ],
  "discriminant": "-1686764636853447808107978396461649924080411289910120862113905703002194688",
  "regulator": "155840385081534211.7142464079746752604834145590779336214451534393302940493876",
  "points": [
    [
      "375978960518",
      "-174322462336973730"
    ],
    [
      "129609235319",
      "-227005936180990902"
    ],
    [
      "48910284590",
      "-270356694031629018"
    ],
    [
      "1067109737918",
      "995028861385638090"
    ],
    [
      "688700725718",
      "460825566704491950"
    ],
    [
      "158457066134",
      "-211870422531688338"
    ],
    [
      "254101519742",
      "171234297195238134"
    ],
    [
      "-142333510106",
      "-355064732240087298"
    ],
    [
      "-51355649110",
      "319670159331037482"
    ],
    [
      "530823683876",
      "-285460429499269596"
    ],
    [
      "-15429738982",
      "-302993323064945370"
    ],
    [
      "-651230677586",
      "-41536726594133082"
    ],
    [
      "269343136418",
      "-167310495760289310"
    ],
    [
      "5586899152190",
      "-13146798516456051018"
    ],
    [
      "-300918817129",
      "384870034355009346"
    ],
    [
      "855153999770",
      "-679959778038916518"
    ],
    [
      "475075133768",
      "235491587787068580"
    ],
    [
      "-9754200295846/121",
      "-442173627512161664418/1331"
    ],
    [
      "523563967646",
      "-278494869711602154"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 3/1 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -208105972076488790307052T^8 - 439527670947297931328940T^7 + 343660503631112086072245T^6 + 613353394224090550622880T^5 - 231043158672102674134740T^4 + 1208678840215888066067520T^3 - 559641271407448823804880T^2 - 714118514352617716439040T - 146036624395308969816000,\nA6 = 48948478213224443067242844627078004T^12 + 208793951588984308688304222760788820T^11 + 53897690802776318918669214864929865T^10 - 939263184673604027480558480888431240T^9 - 926917487525195732269342791952526655T^8 + 1746605331713416582793524688175626496T^7 + 2007083092390584405960569676783621120T^6 - 1692632433459306707439291235219046400T^5 - 1287348467089494424054800792979985760T^4 + 176901482519389361500233479886873600T^3 + 435942394999692519911189932156974336T^2 + 166662302037719363510662729228216320T + 21432169750567610095158106104249600.\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 13:57:13",
  "updated_at": "2026-10-27 13:57:13"
}