{
  "id": 5962,
  "curve_key": "330923948554050506023565871481698547201:-5401851308893395100082629371160726966168131962115328520449",
  "ainvs": [
    "1",
    "0",
    "0",
    "-6894248928209385542157622322535386400",
    "6252142718626614698595189176307466674922202725570348032"
  ],
  "rank_lower_bound": 25,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 266.0848558022599,
  "faltings_height": 20.14889011811301,
  "conductor": "78430510892679442785713283664025259544985871649589693665362745489233014673514150316589744990",
  "bad_primes": [
    "2",
    "3",
    "5",
    "41",
    "53",
    "59",
    "67121",
    "369913",
    "8050057880141222756991211",
    "102022282593753705251183255146754405699229590172773"
  ],
  "discriminant": "4085475903989295462621558659747314733136184331035381704563088842102468726174857953339709898546080053065472000000",
  "regulator": "86174161825056695150155624.16918091009138693816889828459083086482478287363653999504194986",
  "points": [
    [
      "8923493454915604824",
      "-25598786246245520711439943392"
    ],
    [
      "918997548495690564864/841",
      "-3725076398432761614170825389728/24389"
    ],
    [
      "676382329600386684",
      "1377836995309131504598640688"
    ],
    [
      "5079058945149900084",
      "10112344721189684054384244528"
    ],
    [
      "1898293101520002864",
      "73269566385747757526105328"
    ],
    [
      "1286712153709502332104",
      "-46155259930605895286574879766752"
    ],
    [
      "10241267737818614304",
      "31777145285211851162606446848"
    ],
    [
      "2046168377056296864",
      "843952975072551665258927328"
    ],
    [
      "114766335468446256288/49",
      "589443677951367798045686622240/343"
    ],
    [
      "2223591760187663904",
      "-1384336111735695343940727552"
    ],
    [
      "2003456548781519744",
      "693804631101984706487984288"
    ],
    [
      "-28923791139158162655744/27889",
      "-16325522212173044901296568112217376/4657463"
    ],
    [
      "-208126540482659987094/289",
      "-16178333461537729126532458357926/4913"
    ],
    [
      "1908194690368816704",
      "211436369012972757036721248"
    ],
    [
      "-589778145012636096",
      "-3180105761911262731392027552"
    ],
    [
      "663444324402561504",
      "-1403642750340422813746997952"
    ],
    [
      "35582583689871050304",
      "211690262249912396398843978848"
    ],
    [
      "768258023023064304",
      "-1187022416656992176429011152"
    ],
    [
      "3242137311971788104",
      "-4240238129443844857143989352"
    ],
    [
      "707749012507138795584/361",
      "3573117007964719990447295983392/6859"
    ],
    [
      "-1139464579598954496",
      "-3553651317728650321324433952"
    ],
    [
      "4234784802302659491/4",
      "2991766070601049932961020459/8"
    ],
    [
      "1926824540069112384",
      "348948760358408114156351328"
    ],
    [
      "1926011589082554624",
      "343975477701067924004398368"
    ],
    [
      "3241967223193169652",
      "-4239743939066760656979879972"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 253/2 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -7016388255537308794800T^8 - 178679712000491349877440T^7 - 1393427674620775645747200T^6 - 570182635321524575663040T^5 - 753965899387475415418440T^4 - 320804658906630906472920T^3 + 1134421125068367717675300T^2 + 399978175235844546966960T - 422082632478729918479472,\nA6 = 219688715864979146315449005782400T^12 + 6098200250797428195163726469525760T^11 + 54477207303588087906057214569267456T^10 + 264783925318167622977267944863123200T^9 + 1702978825713300190413814657041122400T^8 + 932916852969092429403286366085219040T^7 - 1775033404268099174843557641423862320T^6 - 1248513743927587153502730303378288864T^5 + 1060720915885228836685362726021218580T^4 + 675987962412402587067553913812781760T^3 - 432422499228520607079300144749998800T^2 - 178229177722910279472469086969305280T + 105716686434811400528878525349249664.\nIt is a 2-neighbour of another fibration built here (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 00:49:57",
  "updated_at": "2026-10-27 00:49:57"
}