{
  "id": 4229,
  "curve_key": "15545328925763592485004044492043877758016:-1938514934628334494935002472355579488970897402090418455048064",
  "ainvs": [
    "0",
    "1",
    "0",
    "-323861019286741510104250926917580786625",
    "2243651544708720480140891781019673534792677239743235171875"
  ],
  "rank_lower_bound": 25,
  "torsion": [],
  "naive_height": 277.63405552392163,
  "faltings_height": 20.84663895765074,
  "conductor": "2216987861263300051422436401674628016398716297779675144101794536149207740481628334022892920",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "23",
    "31",
    "190168928111",
    "7939969942969604325803424687821",
    "7059097225133342226646758291845914582637"
  ],
  "discriminant": "-693687100616409141695428967936605468522672942767392990235231206589050846243448668222856042634923056207416620000000",
  "regulator": "26660264120503413718451386.24442109504208931334629285280744213370916622781815374222819576",
  "points": [
    [
      "4098836038201070543375/361",
      "37707438595070887259511871655250/6859"
    ],
    [
      "19522506756144596755",
      "57979753660372621767613951170"
    ],
    [
      "10415626951288492055",
      "-615012044040656760272333130"
    ],
    [
      "10484520083962838750",
      "-797963608950828367992998625"
    ],
    [
      "8781439708559042075",
      "8766680727451714220111651550"
    ],
    [
      "-8323009919515354645",
      "-66049938418316282952259392930"
    ],
    [
      "10572062105689616225",
      "1181621217563192535771148650"
    ],
    [
      "15737710524278094125/4",
      "-256792229536633246454706439875/8"
    ],
    [
      "10549471361402369375",
      "1074180674209142719886774250"
    ],
    [
      "6397011740293513175",
      "-20825123677394052758014394550"
    ],
    [
      "12765629995810018163",
      "13771905430246644508961916354"
    ],
    [
      "10129954580890568975",
      "-1565037881702546408414764650"
    ],
    [
      "-44909572364441741755/4",
      "534535594397099252510491616535/8"
    ],
    [
      "9272667356309689883",
      "6154824535088161466821418274"
    ],
    [
      "9064397760204306950",
      "-7266865940092927740445088325"
    ],
    [
      "97194526113764587455005/8836",
      "2897988979614155666453667236245605/830584"
    ],
    [
      "56865526465954722275",
      "-409527166899325338431744601150"
    ],
    [
      "12870716515068268550",
      "-14402469997005773706011456325"
    ],
    [
      "46620850483880996525/4",
      "-57840049742261978220461964675/8"
    ],
    [
      "9132868524453684275",
      "6901991863645021209469324350"
    ],
    [
      "35546226190928069375",
      "-188800124058527623305922761750"
    ],
    [
      "-19857774939898914325",
      "-29056325447190964033197779550"
    ],
    [
      "10404846374519993375",
      "-603884805231246445383369750"
    ],
    [
      "10098745424903137475",
      "1725881790376505549811283650"
    ],
    [
      "10027552984876205615",
      "2099215440194452562486365290"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -1181/80 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -10669947921935414766592T^8 + 11909462495223346810112T^7 + 29290850738695015599056T^6 + 749826724411797003953776T^5 - 2800296645908250177432680T^4 + 5291011042236720751525024T^3 - 9053743075112346775820704T^2 - 1373686135035664689321352T - 153062929487822447776267,\nA6 = 424084459520579325699737587892224T^12 - 702971076900016054991835746922496T^11 - 1428460164091780099364248773693184T^10 - 45531551300070380060674898437602560T^9 + 178145138683306119166957105019549520T^8 - 224307849011465835658368095576866752T^7 + 1890363249575504635685922631864051728T^6 - 8402714629932209203714457518206796848T^5 + 10932033646871752694840038266436614840T^4 - 1045636958253350245306227479236779680T^3 + 3911537622199302231442442603656239344T^2 + 397823992391227625022128206594583384T + 16543056563137220502197778370669126.\nIt is a 2-neighbour of the fibration given in curve#4205 (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": "2026-10-14 19:20:34",
  "updated_at": "2026-10-14 19:20:34"
}