{
  "id": 4238,
  "curve_key": "7912805081526991645166060885139788203600:-706903308578489460965556055686246823448358613914930372414400",
  "ainvs": [
    "0",
    "1",
    "0",
    "-164850105865145659274292935107078920908",
    "818175125669547987173702806941070455529354454402883846288"
  ],
  "rank_lower_bound": 25,
  "torsion": [],
  "naive_height": 275.61648838846367,
  "faltings_height": 20.797483480751694,
  "conductor": "33272442660136729466590673810285498084436714991504530200336600126639243963197977438568499471400",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "61",
    "107",
    "6467554945998766845309751",
    "77196337530513021426376013464805181856021978117810742058991"
  ],
  "discriminant": "-2472166709253325333479319934465044231752225241395354061996808564498810916685998009674189665929270134415462513120000",
  "regulator": "821134000305051465584043362.4649002253070434962662491182464563095141490348826194145662734",
  "points": [
    [
      "111765820794798158518",
      "1174107043352296859540694269310"
    ],
    [
      "2859708908252356356286/529",
      "112170510933097612739582154674358/12167"
    ],
    [
      "10147040428942970698",
      "-13791242554614047801538157590"
    ],
    [
      "-14255373933311705357",
      "16469955524671092971549890560"
    ],
    [
      "124393623936245709847/49",
      "-6996191311115900337807976568670/343"
    ],
    [
      "116456331457778179054",
      "-1249403892595379570003240389194"
    ],
    [
      "-571969361245061822",
      "-30203927165955365527970312190"
    ],
    [
      "-6387676526320952333",
      "40131679153972837906872148752"
    ],
    [
      "-13461266253416728217",
      "-24454207499005889925712782390"
    ],
    [
      "8573458847295610798",
      "-5918169630028382063716969590"
    ],
    [
      "25722929569619838778",
      "-116609670550174723791026390310"
    ],
    [
      "-12992551374620939702",
      "-27690664219476941702286522090"
    ],
    [
      "31562183576387637703",
      "-164488575395262177770158257810"
    ],
    [
      "49615037498091845344",
      "338783241242130989247146645316"
    ],
    [
      "104708424535034561713/16",
      "283526585982138536332358848785/64"
    ],
    [
      "4771206214914327718",
      "-11842928882696438086445195310"
    ],
    [
      "45896786126162900458",
      "299890567426775646351030390390"
    ],
    [
      "9569970693843016558",
      "-10817757839934886102733581110"
    ],
    [
      "429257447868412754794048/73441",
      "146684876136576960200672789434959660/19902511"
    ],
    [
      "-457631483108564035223/144",
      "62542416725265965776988553030205/1728"
    ],
    [
      "6833453112667827238",
      "-3282550792906126414569052590"
    ],
    [
      "7731558138550529722",
      "2407536338732732017244477862"
    ],
    [
      "-1674479122407794250878507/306916",
      "-6705300268320563068295788167416592615/170031464"
    ],
    [
      "81911276959978334398",
      "732731401703850210935118755910"
    ],
    [
      "1491648518565636544190009404/337273225",
      "82080704299633098121059627069869606596692/6194022777125"
    ]
  ],
  "submitter": "apkorte",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Daniel Błażewicz",
      "at": "2026-10-15 08:46:39"
    }
  ],
  "commentary": "Specialization at T = 239/750 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -32332676430258071809200T^8 - 392497065814316713973280T^7 - 1605286506697565663751840T^6 - 2016536429413138685637600T^5 - 1643121380463324517697040T^4 + 604907641354957338809520T^3 + 2182672220879703769538760T^2 + 284764930480378808601480T - 903774960127741440937707,\nA6 = 2152872548702497670524683858518400T^12 + 37926485183963444897543405698016640T^11 + 273497207298763591399877065140889536T^10 + 1038319980551223501714889156644738240T^9 + 2025026435470961119972063737624451920T^8 + 768757757929830231396275004132348000T^7 - 1622968189285827532493125262292017760T^6 - 620910140516148584947737138229395360T^5 + 1602335569642802776124896462486427520T^4 + 351810003192753644435857685852379600T^3 - 1085870391509042811982855754241980040T^2 - 186927270560088531571177963463660760T + 323553892643757904650299161814986470.\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 08:38:18",
  "updated_at": "2026-10-15 08:46:39"
}