{
  "id": 4192,
  "curve_key": "74990212746399580993172762747766318841:-472196777309363615852184986552364676618219794906266798861",
  "ainvs": [
    "1",
    "1",
    "0",
    "-1562296098883324604024432557245131642",
    "546524047811763443622405545086073864779426011919003944"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "naive_height": 261.63126286827554,
  "faltings_height": 19.826473165115797,
  "conductor": "1313579416141730104084274184163432663820045517198712103598711300093553255800439215630",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19",
    "23",
    "29",
    "71",
    "73",
    "79",
    "83576515082527",
    "85345050910342772012547568624894287280618106178000028121"
  ],
  "discriminant": "115011611774323845477465906815080040282744050265786503715848172026329812188124053537452991083024785900798437500",
  "regulator": "412061463646648447184690.94535341252139133787971596615793707006250202139859542907837032",
  "points": [
    [
      "1512417416644476893",
      "-1281871117517527706963755009"
    ],
    [
      "1456427226005543143",
      "1166403944317428806342551866"
    ],
    [
      "-12356377372728169463/9",
      "8688699787119573646086076757/27"
    ],
    [
      "-1304188956732576182",
      "-604770078207892273850145384"
    ],
    [
      "-1097106665006657482",
      "969538403748371958951978116"
    ],
    [
      "-246560383708345107",
      "-957463037777901726658275009"
    ],
    [
      "-442586230125082857",
      "1072977101499285579023977866"
    ],
    [
      "-750339466352757857",
      "1138564166392752630469480991"
    ],
    [
      "-839818308704980327",
      "-1125277492566638655849584209"
    ],
    [
      "384601572974529643",
      "-50518793506233183228410634"
    ],
    [
      "17650240655034052403327/289",
      "2344420428186604634415544550380783/4913"
    ],
    [
      "-68262423097300297",
      "-807992622900683073085399969"
    ],
    [
      "1297215634979586418",
      "-838333231004115070883722384"
    ],
    [
      "1269096005052811637327/289",
      "-43492600709040145957659848327342/4913"
    ],
    [
      "-3566463324532889491397/2601",
      "-44129621507620689725674337258294/132651"
    ],
    [
      "-1556360155753425844655/5184",
      "-371096001325524539271587995088389/373248"
    ],
    [
      "-1320706243082169757",
      "-553350349292115134802367009"
    ],
    [
      "362410479197279063",
      "167125861156739379287967071"
    ],
    [
      "194400110025824393",
      "500160141411509725017220616"
    ],
    [
      "1010848208068036665",
      "13371143769475303209445272"
    ],
    [
      "21016124361264551833/81",
      "290357776244442223141839228439/729"
    ],
    [
      "1099532101737011038",
      "-397531868881036904397696634"
    ],
    [
      "-1875868522432687829/9",
      "25083833393710394868412283141/27"
    ],
    [
      "336085733160637868",
      "-243763652517759274854503884"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -5938/5319 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -4437370829345071269937785502500T^8 + 24731294533954602783634178920800T^7 - 24905343694917325040325875752236T^6 - 73371957550294374341624859203376T^5 + 11388134363003403434011617130260T^4 - 31974960227112637988116696606080T^3 - 53087557802286047432098781752884T^2 + 33902036804480905040632762295376T - 4900264269756058995659292474432,\nA6 = 3583088599917473486225042501788936057800562500T^12 - 29952862178447015859986519449513030145545410000T^11 + 74261855654700672409867052055125389734923941200T^10 + 34915854636953526118546131005709436129082490240T^9 - 320350491450370659682737733420310606418445799256T^8 + 104052954099599046113301816294931102834227932832T^7 + 846552244341643086726187489356042742190493998112T^6 + 378044570078449717959306675143150641014761409024T^5 - 387170892915283488485440730375460569591982158796T^4 - 122143831120324014405241873122119111177801883600T^3 + 159312688808409642522129729739582813691214920688T^2 - 45075775528724488962464647393974897773506063488T + 4205873318402097235409142015354269085411308544.\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": "2026-10-12 03:55:50",
  "updated_at": "2026-10-12 03:55:50"
}