{
  "id": 5964,
  "curve_key": "208904652798496318614684321:-3015556146987055108759598275142751744369",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-4352180266635339971139257",
    "3490227021976846272797675357148747481"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 181.81176051906664,
  "faltings_height": 12.933404298847197,
  "conductor": "739500266506675650378319244545704385995873198525590862090",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "2518675793",
    "149106332755427072054235932857492555610783"
  ],
  "discriminant": "13461365907308431053449869297177667929321486479170446856427035520000000000",
  "regulator": "35706742234179345.66470070087049244770703486922831491897896595170958197979068",
  "points": [
    [
      "1131535077991",
      "-119866323303634996"
    ],
    [
      "1169066701991",
      "4611661360749004"
    ],
    [
      "1334837176991",
      "-243259625251550996"
    ],
    [
      "-2402448518009",
      "-282421322757910996"
    ],
    [
      "1286217111991",
      "-142258519001740996"
    ],
    [
      "1259280921931",
      "81009076786049324"
    ],
    [
      "2415537121991",
      "-2659248721740830996"
    ],
    [
      "-1295303905721",
      "2637110128396610636"
    ],
    [
      "129904971991",
      "1710862101307759004"
    ],
    [
      "5331095091991",
      "11480464546921189004"
    ],
    [
      "-1400473844309",
      "-2615062301576461396"
    ],
    [
      "1165404705991",
      "-31483700168386996"
    ],
    [
      "-2148403298009",
      "-1710032927002450996"
    ],
    [
      "1248840408991",
      "-52373287296094996"
    ],
    [
      "1272945120391",
      "-113168719465443796"
    ],
    [
      "-121786692281",
      "2004609329761945676"
    ],
    [
      "1255072557511",
      "-70173545984947636"
    ],
    [
      "1157120530741",
      "59420549510771504"
    ],
    [
      "1153937938471",
      "-68069876812222516"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 2/13 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -2241070746096641026608T^8 - 48890065197872193202368T^7 - 1242865024659722240399412T^6 - 129721360166822665555416T^5 - 1095502516682193218704680T^4 + 1203400967658358227986304T^3 + 1102484040584899813957568T^2 - 464205369490492311699008T - 340636802726403331139248,\nA6 = 27904034754823698959642925455232T^12 + 2151919369557120564884658183913728T^11 + 58187531523799496672026563340878192T^10 + 172569984133100265846070068117224880T^9 + 1578209289982661012818716755624428596T^8 - 1284180339848885667921774017393210016T^7 - 1252435512115119963585561517641849552T^6 + 1259494814644547973636042498844029024T^5 + 728092080921839349171124150493358816T^4 - 708127293957126802183009949286197760T^3 - 331295715191254779558572993006363648T^2 + 156934618497934840781513210088796928T + 76614851639845112330141048005286272.\nIt is a 2-neighbour of the fibration given in curve#4191 (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 01:22:33",
  "updated_at": "2026-10-27 01:22:33"
}