{
  "id": 5848,
  "curve_key": "28949670315520641411350524858561:-155713364520982941975436424099702361361272049441",
  "ainvs": [
    "1",
    "0",
    "0",
    "-603118131573346696069802601220",
    "180223801528915391841355267151319727240144400"
  ],
  "rank_lower_bound": 21,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 217.32933481713184,
  "faltings_height": 15.844344358019613,
  "conductor": "3721751310652423631907218719360451502539213263140023266221872454930",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "19",
    "41",
    "43",
    "109",
    "25256113139",
    "27955248379",
    "3701864022353148678780205142029046599"
  ],
  "discriminant": "9020003377463960775252644516792999660198180247330403067491789304734830012476878848000000",
  "regulator": "42821161020576780889.903274401296216091468384589576386030910753803291834016751257",
  "points": [
    [
      "461074509992840",
      "-401370432434712100420"
    ],
    [
      "441791957703560",
      "-8655358189632879940"
    ],
    [
      "531452357324840",
      "3130416191157548023580"
    ],
    [
      "321914045882120",
      "-4408074863735933620420"
    ],
    [
      "461833250815340",
      "-433804211197262744920"
    ],
    [
      "457457519174792",
      "-231980044958289422404"
    ],
    [
      "469114471828360",
      "727751947052105507260"
    ],
    [
      "-631044393011380",
      "-17593336359300637575700"
    ],
    [
      "6443688876407240",
      "513656631226412662709180"
    ],
    [
      "455770269118076",
      "126761815222874584472"
    ],
    [
      "1174373003561540",
      "33039021333788218609580"
    ],
    [
      "-67546004838610",
      "-14854421719701847209670"
    ],
    [
      "472857223371440",
      "873528569517797400980"
    ],
    [
      "1059207375859592",
      "27013752411184529764796"
    ],
    [
      "131478060682380200/289",
      "-95626381526930840206340/4913"
    ],
    [
      "860287558451090",
      "17264501436837513999080"
    ],
    [
      "457065760005140",
      "-210606523337077678420"
    ],
    [
      "207737997868040",
      "-7993634911252422407620"
    ],
    [
      "393252713862440",
      "1965091666421618647580"
    ],
    [
      "428927790911090",
      "665883488728522191080"
    ],
    [
      "912568179577460",
      "19743518415315592350380"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -12/35 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -6276238998830220029652T^8 - 147117265740737393263056T^7 - 1476608115021273186431436T^6 - 2537588378961323810084232T^5 - 2548792821173728264463880T^4 - 1085007595485857335267392T^3 + 1266527474226087852521664T^2 + 648517828968568984999104T - 394596892599474187722672,\nA6 = 183805362097981758392518604760804T^12 + 5732624758080384420828430168047168T^11 + 73959871695264874512454632891659784T^10 + 444783553219225017837165953570627520T^9 + 2344794983173561552804045815952068900T^8 + 3952769116759113473247850984388751264T^7 + 1034132030293362061211853414656889168T^6 - 2105709468706045084822083295783288416T^5 - 399200243459621989020610997025954720T^4 + 954359071876325078141973753377053440T^3 - 120506571390369672930568955416602624T^2 - 234913768366312396616401364230326528T + 83823186438658476366371918607332736.\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": "2026-10-25 11:27:25",
  "updated_at": "2026-10-25 11:27:25"
}