{
  "id": 5925,
  "curve_key": "183982708218032166093439321:-2564841779254664681693476021758546411869",
  "ainvs": [
    "1",
    "1",
    "0",
    "-3832973087875670126946652",
    "2968566874135746309469723125593571316"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 181.4854308379737,
  "faltings_height": 13.033443775688152,
  "conductor": "155521345707521479595468777998377386532951019832912970",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "23",
    "37",
    "41",
    "59",
    "1559",
    "1104111366957443528632646215629080577763"
  ],
  "discriminant": "-202931411617565930323109183902602416853885371727721726441269122850185812500",
  "regulator": "2821640806962604.5697298551684260296826594408458853115098205365717075008739",
  "points": [
    [
      "1293956212482",
      "418768702495309084"
    ],
    [
      "-1846758001218",
      "1936168404670506484"
    ],
    [
      "904600419117",
      "-491420914438809206"
    ],
    [
      "1387295433160",
      "566633064231556306"
    ],
    [
      "296746608007",
      "-1362819354121563791"
    ],
    [
      "1194374015922",
      "-307202373012375076"
    ],
    [
      "4897606005882",
      "10083291640794749084"
    ],
    [
      "10332271430722",
      "32655706295512859554"
    ],
    [
      "-1246191081158",
      "-2410364226551259236"
    ],
    [
      "1126039165250",
      "283312707166010396"
    ],
    [
      "1714718144632",
      "-1199089117670894966"
    ],
    [
      "3477961370143/4",
      "4331685815733197387/8"
    ],
    [
      "50332269636673/64",
      "339839672208008289683/512"
    ],
    [
      "17100527413213/9",
      "43076001995473022518/27"
    ],
    [
      "542139273367",
      "1024648200107879089"
    ],
    [
      "1812588082282",
      "1405765565364363484"
    ],
    [
      "53109670881768/49",
      "-101417208176883132038/343"
    ],
    [
      "-83187702114082/49",
      "-734266484391656624638/343"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -17/6 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -8119975752906226977600T^8 - 1194538691861755286400T^7 + 219976811381682897431760T^6 - 49925350881736309262160T^5 - 1248367217121272445713640T^4 + 42719940029390047184160T^3 - 7362052252021663964833680T^2 + 3955863107039743188539640T - 544141552392814497282747,\nA6 = 282182893507153887108094699833600T^12 - 11546382575277829802734094085120T^11 - 12273663226673659961035941448765824T^10 + 9352497458874682475994018102531840T^9 + 214230436526747031631353358441831440T^8 - 290221811656176148412922343520902080T^7 - 2019839055988652407823845249198695600T^6 + 3106997112557759768822749232574054288T^5 + 9666695459486253875229535486519037880T^4 - 11155397666701195302119070647130234720T^3 + 6035354692251791096533770030129284160T^2 - 1576354013101030906327133713272549480T + 150532543779277207373688778588868886.\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": "2026-10-25 21:57:39",
  "updated_at": "2026-10-25 21:57:39"
}