{
  "id": 5581,
  "curve_key": "41625869288152731473257778779441:-227046577448454824308074663088225531932721447465",
  "ainvs": [
    "1",
    "0",
    "0",
    "-867205610169848572359537057905",
    "262785390565341159570915197753620743108857961"
  ],
  "rank_lower_bound": 21,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 218.41882386511014,
  "faltings_height": 16.197309396114765,
  "conductor": "103134149763387935933021778289156711324736376492762597096652516971174",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "17",
    "19",
    "23",
    "89",
    "241",
    "914536624705317082975307",
    "1296197978682563792580228189192077"
  ],
  "discriminant": "11907139045622975798292362787757407710566953706352327618283033763778911249361160001771487232",
  "regulator": "14730990654664244580.954303987273713160466266371591423004403446676981892417830460",
  "points": [
    [
      "1205600161860118",
      "31138206538456494069763"
    ],
    [
      "2065465434747466",
      "-85341563594705293045637"
    ],
    [
      "84951519996165178/121",
      "79431892335444268437953/1331"
    ],
    [
      "295984243894090",
      "-5660069802866147503301"
    ],
    [
      "755754999926860",
      "-6249135338135881801349"
    ],
    [
      "-152817610430006",
      "-19792445352903829609925"
    ],
    [
      "4825862292510010",
      "-329343320321151271311461"
    ],
    [
      "-504297177033314",
      "-23913679325872579263149"
    ],
    [
      "792104340560914",
      "8535661481761833600715"
    ],
    [
      "-229337634164654",
      "-21203916706569959633309"
    ],
    [
      "1505115146925946",
      "48653737110657441642091"
    ],
    [
      "1001468538979114",
      "19967932418790842359771"
    ],
    [
      "1642468708024714",
      "57177974167639635110971"
    ],
    [
      "13539723390431626",
      "1571839296272892147912763"
    ],
    [
      "8826897756516682",
      "-824832142795302814978181"
    ],
    [
      "745384753136320",
      "-5524323829374023784941"
    ],
    [
      "132407112729370",
      "-12258976935316712709029"
    ],
    [
      "7012851248835274",
      "-582300446054811482496965"
    ],
    [
      "-1012831532672390",
      "10105836565707174682651"
    ],
    [
      "-726311614498334",
      "22572035634658356109363"
    ],
    [
      "-546774188656145/4",
      "-155696661544150147113607/8"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -73/8 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -5295620710700377671600T^8 - 94037966474871021583680T^7 - 590731768793188987891776T^6 - 316565515830122546981184T^5 - 762681779746720476850440T^4 + 1987613918828860347667800T^3 + 1569564836467837283726676T^2 - 3214905333565214256563376T - 2212765344524109268510452,\nA6 = 149936157543712438778032606320000T^12 + 4003077612324280274862537287520000T^11 + 40256463697048454693428799356032000T^10 + 181374780086403872414844938171109120T^9 + 402662249843699366956864710038784096T^8 - 758031533540911762791576885234671328T^7 - 399143032260021392125750735091011632T^6 + 2151897782383821345209559268211414304T^5 + 557784900106071266465324558195950116T^4 - 3137783098558594528537444090769421600T^3 - 420721733859426366310009677118678488T^2 + 2767709433062054442394845582008506272T + 1268413949854822572813035476740281796.\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 19:31:05",
  "updated_at": "2026-10-23 19:31:05"
}