{
  "id": 4191,
  "curve_key": "90096169183339934620156821590109170331094096:-842624850308831704938754606784723800727077900976821662911361112000",
  "ainvs": [
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    "975260243412999658493303275196323797591848333388056722094183504"
  ],
  "rank_lower_bound": 27,
  "torsion": [],
  "naive_height": 303.6283546562169,
  "faltings_height": 23.184493920383908,
  "conductor": "446448313509287809070324734585228960192023626696145072346536211063504119846564087558171963578055559964904",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "23",
    "73",
    "109",
    "4705003832992487",
    "1961986463684002465830810143029032289574150176463092039285383835010095895952673"
  ],
  "discriminant": "12339566426385275008377177211149670702400666253739000858492009025720143119315020247784676189974611382540926217882119691105504512",
  "regulator": "146091809245625170340272562170.67641142638072714666959125825545591553402743486567672688102439",
  "points": [
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      "352480991320283187614",
      "18906227095774470994670977204902"
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    ],
    [
      "675197484412157153426",
      "3965989891988692103533270286286"
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    [
      "124555365558644629963529/256",
      "-54523304724302322896118460688305947/4096"
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    [
      "5637103043893159626962258",
      "13383938969881531695933836294432701170"
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      "1497167464063841800391",
      "-38999847445131056200640354044614"
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      "531816202777546772519",
      "-11289469481144266645532063060478"
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      "-1244947138891099316050",
      "37181918775159734205201549248502"
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      "-14462099282462897059897864859898"
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      "913851159580644340307",
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      "445418383240884550658",
      "-15085697793147535550725104265890"
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    [
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      "4759420178099439989873217316836"
    ],
    [
      "707657119792047992546",
      "1168279279782517478200587449214"
    ],
    [
      "5375338892221430134450/9",
      "221425534435637492851112832664054/27"
    ],
    [
      "951211110870677722226",
      "-7105765295076901478125008194286"
    ],
    [
      "633434365299076062365/4",
      "208919787548125651634809969655859/8"
    ],
    [
      "680156204988318993095",
      "-3640520110503213393499169824698"
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  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 57654/12097 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -4437370829345071269937785502500T^8 + 24731294533954602783634178920800T^7 - 24905343694917325040325875752236T^6 - 73371957550294374341624859203376T^5 + 11388134363003403434011617130260T^4 - 31974960227112637988116696606080T^3 - 53087557802286047432098781752884T^2 + 33902036804480905040632762295376T - 4900264269756058995659292474432,\nA6 = 3583088599917473486225042501788936057800562500T^12 - 29952862178447015859986519449513030145545410000T^11 + 74261855654700672409867052055125389734923941200T^10 + 34915854636953526118546131005709436129082490240T^9 - 320350491450370659682737733420310606418445799256T^8 + 104052954099599046113301816294931102834227932832T^7 + 846552244341643086726187489356042742190493998112T^6 + 378044570078449717959306675143150641014761409024T^5 - 387170892915283488485440730375460569591982158796T^4 - 122143831120324014405241873122119111177801883600T^3 + 159312688808409642522129729739582813691214920688T^2 - 45075775528724488962464647393974897773506063488T + 4205873318402097235409142015354269085411308544.\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": "2026-10-12 03:51:03",
  "updated_at": "2026-10-12 03:51:03"
}