{
  "id": 5530,
  "curve_key": "2081564355205855188080564881:-278573898137184244599938424128289072585529",
  "ainvs": [
    "1",
    "0",
    "0",
    "-43365924066788649751678435",
    "322423493214330002608108351094336749697"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 190.86100398867762,
  "faltings_height": 13.958486001559429,
  "conductor": "3715517879103461115379897535669702437286772338789124390",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "31",
    "41",
    "797",
    "176923589",
    "446702285400683959563492538666559953"
  ],
  "discriminant": "-39689922089037717366607729662193484037995941211866480780708793613816595968000000",
  "regulator": "1395082213618163.4257613784171494446891347614845700728337680680133750226986",
  "points": [
    [
      "8830603734134",
      "-25061584898795830567"
    ],
    [
      "7422669796334",
      "20235909247127414633"
    ],
    [
      "-2962866241426",
      "-20613129724224691927"
    ],
    [
      "3754550565038",
      "-14578428525021727639"
    ],
    [
      "6328915024334",
      "17362887806021642633"
    ],
    [
      "8825165410334",
      "25040906179544561033"
    ],
    [
      "-4257869049616",
      "-20733475630192596817"
    ],
    [
      "2033991948254",
      "-15576663952435526647"
    ],
    [
      "42586812729734",
      "275159223575845842233"
    ],
    [
      "4277302390634",
      "-14669321151047857567"
    ],
    [
      "855690333134",
      "-16909826942419432567"
    ],
    [
      "5837194933934",
      "16376137572826992233"
    ],
    [
      "8771380675694",
      "24837250360809625193"
    ],
    [
      "20694203399534",
      "91034565339104457833"
    ],
    [
      "-4253917006066",
      "-20734521297443447767"
    ],
    [
      "-5009541885166",
      "20345761233460295633"
    ],
    [
      "3765970469534",
      "14578053763445277833"
    ],
    [
      "12651166858694",
      "42410355609594813113"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -3/5 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -4247232044073407555787T^8 + 31562440352380138911048T^7 - 1079699554459262036768544T^6 + 808673010384011405337504T^5 - 370492253920133220842280T^4 - 583074314969616668304144T^3 + 1749298418924942437857936T^2 + 6981774061823935535232T - 733152591313571732712192,\nA6 = 99353320243156880097765275026566T^12 - 1192047168420920079142624551372696T^11 + 51816962014333011197785218484470384T^10 - 160733095313938224161654547702105120T^9 + 1161258380951665950605765814917343480T^8 - 500375410396179478662655437513305328T^7 - 2173656091315178125605895871772822192T^6 + 963181788398399075637606795285979968T^5 + 1772421005485324185894755005716179280T^4 - 460279153080260982936199267860712320T^3 - 927109903404780261014801473928185344T^2 + 58145438007481575316035550439430144T + 241998303936746269490887631501697024.\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": "2026-10-22 22:15:47",
  "updated_at": "2026-10-22 22:15:47"
}