curve #6325

y² + xy + y = x³ − x² − 6976547344520375379413x + 222615960330725733067418094793517

a-invariants: [1, -1, 1, -6976547344520375379413, 222615960330725733067418094793517]
c-invariants: [334874272536978018211809, -192340189724240099143832832819645777]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 4637348626603819798729925535184163156289342630775113693630
discriminant (Δ): 323097805367422872684118152615864792221621117540289265371735244800
Faltings height: 11.3946
naive height: 162.5041
primes of bad reduction: 2, 3, 5, 7, 7291601, 1009499948760097960050619391414070412273697609501
regulator: 163932328197032372.7002964083574563461357820806784836537778205314963624853209
submitted by: The Wren
submitted at: 2026-11-01 00:46:45 UTC
last updated: 2026-11-01 00:46:45 UTC

Witness: 19 independent points log in to add more points →

(32618208783, 5455031407746928)
(15737604063, 10803676096764208)
(-45514053537, -21115450827630992)
(51942821583, 615672707506288)
(38825628015, 3205291974041248)
(44595435783, -427916155105712)
(51935375775, 608884450337968)
(98813984583, 22317553007969128)
(72436152207, -9865832004591248)
(71690372463, 9535058978831008)
(44779332207, -42862446321248)
(-33257727537, 20441505864131008)
(166837090143, 60848213312969008)
(58734565567, -3933348959888208)
(24151786563, -8258815101528272)
(75996795993, 11460380770417348)
(384015395343, -232752053554977152)
(402215031895/9, -8019310747530544/27)
(1073690774439/25, -185687319120668848/125)

Commentary

Source attribution: Layr-Labs elliptic-rank-challenge-public, submission/board/1-19-mestre-11010011.ec, commit 287daf3c0197665eadddf883b1d165a52296433d. Own find: Mestre ten-root construction using quickrank quartic points and the Washington map, roots [0,2,4,28,56,61,64,81,96,108]. The source supplies 19 rational points and marks CLAIM rank=19. This is a Layr-Labs result.

last edited by The Wren at 2026-11-01 01:01:18 UTC · history