{
  "id": 5958,
  "curve_key": "99374079846054829403161:-33744248103673100338015033805753341",
  "ainvs": [
    "1",
    "0",
    "1",
    "-2070293330126142279233",
    "39055842712412082428525406900056"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 159.00823609007992,
  "faltings_height": 11.206904930272072,
  "conductor": "71625677885791332511125627632333082700595776460135953470",
  "bad_primes": [
    "2",
    "3",
    "5",
    "31",
    "2309",
    "13177",
    "61379299273",
    "41240449649634665571365798587847011"
  ],
  "discriminant": "-91050114067931155692314703311049112647230472312521948201354812500",
  "regulator": "15864809086869188.722156591536115528305853242967029745996981048166112121617",
  "points": [
    [
      "8003926365",
      "-4795639682066558"
    ],
    [
      "-37567852725",
      "-7988170666216508"
    ],
    [
      "-40552917435",
      "7504779989349442"
    ],
    [
      "-52983162930",
      "-106615223152433"
    ],
    [
      "6116351865",
      "-5159655323376308"
    ],
    [
      "22031851065",
      "-2034160257595508"
    ],
    [
      "25350133650",
      "-1692457101044018"
    ],
    [
      "-42043347525",
      "7195872099293992"
    ],
    [
      "31513472997",
      "2260450491169474"
    ],
    [
      "-128863192665/4",
      "68031454426780661/8"
    ],
    [
      "107222218935/4",
      "13437237548358161/8"
    ],
    [
      "21352335405",
      "2141308883291842"
    ],
    [
      "67462581705",
      "14367436711710202"
    ],
    [
      "-19689934485",
      "8496251528082292"
    ],
    [
      "33540714990",
      "-2710983948544433"
    ],
    [
      "-18090289110",
      "8401666359707542"
    ],
    [
      "-22569895710",
      "-8618865558723233"
    ],
    [
      "-51494164875",
      "3019863021626242"
    ]
  ],
  "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 = -2543951687432473887460672377483T^8 - 24818956579468052738105064515028T^7 - 77370351271537068433100341247904T^6 - 67467015005869076752518330881556T^5 + 17016806163007175905444072313970T^4 + 82892666432004286839667115406660T^3 + 60326950313063858115906668276136T^2 - 19915299958127111246160446427612T - 27289787224140550157486254128927,\nA6 = 1550015425870788606577153334191333100109899718T^12 + 22628758087381124339269406905403241577644202332T^11 + 129666144682594016426381124339897213302125685892T^10 + 345383914891725536644308394433318665228830332532T^9 + 290839421645428584216690391576246831863346739238T^8 - 501824346857271485681078887124327532393736266360T^7 - 846300710982340207425925322969763595750992960552T^6 + 305997138248518386594529888488269900783383863000T^5 + 830499992755676217073833197525717220681011885394T^4 - 107750490807943398511372493107734289465806190692T^3 - 406158893855534218232938145420042389062774860796T^2 + 16099138820538211319454876432431072682872064564T + 80603603306668130852282428774716725293282315746.\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": "2026-10-26 20:38:07",
  "updated_at": "2026-10-26 20:38:07"
}