{
  "id": 5944,
  "curve_key": "34389642945313404417917136:-207625628024537495263708895559134951616",
  "ainvs": [
    "0",
    "0",
    "0",
    "-716450894694029258706607",
    "240307439843214693592255666156406194"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 176.45759988103327,
  "faltings_height": 12.617243744252495,
  "conductor": "41367551799560553907366455331338740804438392173611229882741687160",
  "bad_primes": [
    "2",
    "5",
    "11",
    "31",
    "95246324630436047692411577",
    "31841771609328501683211728390856847"
  ],
  "discriminant": "-1410633516365014888241196126798651061431349173120142939001491532156000000",
  "regulator": "6251807667781847936.909077433435333610152870402442557960564322454027365135280",
  "points": [
    [
      "361207421363",
      "-169254486851661200"
    ],
    [
      "2577751052313",
      "-3939811777445174950"
    ],
    [
      "504872888803",
      "-85329987874668680"
    ],
    [
      "-575903373967/16",
      "-33011142476283344375/64"
    ],
    [
      "923004094263",
      "-604451207139834400"
    ],
    [
      "453959096049",
      "92840792364466190"
    ],
    [
      "8783095734137/4",
      "-24336176927256088235/8"
    ],
    [
      "1002240400873",
      "727315392379348630"
    ],
    [
      "15532624951863",
      "61127333552143355200"
    ],
    [
      "-140668578867",
      "-581640841544459510"
    ],
    [
      "411677603873",
      "123008675441142370"
    ],
    [
      "-912340564237",
      "366816059084833600"
    ],
    [
      "-1141308592583/9",
      "15489689744819496250/27"
    ],
    [
      "1917814707113",
      "2433112262607659050"
    ],
    [
      "17762406869269/81",
      "-223201122739390874530/729"
    ],
    [
      "664232889449",
      "-239750462034006550"
    ],
    [
      "220087198613",
      "305428282488497950"
    ],
    [
      "172284563713",
      "-349267455447314750"
    ],
    [
      "19378707894487/49",
      "47053944796391277800/343"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -3/8 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = 1840758517133685517328T^8 - 28551969868039231295840T^7 - 1772998693252999313402080T^6 - 759387847760867496814400T^5 - 598922555435041558626640T^4 - 544800986643777256848080T^3 + 926816232306216461908040T^2 + 288493294443742559437240T - 230970134041531372322875,\nA6 = 325113825546664597334681997252736T^12 + 13439521326531181915894800771978880T^11 + 138327069120450496577609764257248960T^10 + 3518007078129231511599849398766400T^9 + 1769321142185421847687389290390981520T^8 + 1594947821477300217886357939071742368T^7 - 1479100347162091017597427825166729760T^6 - 1235366662137150944785202891205624960T^5 + 731032719531350653488345005675279040T^4 + 467848968404338281084037609996168720T^3 - 249593152301734103394166433543833544T^2 - 84246673758026015337923892531146920T + 42769382258496484819391456728787350.\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": "2026-10-26 03:07:49",
  "updated_at": "2026-10-26 03:07:49"
}