{
  "id": 5560,
  "curve_key": "72403583162897382601263702736:-20687135051976962525080287508271396341823680",
  "ainvs": [
    "0",
    "1",
    "0",
    "-1508407982560362137526327140",
    "23943443347195055675441331162009014768064"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 199.47617183547908,
  "faltings_height": 14.569161188158024,
  "conductor": "1055209752934960036137349279339074457897418025837973243904232",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "23",
    "53",
    "643",
    "2963",
    "2480483",
    "1053600773",
    "7236604065768609105668696459387"
  ],
  "discriminant": "-28007976637845999913235644898838004937113222162063071196466762528112078675130568448",
  "regulator": "957021266055111100.744548368813583921804885661324761057106752178219256891574787",
  "points": [
    [
      "31164302552542",
      "-84865539920342187006"
    ],
    [
      "-33723266908718",
      "-190944517126443570126"
    ],
    [
      "31146854359318",
      "-84721128072196679910"
    ],
    [
      "-36756597733004",
      "-172416588971596637976"
    ],
    [
      "6866035343326",
      "-117942115019033278974"
    ],
    [
      "-30954447564882",
      "-202424094261314875950"
    ],
    [
      "-30981785811818",
      "202331651100168916326"
    ],
    [
      "15861009045040",
      "-63314692141696003008"
    ],
    [
      "-38379348396230",
      "159070304574440901642"
    ],
    [
      "76974195376510",
      "-603248804021083899042"
    ],
    [
      "477214598215897/16",
      "4740531786784064730459/64"
    ],
    [
      "27834871665760",
      "-59354905838367347208"
    ],
    [
      "29907862079254",
      "-74713963373688560922"
    ],
    [
      "-45148783404566",
      "-3791798195015688858"
    ],
    [
      "138726088582786",
      "-1576217447678269424574"
    ],
    [
      "597850226298484",
      "14587964032218166181592"
    ],
    [
      "22860904112095",
      "37516132791569354142"
    ],
    [
      "260269665351910",
      "4154767800566351140458"
    ],
    [
      "1338218394257254/25",
      "38846155988677510246158/125"
    ],
    [
      "-5351309039918",
      "-178499741774783455026"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -7/6 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -25587393138499560595632T^8 + 221437887745294106450208T^7 - 409046233823443618010496T^6 - 337430027367784463054400T^5 + 385077858934643123416560T^4 - 2022438225360352683878928T^3 - 482435290242461337479784T^2 + 2239541715059421343407000T - 777998140618398505576875,\nA6 = 1764219405629347358705661608694144T^12 - 25198292331980051240841044609464704T^11 + 115199016267831836970321760720675392T^10 - 75546422101413012064473686732126400T^9 - 692303544256347632957776668963449136T^8 + 753807318552830839318219503747529632T^7 + 2470157439450075720627076783725847488T^6 - 866460061617253657076985369541871616T^5 - 2899680871912044976732713869657546496T^4 + 1311833024050784553300452787956054160T^3 + 1368776544240715088543951830367560200T^2 - 1167871608295534448326902047444325000T + 245730438412887456689875458237843750.\nIt is a 2-neighbour of the fibration given in curve#4647: 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": "2026-10-23 06:04:13",
  "updated_at": "2026-10-23 06:04:13"
}