{
  "id": 4301,
  "curve_key": "420286550724258115551058819561:-272185229017268601994575740175129985861661941",
  "ainvs": [
    "1",
    "0",
    "1",
    "-8755969806755377407313725408",
    "315029200251467559681423210402727614899806"
  ],
  "rank_lower_bound": 15,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 204.63220275932943,
  "faltings_height": 14.827690309501149,
  "conductor": "3596232705771186622110065084714548320296938776703770",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "29",
    "53",
    "71",
    "137",
    "199",
    "277",
    "281",
    "397",
    "829",
    "1249",
    "5581",
    "1031299",
    "6764341",
    "10464199"
  ],
  "discriminant": "89668536969696923914675439481066541107743317988128172876213023517882222584004106000",
  "regulator": "5867625696675018529357.6872929071579307761413198589776882709519616073",
  "points": [
    [
      "206810444812826",
      "-2711014995571635481761"
    ],
    [
      "106626251406770",
      "-770495742488560348713"
    ],
    [
      "628880175926918029365833/9831119104",
      "125891078265526276253924464594286259/974775121399808"
    ],
    [
      "187414065151588744730/2719201",
      "884932852584282776460671254758/4483962449"
    ],
    [
      "20176750303068185/256",
      "1386089184327666654228507/4096"
    ],
    [
      "156630756131218625/256",
      "61303003422706405912779447/4096"
    ],
    [
      "24539974683015940384202/46389721",
      "-3787779416007929031649119762508206/315960389731"
    ],
    [
      "815791728677922393905/14622976",
      "751066438457363196976616050623/55918260224"
    ],
    [
      "10734988103673813405245/178409449",
      "-184968468132978233454464015801769/2383015010293"
    ],
    [
      "492290946357262070377745/8780439616",
      "-15506001191190941182198088947265637/822762313777664"
    ],
    [
      "215772555103755127741/2975625",
      "1271825203519580004138382210411/5132953125"
    ],
    [
      "4943844309075194654245/84768849",
      "40871908025247727059274773733661/780466792743"
    ],
    [
      "4153441334600565126488958005/74618101883329",
      "-6760569382104404787670192600316859140229/644564371472229251233"
    ],
    [
      "933862619476012415144155528945/16821403375206609",
      "-12854087633732238177879478079450254749818921/2181691491509563015405977"
    ],
    [
      "4778980800137638033690275331570/83833225715423041",
      "-818719859923907413362791157840796183017025207/24273045263178132640343839"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from my curve#4255, found by specializing the family associated with curve#802 at T = 246/277. This isogenous curve has the same rank and conductor, with smaller absolute minimal discriminant, Faltings height and naive height. The fifteen supplied points were transported from the source curve.",
  "created_at": "2026-10-16 19:10:00",
  "updated_at": "2026-10-16 19:10:00"
}