{
  "id": 5558,
  "curve_key": "13625432954645905475762712101281:-49523442864791885706289454326716922457123854321",
  "ainvs": [
    "1",
    "0",
    "0",
    "-283863186555123030745056502110",
    "57318799612027621838125025877151283348444100"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 215.06847271906076,
  "faltings_height": 15.806464420632272,
  "conductor": "238163996288847216235337930011842913023549489418195171042770",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "23",
    "128853307177068197",
    "140845757566272045214583721602499031"
  ],
  "discriminant": "44573641214103001439289257467906432241302792806745722340386716534315271559104356352000000",
  "regulator": "106903849032618723.6233555098672867164127619931877566335846752852252402141833",
  "points": [
    [
      "-97200773502180",
      "-9164724112116630140910"
    ],
    [
      "229286923959900",
      "-2070475437035441030190"
    ],
    [
      "-63184120431780",
      "-8660381001716427467310"
    ],
    [
      "-401151692482980",
      "-10326499290447552932910"
    ],
    [
      "978365701607100",
      "-26759819277446581825710"
    ],
    [
      "356431298699100",
      "-1193010378996718713390"
    ],
    [
      "-564149720828580",
      "6157197561581737217490"
    ],
    [
      "409740848564700",
      "3130311152897241149010"
    ],
    [
      "249895617419100",
      "-1409989409310751833390"
    ],
    [
      "833732284739916",
      "20004702704358868389522"
    ],
    [
      "269517403322820",
      "624800085865157118090"
    ],
    [
      "389847236746620",
      "2429987901173960043090"
    ],
    [
      "2114003732408220",
      "94364921176748605299090"
    ],
    [
      "371789754041820",
      "1781288278335526107090"
    ],
    [
      "339905333701740",
      "321507727658773821570"
    ],
    [
      "18451864027171884/25",
      "1975932150175344082731738/125"
    ],
    [
      "-228408453798180",
      "-10499494434278955188910"
    ],
    [
      "347231901584220",
      "-786253099859987243310"
    ],
    [
      "-11244002444484",
      "7778761888043297481042"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -17/2 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -113946597679617331526187T^8 - 628704898397157619416528T^7 - 910139814353468861642484T^6 + 13879376823678260295456T^5 - 533762798296920925528530T^4 + 1639003787601085356814224T^3 + 806892413125232101174956T^2 - 592355532948433669282752T - 295458143973808062849867,\nA6 = 15882493844523546552540807840095910T^12 + 145809795943145321517489625166050800T^11 + 489200782557326126999832807296770620T^10 + 474439873253302462549441686771960000T^9 - 939321256931213164482716468158448790T^8 - 1775504390224299025107326496664527360T^7 + 1396226578858524162480471413923945800T^6 + 1631143206019716771050709031938957120T^5 - 432541045559235732878122118765459190T^4 - 878384718510400823408137143448720560T^3 - 116676491482650081744926274060252324T^2 + 185829851435689714140802850197329216T + 61035568685910358648726719363207174.\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": "2026-10-23 03:58:55",
  "updated_at": "2026-10-23 03:58:55"
}