{
  "id": 4171,
  "curve_key": "1633802384680099376078715330960530124583201:-2092538445561914293320053415723812368051304130209798668938566449",
  "ainvs": [
    "1",
    "0",
    "0",
    "-34037549680835403668306569395011044262150",
    "2421919497178141543191669805725453957161094973626571613138532"
  ],
  "rank_lower_bound": 25,
  "torsion": [],
  "naive_height": 291.60247750973195,
  "faltings_height": 22.099771661343162,
  "conductor": "1639273270253829061085618912592117264758680112319811738008352311590419724053396328877724528890",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "23",
    "67",
    "482971",
    "4046766271351",
    "82010967778567575483026658540263840590868971744475882772604877623"
  ],
  "discriminant": "-10180395461560240461826647859544283347335567998835505161890560874626445722868962817869037102219024785187411434741760000000",
  "regulator": "51318897545768907285166479.33272986114452805547995859333712934938264946342400439520966357",
  "points": [
    [
      "106798739081934637804",
      "69967101740219665272213053098"
    ],
    [
      "112113535405647113404",
      "-122696222084389444677200283302"
    ],
    [
      "100458810644316502444",
      "127966038683592723231404557738"
    ],
    [
      "-133447415634902951516",
      "-2141887618238554610752743203822"
    ],
    [
      "53467271186414303284",
      "-868834915658222250415826137022"
    ],
    [
      "108509684195127496204",
      "-78402170690530526307756671702"
    ],
    [
      "128682297119540629804",
      "415640186696685132348547421098"
    ],
    [
      "69457495310749684204",
      "-626772188804936431336486876502"
    ],
    [
      "112964249695617464782",
      "-135724656328502531338643061500"
    ],
    [
      "-132502898557484424596",
      "2146074951680017696836241905898"
    ],
    [
      "-111013139693633813696",
      "-2198276146095086187705409427402"
    ],
    [
      "104035341817632563404",
      "-82598683711117349351236730102"
    ],
    [
      "104474777083092113764",
      "-78702506837941720975395663542"
    ],
    [
      "107692483567124994604",
      "72891926173998698193739843498"
    ],
    [
      "105406960707193840684",
      "72541695210355601114501566378"
    ],
    [
      "148417399839682471564",
      "799657728248519305540154991178"
    ],
    [
      "113305545094618214404",
      "-141101274559541996833101237302"
    ],
    [
      "120909607814021703964",
      "272114651467208537629083873658"
    ],
    [
      "91391646683396885164",
      "-272973251652646268885913832022"
    ],
    [
      "-57796346733064544033/4",
      "13648652690077692559845370158713/8"
    ],
    [
      "47339156076579598804",
      "957443191758136383587091416098"
    ],
    [
      "3809731822234704103804",
      "234877438505009286561981055781098"
    ],
    [
      "126109533771144661804",
      "-367501547124580043453155746902"
    ],
    [
      "92518318565833658872",
      "-254452481699998030268580612962"
    ],
    [
      "-160556876143469477606",
      "-1935966175166728730009591656082"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 2748/203 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -8601190111439927121627T^8 + 70553802194275661608968T^7 - 40117514965744884873804T^6 - 394125757357369375667736T^5 - 727539205447352323463130T^4 - 3371639403550126915091304T^3 - 358500560703347306973924T^2 + 5575527756032095197563112T - 2574982297007819942866587,\nA6 = 311073935845060124132541860022390T^12 - 4299424530738788428378210804267800T^11 + 17883941445167312163435648485037300T^10 + 19652059401694206221665695004579800T^9 - 317465301013995782557083261357635310T^8 + 112305603376549774936723074091082640T^7 + 2598376408341179206723494257772920880T^6 + 911887687830002593185098844364676160T^5 - 4509956533653094383564183143089914510T^4 + 1581320920924061257174062701329500840T^3 + 3668404075692271898587012925610059196T^2 - 4676936909330964399995425467736251576T + 1568898839279682527117596188509969334.\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": "2026-10-11 22:17:25",
  "updated_at": "2026-10-11 22:17:25"
}