{
  "id": 4267,
  "curve_key": "210215786363275056833601768561683209306201:-96409624836760540526849786337825143091229062330635737952974301",
  "ainvs": [
    "1",
    "1",
    "0",
    "-4379495549234897017366703511701733527212",
    "111585213931435810793140240671412708524278991975026752179604"
  ],
  "rank_lower_bound": 25,
  "torsion": [],
  "naive_height": 285.44742323796055,
  "faltings_height": 21.51644237054305,
  "conductor": "174164423262524400823734779124493200445680667881133146381966747877983549516873060814351057410",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "23",
    "41",
    "83",
    "137",
    "197",
    "199",
    "9931",
    "738643",
    "113737357693089399173",
    "59771131561917581425523",
    "3043301382609038760288509"
  ],
  "discriminant": "-3031180607881395918727990838810988530528252705643095198533912996987108676033069476084758856941922656575825242518712500",
  "regulator": "50434703246724614652393520.57532618660335327308413860702957644347421379819732226639379265",
  "points": [
    [
      "34387753032792608958",
      "40599560814594306229427654996"
    ],
    [
      "38834803367625820518",
      "8761370151871570915303170886"
    ],
    [
      "-45401540254074511817",
      "-465655311285113394663609577304"
    ],
    [
      "39245657878937474473",
      "-12491690944951924231509326279"
    ],
    [
      "42023100720743152813",
      "41899255645973096717899418041"
    ],
    [
      "38075066788914526698",
      "-5784508446117612972728780294"
    ],
    [
      "4268514672276749946943/121",
      "-41896164838877690131857340285549/1331"
    ],
    [
      "49764927272512310347/4",
      "-1943598333573549243904701324607/8"
    ],
    [
      "38810497566553665864",
      "-8561995885386226604827699142"
    ],
    [
      "11079579018889942751382/289",
      "-28385642159194136562945440581292/4913"
    ],
    [
      "1895458537976506789462/49",
      "-2599184883101323152012300405812/343"
    ],
    [
      "48667268157246151155",
      "-117114046080035887415174606927"
    ],
    [
      "292476445850736421510",
      "-4883630198968158578558532632108"
    ],
    [
      "41858051743336234733",
      "-40092498074565265955391799879"
    ],
    [
      "41105139136600020718",
      "31906386979565847478717678846"
    ],
    [
      "19071519577852573158",
      "-187078396543116684038377503404"
    ],
    [
      "-75546528611020948427",
      "-106187853059531532529102478279"
    ],
    [
      "-52600862430709450167",
      "443183621450767935352605028921"
    ],
    [
      "38272664459386733833",
      "5650523601379774333085284921"
    ],
    [
      "400204080809931534622/9",
      "1864290343188499468963302133642/27"
    ],
    [
      "1586799850900662734776/25",
      "37357885249383856179289071737834/125"
    ],
    [
      "12711137735653318359352/289",
      "-312561543734160543700659474738382/4913"
    ],
    [
      "38346640398488249658",
      "-5801640051510814567063236004"
    ],
    [
      "-63659421119248285592",
      "363868337949293874269000692846"
    ],
    [
      "4504756476787142172943/121",
      "-15761153074852032267030414123949/1331"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 602/177 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -527341140801402202800T^8 + 28147421355562296077760T^7 - 459551759375096200061280T^6 + 302351267241048825914400T^5 - 781968800173412856857040T^4 + 675358902068135754436560T^3 + 3773048587407798267814920T^2 - 1117382211836832683478780T - 4020150123856377627416667,\nA6 = 17121088738199440047220335446400T^12 - 754628062801204312746404692573440T^11 + 9968619820015289906033818763984256T^10 - 51608554478585574595758963618583680T^9 + 526057596644710242384434966047683840T^8 - 378806199877031919118656099183432000T^7 - 1773421996954369325651890262968908960T^6 + 1196920464887427116679365802787354320T^5 + 3649727616935479672514463019748893140T^4 - 2090084281847145605737007981579064600T^3 - 4861031233659870921990346669248956340T^2 + 1412045054473207996392438591189858420T + 3148792632832054337655276106728582390.\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 23:48:47",
  "updated_at": "2026-10-15 23:48:47"
}