{
  "id": 6162,
  "curve_key": "558596957943550270450158544:-12852568677806347538631392475348939547328",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-11637436623823963967711636",
    "14875658191909373981920201130754213540"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 184.7624113184851,
  "faltings_height": 13.305989472223951,
  "conductor": "1025046796300906267983848459792989028115688973250849819756152253240",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "83",
    "97",
    "11066091631917967",
    "159890018701359307",
    "54513531749367098070541253"
  ],
  "discriminant": "5272454154524040844737134408243978428604821089776779112341620750528818131200",
  "regulator": "9576107580882334119.10038584010009240369968345489113465132191141746551903538851",
  "points": [
    [
      "3262193101253",
      "-3409990906053425430"
    ],
    [
      "2230212750808",
      "120166197534812770"
    ],
    [
      "20943957446812/9",
      "16998707121319580030/27"
    ],
    [
      "3710822685749/4",
      "-17668884858981208941/8"
    ],
    [
      "2244267156008",
      "-248838265781008530"
    ],
    [
      "25922207971144/49",
      "1021381430266841790014/343"
    ],
    [
      "37334676450604/25",
      "-113675806249316436158/125"
    ],
    [
      "-3379894125192",
      "-3949445331165054270"
    ],
    [
      "65434480355368/81",
      "-1785936788295335678530/729"
    ],
    [
      "-3098366591311",
      "4603126046492119872"
    ],
    [
      "-220678107982",
      "-4175289082535045640"
    ],
    [
      "2814563066984",
      "2101824635094192558"
    ],
    [
      "3128088006662782/1849",
      "13719072297729068794480/79507"
    ],
    [
      "24543653879273/16",
      "50946200966682264045/64"
    ],
    [
      "203689306391488/121",
      "314213052583295697170/1331"
    ],
    [
      "1503102321774",
      "-882827386737505968"
    ],
    [
      "-3089838867282",
      "4618922870210816640"
    ],
    [
      "1448110840193",
      "-1029604150868974860"
    ],
    [
      "966633530033",
      "-2128315097474294880"
    ],
    [
      "3596279257430660/529",
      "-192358676740978193082450/12167"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 3/7 of a rank-17 fibration of X1008 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -56986316681380998912T^8 + 24457666340476410624T^7 + 535487594425392365712T^6 + 48800690383254862104T^5 - 361470535143673852503T^4 - 1833035186758586060700T^3 - 8027564283553513223079T^2 - 1856193563269433892114T - 193818285257580953532,\nA6 = 176927718245814623549804322816T^12 - 116292625590383842700445954048T^11 - 3367104967138625608924904544000T^10 + 2020152346629037937923069338624T^9 + 29203681898463675958459856569392T^8 - 13720510267525899173180962213992T^7 - 142330533991632689827729911017922T^6 + 21328459230505455903018021874128T^5 + 318228745035755178053554583805228T^4 + 157407522251338495321687387801980T^3 + 99390588041592331039607736906018T^2 + 19564837728780267552757168309932T + 952356233459948553164561681844.\nIt is a 2-neighbour of the fibration given in curve#3589: 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": "2026-10-29 23:20:08",
  "updated_at": "2026-10-29 23:20:08"
}